JP2016177327A - Method of associating two element strings having feature in configuration of directed acyclic graph and cost of lattice point for applying dynamic programming - Google Patents

Abstract

PROBLEM TO BE SOLVED: To perform association based on only properties of two element strings in elastic mapping for associating each element so that two element strings are made similar, and thereby any number of elements are skipped from the association and association results of assuming any correspondence as beginning or end are obtained.SOLUTION: A directed acyclic graph is constituted on a lattice space being a cartesian product of the set of each element, when associating two element strings of lengths I, J. The directed acyclic graph is constituted which comprises directed sides of the number in proportion to IJas a first feature, in a procedure for finding association by the search for the shortest path in the graph using the dynamic programming. As a second feature, the cost of a lattice point being the cost between the elements is set so as to mix the lattice point being set when having to associate the elements and having the cost of a negative value with the lattice point being set when it is not so and having a non-negative cost.SELECTED DRAWING: Figure 6

Description

  The present invention relates to an element method that is a set of elements having an order by comparing two element strings and determining a correspondence between an element in one element string and an element in the other element string. The present invention relates to an attaching device and an association program.

  The technique for associating each element of the first element string and the second element string has applications in various fields such as recognition of time-series patterns such as speech and recognition of image patterns such as characters and fingerprints. The element here may be any element that can define a numerical value as an index of association between the elements of the two element strings. For example, in the case of a sequence of points on an N-dimensional space, the distance between two points can be defined as an association index.

  If the element sequence is distorted, the association becomes difficult, and a technique for obtaining the most consistent association by expanding and contracting the element sequence is called elastic matching. DP matching using dynamic programming is widely used for elastic matching.

  For example, DP matching is also used in searching for similar images. The similar image search described in Patent Document 1 includes a process of generating a feature quantity matrix for each image data divided into blocks and obtaining a distance between each feature column constituting the feature quantity matrix by DP matching. .

  Alternatively, DP matching is also used in the recognition of gestures that are image information. In the gesture recognition apparatus described in Patent Document 2, a feature parameter series is taken as an element sequence, and used as a standard pattern by allowing reversal of the order of distance calculation between feature parameters in a technique called continuous DP matching. To reduce the amount of information in the element sequence.

  The principle of DP matching will be described as a conventional technique by taking DP matching having a monotonic continuity constraint described in Section 2 of Non-Patent Document 1 as an example. In this DP matching, two element strings, X and Y shown in the following formula (1), are to be matched.

In the DP matching described in Non-Patent Document 1, the correspondence between the i-th element x _i of X and the j-th element y _j of Y shown in the following equation (2) is optimized. Equation (2) means that the value of i increases by one, and this is called a continuity constraint. This continuity constraint is not a constraint imposed on DP matching in general.

  Next, the cost of association between elements is expressed as shown in Equation (3). In DP matching, values used as indices in association between elements in two element strings are referred to as cost, distance, similarity, and the like. When it is called cost or distance, the formulation is aimed at minimizing the sum of index values for the purpose of associating element strings, whereas when it is called similarity, the sum of index values is maximized. (For example, nonpatent literature 2). If appropriate conversions are made, they have the same meaning, and the term cost will be used in this application.

  In Non-Patent Document 1, the cost is described in the form of a norm as shown in Equation (3), which is also called a local distance. The norm, which is regarded as a generalization of distance, has positive definiteness, that is, non-negative.

  When the equations (1), (2), and (3) are determined, the optimization problem is formulated as the following equation (4). As shown in the equation (4), in this example, a monotonic constraint is imposed, and other conditions regarding inclination limitation, a start end, and an end are imposed. Of these, the monotonic constraint is generally imposed as a condition, but other cases have been reported. There are various types of tilt limitation as described later with reference to FIG. In general, the condition shown in the equation (4) is imposed on the start end and the end, but a method for making the start end free is also reported.

When obtaining the optimal solution of equation (4), the DP matching method uses a value that is the sum of costs and is also called the cumulative distance (g _i (u _i ) in equation (5)) in the following equation (5): The recursion formula shown below is used in order from the beginning. Equation (5) is called the DP recurrence equation. The minimum value selection range in cases other than the starting point of the DP recurrence formula of Formula (5) is determined by the monotonicity constraint and the tilt limit in Formula (4).

The minimum value selection range in the DP recurrence formula varies depending on various types of tilt restrictions. FIG. 1 shows the tilt limit shown in Non-Patent Document 1 (Section 2.2), that is, the type of the minimum value selection range. In the case of equation (4), a comparison is made when determining the value of g _i (u _i ) of a point marked with a black circle with the coordinates of i and j in the lattice shown by the broken line 101 in FIG. The point of the value of _i-1 (u _i-1 ) is indicated by a white circle. In FIG. 1, reference numeral 104 denotes a tilt limit without a monotonic constraint.

The value g _I (J) at the end of g _i (u _i ) obtained using the DP recurrence formula is the minimum value of the objective function F in formula (4). The correspondences u ₁ ,..., U _i ,..., U _I in this optimal solution are the DP recurrence formulas of Equation (5), and the minimum value is any g _i-1 (u _i-1 ) Is obtained by tracing back from the end, that is, by backtracking.

  In the DP matching formulation, the lattice on the DP plane is the Cartesian product set of {1, ..., i, ..., I} and {1, ..., j, ..., J}. Some assign costs to directed edges that connect grid points instead of points. A different formulation including this can be replaced by a formulation in which costs are assigned to grid points. In the present application, a formulation for assigning costs to lattice points is basically used, but an example of assigning costs to directed edges (FIG. 5) is also used when a simpler explanation can be made.

  The principle of DP matching has been described above based on the example described in Non-Patent Document 1. DP matching is a technique using DP (Dynamic Programming) in elastic matching, and examples of DP matching according to the above formulas (1) to (5) are configured on the DP plane shown in FIG. This is equivalent to obtaining the minimum cost path in the directed acyclic graph (DAG) by dynamic programming. That is, FIG. 2 shows that in the lattice space, which is a Cartesian product set of the element set in the element sequence X and the element set in the element sequence Y, the distance between the lattice points is expressed by Equations (2) and (4). A directed acyclic graph connected by directed edges restricted by monotonicity restrictions and slope restrictions is indicated by an arrow. The DP matching in the above-mentioned example is to obtain a minimum cost route from the start end of 201 to the end of 202 by dynamic programming, and a set of lattice points included in the route is used as an association result.

  In the above description, DP matching, which is a matching method, is distinguished from dynamic programming (DP) used in DP matching. In the following description, the two are also distinguished.

  The dynamic programming method used in DP matching can be applied if a directed acyclic graph is configured on a lattice space that is a Cartesian product set as shown in FIG. That is, the basic idea of DP matching is to obtain a minimum cost path by processing lattice points in a topologically sorted order according to a semi-order defined by a directed acyclic graph. Formulations shown in equations (1) to (5) are examples and are not necessary conditions for applying DP matching.

  Conversely, if a monotonic constraint is imposed as a constraint condition of the optimization problem according to the order of the two element sequences to be matched, a directed acyclic graph is clearly constructed in the lattice space, so DP matching Is applicable.

  As described above, based on the description in Non-Patent Document 1, the principle of DP matching has been described in the examples using the formulas (1) to (5). However, from the viewpoint of cost, a different view from the formula (3) is used. Some DP matching is done. For example, in the comparison method of DNA base sequences that can be seen in Non-Patent Document 2, that is, the application of DP matching to the correspondence between base sequences, the value corresponding to the cost called similarity is only a non-negative value such as a norm. Instead, both positive and negative values are used. In Patent Document 3, comparison is made after translation into an amino acid sequence that is not a DNA base sequence but a combination thereof, but both positive and negative values are used in the cost score.

  In Non-Patent Document 2 and Patent Document 3, the objective function maximization formulation is performed in the optimization problem. Compared with the minimization formulation in Equation (4), the sign of the index corresponding to the cost is positive or negative. The meaning of is reversed. In the following, the description will be made on the premise of the significance of the cost as an index based on the objective function minimization formula.

  When dynamic programming is applied to a directed acyclic graph to find a path with the lowest cost, the cost need not be non-negative. Therefore, DP matching operates without any problem even in association in Non-Patent Document 2 and Patent Document 3 where an index corresponding to a negative cost is used. Note that in any of the DP matching examples in Non-Patent Document 2 and Patent Document 3, since the monotonic constraint is imposed, the graph for obtaining the path with the minimum cost is a directed acyclic graph. .

  In Non-Patent Document 2, an inclination restriction corresponding to 102 in FIG. 1 is imposed. The tilt restriction of Patent Document 3 is complicated by considering amino acid sequences for every three base sequences, but the fixed range is the minimum value selection range (7 lattice points in claim 2). Is unchanged. The calculation amount of DP is O (IJ), which is based on the fact that the minimum value selection range is fixed.

JP 2006-146715 A

JP 9-330400 A

JP-A-10-334104

Seiichi Uchida “DP Matching Overview: Basics and Various Extensions”, IEICE Technical Report, PRM2006-166, December 2006

Nakagawa Takumi, Yoshihara Ikuo, Yamamori Kazutoshi, Yasunaga Moritoshi “Speed-up of DP matching used for genome analysis by the division rule method” Bulletin of Faculty of Engineering, Miyazaki University, 35, 257-262, August 2006

  In the related arts including the DP matching methods described in Patent Documents 1 to 3 and Non-Patent Documents 1 and 2, all adopt a fixed minimum value selection range in the DP recurrence formula. This supports the advantage of DP matching, which is a small calculation amount of O (IJ), as described above. However, the fixed minimum value selection range realized by the tilt restriction is “two to be similar. There is no direct relationship with the original meaning of elastic matching, which refers to associating elements of a set. That is, the fixed minimum value selection range is a means for quickly calculating the association, and is limited to “similar”.

  The costs having positive and negative values described in Patent Document 3 and Non-Patent Document 2 are considered to give a definition and scale of “similar” with cost 0 as a boundary. That is, it can be considered as a method of setting the cost given to the elastic mapping that a negative value is preferably associated and a positive value is preferably not associated. However, since the fixed minimum value selection range is used together as described above, the effect of the cost having positive and negative values is limited with respect to the association result.

  An object of the present invention is to obtain a correspondence in accordance with the original principle of elastic matching, “to associate elements of two sets so as to be similar”. That is, it is an object to realize a flexible association that eliminates the restriction that has been an obstacle to making it correspond to be similar, and an association that can clearly set a similarity criterion. In order to eliminate the restriction, it is necessary to prevent an unintended association from becoming an optimal solution by eliminating the restriction.

The first configuration of the method for associating two element sequences according to the present invention is as follows:
When the first element sequence is compared with the second element sequence to obtain an association including one or more pairs of elements of the first element sequence and elements of the second element sequence,
On a lattice space that is a Cartesian product set of a set of elements of the first element sequence and a set of elements of the second element sequence,
A first directed acyclic graph is formed by providing a plurality of directed edges with a point in the lattice space as a lattice point, one lattice point as a start point, and another lattice point as an end point so as not to cause a cycle. And the steps
For all the grid points included as vertices in the directed acyclic graph, the cost is determined for each combination of the elements of the first element sequence and the elements of the second element sequence constituting each grid point. A second step for the cost of the grid points;
A route that connects two or more directed edges in succession by repeating the connection of two directed edges by matching the end point of the directed edge on the directed acyclic graph with the start point of another directed edge. age,
The total cost of the grid points included as the start point or end point of the directed side in the route is defined as the route cost.
The lattice points are sequentially processed in a topologically sorted order according to the semi-order defined by the directed acyclic graph, and the route that minimizes the route cost to the lattice point and the minimum route cost are obtained. A third step of determining a minimum cost path in the directed acyclic graph by dynamic programming;
A set of sets of elements of the first element sequence and elements of the second element sequence of the grid points included in the determined minimum cost path, and a result of associating the first element sequence with the second element sequence A fourth step to:
In the element string matching method having
In the first step,
In a partial order defined by the directed acyclic graph, in an order relationship in which the start point side of the directed edge is higher and the end point side is lower,
Configuring the directed acyclic graph so as to provide directed edges from the upper grid point to the lower grid point for all the upper grid points and the lower grid points in the order relationship; ,
In the second step,
For the purpose of associating the element strings, associating the elements of the first element string and the elements of the second element string constituting the lattice points is a negative cost when the object is met. If the cost is not positive, the cost of the positive value, if not, the value 0 is the cost of the grid point.
Mixing lattice points with negative cost and non-negative cost points,
It is characterized by.

  According to this configuration, the minimum value of the path cost that ends each grid point on the directed acyclic graph is determined by setting all grid points positioned higher in the partial order of the directed acyclic graph as the minimum value selection range. A number of elements corresponding to the first set and many elements of the second set on the directed acyclic graph that is the DP plane can be flexibly skipped without being associated with each other. The route can be the least cost route. In this way, if various routes are allowed on the DP plane, it is feared in the prior art that a preferable association is skipped by avoiding an increase in cost, resulting in an unexpectedly small set of associations. Is set as a grid point, and the preferred correspondence is less likely to be skipped as a negative cost grid point that is advantageous for minimizing the objective function, and there is no possibility of concern in the prior art.

The second configuration of the method for associating two element sequences according to the present invention is as follows:
When the first element sequence is compared with the second element sequence to obtain an association including one or more pairs of elements of the first element sequence and elements of the second element sequence,
On a lattice space that is a Cartesian product set of a set of elements of the first element sequence and a set of elements of the second element sequence,
A first directed acyclic graph is formed by providing a plurality of directed edges with a point in the lattice space as a lattice point, one lattice point as a start point, and another lattice point as an end point so as not to cause a cycle. And the steps
For all the grid points included as vertices in the directed acyclic graph, the cost is determined for each combination of the elements of the first element sequence and the elements of the second element sequence constituting each grid point. A second step for the cost of the grid points;
A route that connects two or more directed edges in succession by repeating the connection of two directed edges by matching the end point of the directed edge on the directed acyclic graph with the start point of another directed edge. age,
The total cost of the grid points included as the start point or end point of the directed side in the route is defined as the route cost.
The lattice points are sequentially processed in a topologically sorted order according to the semi-order defined by the directed acyclic graph, and the route that minimizes the route cost to the lattice point and the minimum route cost are obtained. A third step of determining a minimum cost path in the directed acyclic graph by dynamic programming;
A set of sets of elements of the first element sequence and elements of the second element sequence of the grid points included in the determined minimum cost path, and a result of associating the first element sequence with the second element sequence A fourth step to:
In the element string matching method having
In the first step,
The number of elements in the first element row is I, the number of elements in the second element row is J, and there are a number proportional to I ² J ² according to the two values I and J. Providing a directed edge to construct the directed acyclic graph;
In the second step,
For the purpose of associating the element strings, associating the elements of the first element string and the elements of the second element string constituting the lattice points is a negative cost when the object is met. If the cost is not positive, the cost of the positive value, if not, the value 0 is the cost of the grid point.
Mixing lattice points with negative cost and non-negative cost points,
It is characterized by.

  According to this configuration, two element sequences are associated with each other while maintaining the two features that various routes can be the least cost route and that the preferable association is difficult to be skipped as a negative cost lattice point. Based on the unique property of the event to be processed, it is possible to constrain the cost shortest path to be associated.

The third configuration of the method for associating two element sequences according to the present invention is as follows:
In the first configuration or the second configuration,
In the third step of obtaining the minimum cost path,
When sequentially calculating the minimum path cost of the path to the grid point for each grid point in the order topologically sorted by the semi-order defined by the directed acyclic graph,
For all of the second grid points that are the starting points of the directed sides that end at the first grid point that is the target for which the minimum path cost is to be calculated,
When there is a negative or zero value in the calculated minimum path cost of the second grid point, the cost of the first grid point is added to the minimum value among the negative or zero values. The obtained value is set as the minimum path cost of the path to the first grid point, and the second grid point having the minimum path cost of the minimum value is stored as the parent grid point of the first grid point;
If the calculated minimum path cost of the second grid point is a positive value without exception, the cost of the first grid point is set as the minimum path cost of the first grid point, and the first grid point Remember the point as a starting point candidate,
After calculating the minimum path cost at all the lattice points, the lattice point having the smallest value among them is defined as the end point,
Starting from the lattice point that is the end, a backtrack procedure for repeatedly obtaining the parent lattice point from the lattice point is performed,
When the lattice point stored as the starting edge candidate in the backtrack procedure becomes the parent lattice point, the lattice point is determined as the starting edge, and the repetition is ended.
A path obtained by connecting the obtained lattice points appearing in the backtrack procedure with the end and the start as both ends and the directed side is defined as a minimum cost path.

  According to this configuration, the start and end of the path with the lowest cost are not fixed, and the first and second end points included in the association in the first and second element sequences are It will not be fixed. This property is also described in Non-Patent Document 1 (Section 2.5) as making the start / end free, and it is possible to skip an unstable portion near the start / end. The free end-to-end according to the present invention according to the present invention is a complete generalization in the sense that there is no restriction on the start-end end.

A fourth configuration of the method for associating two element sequences according to the present invention is as follows.
In the third configuration,
When at least one of the starting edge candidate and the terminal end is determined in the third step, only lattice points that satisfy a predetermined condition are set as objects to be determined as the starting edge candidate and the terminal end. And

  According to this configuration, the position of the start end / end determined by making the start / end end free can be set within an appropriate range based on the inherent property of the event that is the target of the process of associating the two element strings.

The first configuration of the device for associating two element sequences according to the present invention is as follows:
When the first element sequence is compared with the second element sequence to obtain an association including one or more pairs of elements of the first element sequence and elements of the second element sequence,
On a lattice space that is a Cartesian product set of a set of elements of the first element sequence and a set of elements of the second element sequence,
A first directed acyclic graph is formed by providing a plurality of directed edges with a point in the lattice space as a lattice point, one lattice point as a start point, and another lattice point as an end point so as not to cause a cycle. Means of
For all the grid points included as vertices in the directed acyclic graph, the cost is determined for each combination of the elements of the first element sequence and the elements of the second element sequence constituting each grid point. A second means for the cost of the grid points;
A route that connects two or more directed edges in succession by repeating the connection of two directed edges by matching the end point of the directed edge on the directed acyclic graph with the start point of another directed edge. age,
The total cost of the grid points included as the start point or end point of the directed side in the route is defined as the route cost.
The lattice points are sequentially processed in a topologically sorted order according to the semi-order defined by the directed acyclic graph, and the route that minimizes the route cost to the lattice point and the minimum route cost are obtained. A third means for determining a minimum cost path in the directed acyclic graph by dynamic programming;
A set of sets of elements of the first element sequence and elements of the second element sequence of the grid points included in the determined minimum cost path, and a result of associating the first element sequence with the second element sequence A fourth means to:
In the inter-element string association device having
In the first means,
In a partial order defined by the directed acyclic graph, in an order relationship in which the start point side of the directed edge is higher and the end point side is lower,
Configuring the directed acyclic graph so as to provide directed edges from the upper grid point to the lower grid point for all the upper grid points and the lower grid points in the order relationship; ,
In the second means,
For the purpose of associating the element strings, associating the elements of the first element string and the elements of the second element string constituting the lattice points is a negative cost when the object is met. If the cost is not positive, the cost of the positive value, if not, the value 0 is the cost of the grid point.
Mixing lattice points with negative cost and non-negative cost points,
It is characterized by.

The second configuration of the device for associating two element sequences according to the present invention is as follows:
When the first element sequence is compared with the second element sequence to obtain an association including one or more pairs of elements of the first element sequence and elements of the second element sequence,
On a lattice space that is a Cartesian product set of a set of elements of the first element sequence and a set of elements of the second element sequence,
A first directed acyclic graph is formed by providing a plurality of directed edges with a point in the lattice space as a lattice point, one lattice point as a start point, and another lattice point as an end point so as not to cause a cycle. Means of
For all the grid points included as vertices in the directed acyclic graph, the cost is determined for each combination of the elements of the first element sequence and the elements of the second element sequence constituting each grid point. A second means for the cost of the grid points;
A route that connects two or more directed edges in succession by repeating the connection of two directed edges by matching the end point of the directed edge on the directed acyclic graph with the start point of another directed edge. age,
The total cost of the grid points included as the start point or end point of the directed side in the route is defined as the route cost.
The lattice points are sequentially processed in a topologically sorted order according to the semi-order defined by the directed acyclic graph, and the route that minimizes the route cost to the lattice point and the minimum route cost are obtained. A third means for determining a minimum cost path in the directed acyclic graph by dynamic programming;
A set of sets of elements of the first element sequence and elements of the second element sequence of the grid points included in the determined minimum cost path, and a result of associating the first element sequence with the second element sequence A fourth means to:
In the inter-element string association device having
In the first means,
The number of elements in the first element row is I, the number of elements in the second element row is J, and there are a number proportional to I ² J ² according to the two values I and J. Providing a directed edge to construct the directed acyclic graph;
In the second means,
For the purpose of associating the element strings, associating the elements of the first element string and the elements of the second element string constituting the lattice points is a negative cost when the object is met. If the cost is not positive, the cost of the positive value, if not, the value 0 is the cost of the grid point.
Mixing lattice points with negative cost and non-negative cost points,
It is characterized by.

A third configuration of the device for associating two element sequences according to the present invention is as follows.
In the first configuration of the device or the second configuration of the device,
In the third means for obtaining the minimum cost route,
When sequentially calculating the minimum path cost of the path to the grid point for each grid point in the order topologically sorted by the semi-order defined by the directed acyclic graph,
For all of the second grid points that are the starting points of the directed sides that end at the first grid point that is the target for which the minimum path cost is to be calculated,
When there is a negative or zero value in the calculated minimum path cost of the second grid point, the cost of the first grid point is added to the minimum value among the negative or zero values. The obtained value is set as the minimum path cost of the path to the first grid point, and the second grid point having the minimum path cost of the minimum value is stored as the parent grid point of the first grid point;
If the calculated minimum path cost of the second grid point is a positive value without exception, the cost of the first grid point is set as the minimum path cost of the first grid point, and the first grid point Remember the point as a starting point candidate,
After calculating the minimum path cost at all the lattice points, the lattice point having the smallest value among them is defined as the end point,
Starting from the lattice point that is the end, a backtrack procedure for repeatedly obtaining the parent lattice point from the lattice point is performed,
When the lattice point stored as the starting edge candidate in the backtrack procedure becomes the parent lattice point, the lattice point is determined as the starting edge, and the repetition is ended.
A path obtained by connecting the obtained lattice points appearing in the backtrack procedure with the end and the start as both ends and the directed side is defined as a minimum cost path.

A fourth configuration of the device for associating two element sequences according to the present invention is as follows.
In the third configuration of the apparatus,
When at least one of the starting edge candidate and the terminal end is determined by the third means, only lattice points that satisfy a predetermined condition are set as objects to be determined as the starting edge candidate and the terminal end. And

  The configuration of the program according to the present invention is characterized by causing a computer to execute the element sequence correlation method according to the first to fourth configurations.

  As described above, according to the present invention, in the association between two element sequences, the directed acyclic graph configured on the DP plane used for determining the association that is the first feature is directed. By having a sufficient number of sides, flexible association with less restrictions on the positions of the skip and the start / end is possible. In addition, the second feature, which is the cost between lattice points on the DP plane, which is the cost between corresponding elements, is a negative cost if the elements corresponding to the lattice points should be associated with each other. When dynamic programming is used to determine the path to obtain the minimum path cost by mixing negative cost grid points and non-negative cost grid points, the negative cost is reduced. The route is determined so as to positively seek to go through a grid point that has, and avoid going through a grid point having a positive cost. As a result, it is possible to prevent the occurrence of an unintended association due to the absence of a restriction, and to obtain an association according to a standard in which costs are defined as negative and non-negative.

The minimum value selection range in the DP recurrence formula in the prior art is illustrated. FIG. 3 is a diagram illustrating a directed acyclic graph on a DP plane according to a conventional technique. FIG. FIG. 6 illustrates a minimum value selection range in an embodiment of the present invention. FIG. It is the figure which compared the start end termination | terminus and path | route on DP plane with the Example of this invention, and the Example of a prior art. FIG. 6 is a diagram comparing minimum cost route selection with a negative cost to minimum cost route selection with a positive cost. It is a figure explaining the example in which optimal matching changes with the boundary value in the Example of this invention. It is a figure which shows the existing range of the directed acyclic graph on DP plane at the time of imposing a restriction condition in the Example of this invention. It is a JavaScript (registered trademark) program in which an association method is implemented in an embodiment of the present invention.

  The best mode for carrying out the present invention will be described below with reference to the drawings.

  First, the association method in the present invention is formulated so that the comparison with the prior art shown by the above-described equations (2) to (5) is possible. In the description of the prior art, the formulation shows an example of various methods, but the formulation in the present invention is an example of various methods. The formulation is as general as possible.

  The correspondence targets in the first embodiment are the two element strings X and Y shown in Formula (1), as in the conventional formulation.

  In the formulation of the association in the example of the prior art shown in Expression (2), the continuity constraint in which the value of i increases by one is assumed. In the conventional DP matching, the continuity constraint in which the value of i is incremented by one is not essential, and Equation (2) follows the example described in Section 2 of Non-Patent Document 1. In the present invention, since it is common not to impose a continuity constraint in which the value of i increases one by one, the association is formulated as in the following equation (6). That is, the association is simply represented by a set of i and j (a subset of the direct product) U.

  As shown in the equation (7), the cost according to the present invention is not a norm in which the value range is non-negative, but a general function including a negative value in the value range.

The cost of taking a positive or negative value as in equation (7) is the border value for a non-negative physical quantity (for example, distance between two points, norm) representing the property between x _i and y _j. This can be realized by setting a cost obtained by subtracting the boundary value from a non-negative physical quantity. That is, the function f of Expression (7) can be realized by defining it as Expression (8).

  The matching optimization problem according to the embodiment of the present invention is formulated as the following equation (9) using equations (1), (6), and (7). Unlike Equation (4), which is an example of the prior art, Equation (9) uses only the monotonicity constraint as the constraint condition. The monotonicity constraint is a sufficient condition that a directed acyclic graph is constructed on the DP plane, thereby ensuring the applicability of dynamic programming. However, it is not a necessary condition, and a formulation that does not impose a monotonic constraint is also conceivable. In many cases, imposing a monotonic constraint will not narrow the scope of application.

  Formula (10) shows the DP recurrence formula of the embodiment according to the present invention. The first feature of this recurrence formula is that the minimum value selection range is not fixed and increases as i and j increase. The second feature is that the starting edge is not uniquely determined. That is, when there is no minimum cost of a negative or zero value route in the minimum value selection range, they are not taken over, and the cost of the grid point is set as the minimum cost of the route and becomes a starting candidate.

FIG. 3 shows the minimum value selection range of the DP recurrence formula in the embodiment according to the present invention. While the size of the minimum value selection range in FIG. 1 of the prior art is fixed, in FIG. 3, the minimum value selection range for the specific lattice point (i, j) of 301 is i × j−. The size is one. For this reason, the calculation amount in the conventional DP matching is O (IJ), whereas in the association according to the present invention, it is O (I ² J ² ). Although the amount of calculation increases, it is in the range of polynomial time.

  Although the minimum value selection range in FIG. 3 is described for a specific grid point 301, the same minimum value selection range is set for other grid points. This is because the directed acyclic graph in which the shortest path search by dynamic programming is performed has two high order subordinate relations in the semi-order in which the start point side of the directed edge is high and the end point is low. The grid points always have a directed side from the upper grid point to the lower grid point. Thus, one of the features of the present invention can be expressed as a shape of a directed acyclic graph to which dynamic programming is applied.

After obtaining the minimum cost of the route at all grid points according to equation (10), the end cost (i _e , j _e ) in the embodiment of the present invention is set to the minimum cost of the route according to the following equation (11). Obtained as the smallest grid point. That is, the end is not fixed. When all costs are non-negative, g _{I, J} is always the minimum, but since negative costs are introduced, g _{I, J} is not necessarily the minimum.

  Also in the embodiment according to the present invention, the association is obtained by a backtrack procedure based on the selection of the minimum value in the DP recurrence formula from the end to the start. The end point is determined by the condition shown in Expression (11). The backtrack procedure is performed from this end point, and the start end candidate in the formula (10) that has been reached becomes the start end.

The embodiment according to the present invention in which the start end is not fixed as described above is a complete generalization of “free start end” described in Non-Patent Document 1. With reference to FIG. 4, “free start / end termination” according to the present invention will be described. In FIG. 4, an example of a minimum cost path that can be an embodiment according to the present invention formulated by the equations (6) to (11) is shown on the DP plane 410, and the equation ( The example of the path | route of the minimum cost which can be the conventional DP matching formulated in 1)-(5) is shown. As shown on the DP plane 420 in FIG. 4, in the conventional DP matching formulated by the equations (1) to (5), u ₁ = 1 and u _I = J shown in the equation (4). The start end (441) and the end end (461) are fixed by the above conditions, and any of the paths obtained by the dynamic programming has both ends. On the other hand, since there is a possibility that all the lattice points may be the start end in the association between the element sequences in the embodiment according to the present invention, as shown on the DP plane 410 in FIG. 432, 433) and paths having different end points (451, 452, 453) are obtained by dynamic programming. That is, the end point obtained by the equation (11) is not fixed, and the start end candidate that reaches from the end point by backtracking is not fixed.

  The role of negative costs in the embodiment according to the present invention will be described with reference to FIG. That is, the reason why the minimum value selection range as shown in FIG. 3 does not result in unintended extreme association due to the costs described in the equations (7) and (8) will be described. In FIG. 5, a simplified notation is used in order to explain only the role of negative costs. That is, the cost from the start point to the end point of each side of the grid is written on each grid-like side, and in the case of other combinations of the start point and the end point, the cost is set to 0 although not shown in the figure.

  On the DP plane 510 in FIG. 5, all the costs listed are positive and all are non-negative including the costs not listed. At this time, the minimum cost route from the start end (531) of the lower left circle to the end (551) of the upper right square is a route directly connecting the start and end as shown in the figure, and the minimum cost of the route is 0. The route on the DP plane 510 is an example of an unintended extreme correspondence.

  On the other hand, the cost indicated on the DP plane 520 in FIG. 5 is a numerical value obtained by subtracting 10 from the cost of the corresponding side at 501 and is all negative. Including the costs not listed, the costs of 520 are all 0 or less. At this time, the minimum cost path from the start point (541) of the lower left circle mark to the end point (561) of the upper right square mark is selected as having a small negative cost value (having a large absolute value) as shown in the figure. The total cost is −39, which is calculated by (−8) + (− 7) + (− 7) + (− 9) + (− 8).

  As described with reference to FIG. 5, when a negative cost is introduced, the larger the number of associations (| U |) is (the more the number of edges of the path is), the more the cost tends to be minimized. On the other hand, if all the matching costs are non-negative, the cost increases as | U | In other words, if a negative cost is introduced, the number of associations (| U |) will be obtained aggressively, but if the cost is non-negative, the number of associations should be increased. Become passive. Inclination restriction and fixation of the start end in conventional DP matching according to equations (1) to (5) have a function of forcing the association against the property of avoiding the association while avoiding the increase in cost. In other words, the conventional DP matching works so as to obtain a solution that avoids associating as much as possible under conditions of tilt restriction.

  On the other hand, in the embodiment according to the present invention, optimization works not to avoid cost but to try to increase the association positively by obtaining negative cost. This eliminates the need to provide a fixed minimum value selection range for the purpose of preventing a short-circuited minimum solution that avoids costs.

  When applying general dynamic programming to directed acyclic graphs instead of DP matching, search for “routes with many edges” in the shortest route search problem for networks with negative weights. Changes in properties are also noted in textbooks (eg, R. Sedgewick, Algorithms in Java® Third Edition Part 5: Graph Algorithms, Addison Wesley, 2003.).

  As described above, the correspondence problem between two element sequences in the embodiment according to the present invention has been formulated by the equations (6) to (11). In the embodiments of the formulas (6) to (11), a general formulation is performed as much as possible, but more restrictive conditions may be used.

  For example, the minimum value selection range shown in Expression (10) and FIG. 3 may be narrowed by imposing conditions according to the properties of the target to be applied. For example, for a specific element in the first element row, if there is a condition that must correspond to any one of a plurality of specific elements in the second element row, a minimum value is partially selected according to this condition. The range may be narrowed.

  In addition, the “pruning” process performed to reduce the amount of calculation in the conventional DP matching can be applied to the embodiment of the present invention. “Pruning” is a process for finding a route with a low possibility of minimizing the route cost and not performing the calculation. Such pruning does not change the shape of the directed acyclic graph to which dynamic programming is applied, and does not relate to the requirements of the present invention.

  Moreover, you may add a restriction | limiting also about a start end. As in conventional DP matching, the start end may be fixed, or conditions may be imposed when determining the end and start end candidates. For example, the termination may be selected from the lattice points within a fixed distance range from (I, J) on the DP plane, with the minimum path cost.

  Next, embodiments of the present invention for objects with specific numerical values will be described with reference to the drawings. Two element sequences to be associated are set as point sequences on a two-dimensional plane as shown in Expression (12).

The Manhattan distance between the corresponding points (the sum of the absolute values of the differences between the coordinates) is the physical quantity that is the basis of the cost. That is, || x _i -y _j || in Expression (8) is as shown in Table 1.

  FIG. 6 shows how the obtained association changes when the boundary value subtracted from the physical quantity based on the Manhattan distance in Table 1 is changed when determining the cost between elements. In FIG. 6, “(a) boundary value = 0” (610), “(b) boundary value = 4” (620), and “(c) boundary value = 8” (630) arranged in the vertical direction. In the case of [3], the total cost of the three associations [correspondence 1] (601), [association 2] (602), and [association 3] (603) arranged in the horizontal direction and the breakdown of the calculation are shown Has been. Reference numerals 661, 662, and 663 in FIG.

  In FIG. 6, an X point sequence of Formula (12) is shown at 640, and a Y point sequence is shown at 650. In the two-dimensional plane shown in FIG. 6, the x axis is the right direction, the y axis is the downward direction, and the upper left corner is the origin.

  In FIG. 6, reference numerals 641 and 651 denote points in the point sequence X and points in the point sequence Y that are associated by [Association 1] connected by arrows. Similarly, the points 642 and 652 in [Association 2] and 643 and 653 [Association 3] in the point sequence X and the points in the point sequence Y are connected by arrows. It is shown.

In the example of FIG. 6, for easy understanding, the association is performed by providing a constraint condition that the association is one-to-one and there are two or more correspondences.

In the case of “boundary value = 0” (610) in FIG. 6 (a), this is the same as the conventional DP matching without tilt restriction, and thus [Uncorresponding extreme association [association 1] (661, U = {(x ₁ , y ₁ ), (x ₄ , y ₃ )}), the total cost is 1, which is an optimal solution. A breakdown of this cost is shown at 611. The cost of associating x ₁ with y ₁ is “(0−0)” by subtracting “0” as the boundary value from “0” as the Manhattan distance between the two points shown in Table 1. As required. The cost of associating x ₄ with y ₃ is “(1−0)” by subtracting “0” as the boundary value from “1”, which is the Manhattan distance between the two points shown in Table 1. As required. “1”, which is the sum of these two costs, is the total cost of [Association 1]. The total cost of [Association 2] (612) and the total cost of [Association 3] obtained by the same method. It is smaller than (613) and has a minimum value.

In the case of “boundary value = 4” (620) in FIG. 6B, it is better to associate as “similar if the distance is within“ 4 ”, and not to associate otherwise. It means "good". According to this criterion, the total cost in [Association 2] (662, U = {(x ₁ , y ₁ ), (x ₂ , y ₂ ), (x ₄ , y ₃ )}) is −9, It is an optimal solution. A breakdown of this cost is shown at 622. The cost of associating x ₁ with y ₁ is “(0 − 4)” by subtracting “4” as the boundary value from “0” which is the Manhattan distance between the two points shown in Table 1. As required. The cost of associating x ₂ with y ₂ is “(2 − 4)” by subtracting the boundary value “4” from the Manhattan distance “2” between the two points shown in Table 1. As required. The cost of associating x ₄ with y ₃ is “(1-4)” by subtracting the boundary value “4” from the Manhattan distance “1” between the two points shown in Table 1. As required. “−9”, which is the sum of these three costs, is the total cost of [Association 2]. The total cost of [Association 1] (621) obtained by the same method and the sum of [Association 3] It is smaller than the cost (623) and has a minimum value.

In the case of “boundary value = 8” (630) in FIG. 6C, it means that “if the distance is within“ 8 ”, it is better to associate”, and the vertical and horizontal dimensions of the square are 5. Therefore, in most cases, it is better to associate them even if they are far away. Total in this result, [correspondence 3] (663, U = { (x 1, y 1), (x 2, y 2), (x 3, y 3), (x 4, y 4)}) The cost is -22, which is an optimal solution. A breakdown of this cost is shown at 633. The cost for associating x ₁ with y ₁ is “(0-8)” by subtracting “8” as the boundary value from “0”, which is the Manhattan distance between the two points shown in Table 1. As required. The cost of associating x ₂ with y ₂ is “(2 − 8)” by subtracting the boundary value “8” from the Manhattan distance “2” shown in Table 1 As required. The cost of associating x ₃ with y ₃ is “(5-8)” by subtracting the boundary value “8” from the Manhattan distance “5” between the two points shown in Table 1. As required. The cost of associating x ₄ with y ₄ is “(3-8)” by subtracting the boundary value “8” from the Manhattan distance “3” between the two points shown in Table 1. As required. “−22”, which is the sum of these four costs, is the total cost of [Association 3]. The total cost (631) of [Association 1] obtained by the same method and the sum of [Association 2] It is smaller than the cost (632) and is the minimum value.

  For the purpose of “finding a polyline composed of two point sequences and finding similar ones by human beings”, it means that the point sequences of 642 and 652 in FIG. 6 are similar. “Boundary value = 4” (620) is relatively suitable for this. For example, in an automatic scoring system for writing kanji characters, there is a method to find a similar polyline for the application that associates the edges that make up an image in the correct kanji and the corresponding image in the input kanji. Applicable. This boundary value may be determined according to the purpose of various application fields. As a simple method, it is conceivable to use the average value or the median value of the costs in the combination of all elements between the element sequences as the boundary value.

In addition, in the case of “boundary value = 4” (620) in FIG. 6B, y ₄ is out of association in [association 2] which is the optimal solution. This is an example of the above-mentioned “free start / end”.

  In the second embodiment, the minimum value selection range shown in FIG. Example 3 shows an example for clarifying conditions related to the number of directed edges on a directed acyclic graph when the constraint condition is changed in this way.

  Prior to showing Example 3, the number of directed sides of Example 1 and Example 2 will be shown.

In the first embodiment, the minimum value selection range shown in FIG. 3 is taken at all the lattice points on the directed acyclic graph, and I and J in the equation (1) are used on the directed acyclic graph. The number of directed sides | E | at is expressed as the following equation (13).

  In the second embodiment, there is a constraint condition of “one-to-one correspondence”. For I and J in Equation (1), I = 4 and J = 4, but without assigning values to I and J, the number of directed edges on the directed acyclic graph | E | Is expressed as the following equation (14). In order to simplify the notation, the variables i ′ = i−1 and j ′ = j−1 are replaced in Equation (14).

Equation (14) is smaller than the value of Equation (13), but it is still a number proportional to I ² J ² . That is, even when the constraint condition for reducing the minimum value selection range shown in FIG. 3 is imposed, when the constraint condition reduces the minimum value selection range in FIG. 3 as a percentage, the number of directed sides is I ² J ^2. The number is proportional to. When a constraint condition is set such that the fixed minimum value selection range shown in FIG. 1 is provided, the number of directed sides is a number proportional to IJ. This difference in the number of directed sides is directly related to the presence or absence of the effect of the present invention. That is, in applying the present invention, it is possible to impose a constraint condition for reducing the minimum value selection range, but it is necessary to make a directed acyclic graph having a number of directed edges proportional to I ² J ^2. .

  In order to represent the number of directed sides in the third embodiment, a function representing the number of directed sides when no constraint is imposed is defined as e (m, n) as follows. That is, in the case of the first embodiment, | E | = e (I, J).

The number of directed edges on the directed acyclic graph in Example 1 and Example 2 has been arranged as described above.

In the third embodiment, “(x _i1 , y _j2 ) or (x _i2 , y _j1 ) is always associated with the first embodiment according to the expressions (1) and (6) to (11). Include (however, i ₁ <i ₂ , j ₁ <j ₂ ) ”. That is, the following equation (16) is imposed as a constraint condition. This constraint condition is macroscopically imposed on the DP plane, unlike the constraint condition in the second embodiment in which the minimum value selection range of all grid points is uniformly restricted. This affects the minimum value selection range at partial grid points.

The directed acyclic graph in the correspondence of the third embodiment according to the expressions (1), (6) to (11), and (16) is configured inside the hatched portions (741, 742) in FIG. become. The path from the start end (711) passes through either the lattice point 731 whose coordinates are (i ₁ , j ₂ ) or the lattice point 732 whose coordinates are (i ₂ , j ₁ ). In other words, the path from the start end 711 to the lattice point 731 or the lattice point 732 is formed by connecting the directed edges in the hatched portion of the start point 741 and the start point end point. The path from the lattice point 731 or the lattice point 732 to the end point 721 is formed by connecting the directed sides in the hatched portion 742 with the start point and the end point. Note that if there is a directed acyclic graph within the hatched range of FIG. 7, equation (16) is not satisfied.

Since it is only necessary to count the number of directed edges in the hatched portion in FIG. 7, the number of directed edges | E | in the directed acyclic graph in the third embodiment that imposes the constraint condition according to the equation (16) is: Using e (m, n) in equation (15), the following equation (17) is obtained. In Expression (17), the first three terms are the number of directed sides in the hatched portion of 741, and the number of directed sides in a rectangle whose diagonal line is a line connecting grid points 711 and 731 e ( i ₁ , j ₂ ) and the number of directed sides e (i ₂ , j ₁ ) in the rectangle whose diagonal is a line segment connecting the grid points 711 and 732, the grid points 711 and 751 Is obtained by subtracting the number e (i ₁ , j ₁ ) of directed sides in a rectangle whose diagonal is a line connecting the two. The last three terms are the number of directed edges in the 742 hatched portion.

The value of equation (17) is a number proportional to I ² J ² , as in equations (13) and (14).

Conversely, if the directed acyclic graph has a number of directed edges proportional to I ² J ² , not all grid points, but i × j grid points with coordinates (i, j) There is always a group of grid points such that there is a minimum selection range proportional to. In this part, according to the criteria set by the boundary value, the present invention effect that the arbitrary number of elements in the part can be skipped and the similar parts can be flexibly associated with each other is a constraint condition. It is demonstrated within the range.

An embodiment of the associating method according to the present invention will be described with reference to FIG. FIG. 8 shows an implementation of the association method according to the present invention according to the formulas (1) and (6) to (10) using the programming language JavaScript (registered trademark). In the program of FIG. 8, as variables, I is the number of elements of the first element sequence, J is the number of elements of the second element sequence, BV is the boundary value, and md is the physical quantity of x _i and y _j ( It is assumed that the variable name (conscious of the Manhattan distance) has been set.

In the program of FIG. 8, nodes is a two-dimensional array of objects that store information on lattice points. The lattice point object corresponds to g _{i, j} in the equation (10), and includes a g field that holds the minimum cost of the route, and the object of the previous lattice point in which the minimum cost is set for backtracking. And a previous_node field for holding the. In addition, a field for holding the element number i of the first element row and the element number j of the second element row which are coordinate values of the lattice point (i, j) is also provided. In JavaScript (registered trademark), the array index is from 0, but in order to match the notations of the expressions (6) to (10), the index in FIG.

  The repetition of the second and fourth lines in the program of FIG. 8 is for processing all the grid points in order. If both variables i and j are looped in ascending order, it becomes the semi-ordered topological sort order of the directed acyclic graph on the DP plane constructed under the monotonic constraint, and the requirement to apply dynamic programming Fulfill.

  In the 5th to 7th lines in the program of FIG. 8, the grid points are initialized. Of these, the seventh line sets the cost of the route in the case of being the starting end candidate of the recurrence formula of Expression (10). The value of the path cost as the starting end candidate is updated when the lattice point becomes other than the starting end candidate in later processing.

The repetition of the 8th and 9th lines in the program of FIG. 8 is for sequentially processing the minimum value selection range for the grid points. That is, it corresponds to the range setting “1 ≦ i _t ≦ i, 1 ≦ j _t ≦ j” for the minimum value of the equation (10).

  Lines 11 to 13 in the program of FIG. 8 are processes for updating the minimum value. It is determined whether or not the minimum value is updated in the 11th row, the minimum value is updated in the 12th row, and the previous grid point is stored in the pvevious_node field for backtrack processing in the 13th row. At the end of the repetition of the 8th and 9th lines, if the pvevious_node field is set by the processing from the 11th line to the 13th line, it is a start end candidate, and if it is set, it is not a start end candidate.

  Lines 15 to 22 in the program of FIG. 8 are processes for obtaining the end point according to equation (11).

  Lines 23 to 29 in the program of FIG. 8 are processes for performing a backtrack process from the end and obtaining a path representing the correspondence as a character string. In the 26th line, it is determined that the start end candidate has been reached because the pvevious_node field is not set. The obtained association result is output in the 30th line.

  In the program of FIG. 8, I is set to 4, J is set to 4, md is set to the value of Table 1, and BV is set to the values of 0, 4, and 8, respectively, and the result shown in FIG. 6 is obtained. In order to operate in such a manner, it is necessary to include the above-described condition that “correspondence is one-to-one, two or more correspondences”. For example, the condition of “one-to-one correspondence” may be changed by changing “<=” to “<” in the determination unit in the repetitive sentences in the 8th and 9th lines.

  The program in FIG. 8 or an equivalent program in another programming language can be executed by a general computer including a CPU, a memory, and the like. It is also possible to configure an apparatus that executes the program of FIG. 8 or an equivalent program in another language as an embedded system. Furthermore, the internal processing of the repetition of the second and fourth lines in the program of FIG. 8 can be parallelized within a range that keeps the partial order relation in the directed acyclic graph, and is divided into threads. It can also be executed by another core on the multi-core CPU. Either implementation can be realized by a general well-known method.

  Various objects such as images, audio signals, and sentences can be used for association between two element strings, and can be applied to uses such as authentication, recognition, and search.

101-104 Example of minimum value selection range 201 Start end 202 End 300 DP plane 301 Specific lattice points of interest 410, 420 DP planes 431-433, 441 Start end 451-453, 461 End 510, 520 DP plane 531, 541 Start end 551 , 561 Terminals 601 to 603 Columns 610, 620, 630 for each association Boundary values 611 to 613, 621 to 623, 631 to 633 Total cost and calculation 640, 650 Point sequence shown 641 to 643, 651 to 653 661 to 663 shown by arrows of the point sequence that is the target of the representation 700 DP plane 711 Start point 721 End point 731, 732 Lattice points 741 and 742 that are mentioned in the constraint condition Lattice points 751 and 752 Lattice points

Claims (9)

When the first element sequence is compared with the second element sequence to obtain an association including one or more pairs of elements of the first element sequence and elements of the second element sequence,
On a lattice space that is a Cartesian product set of a set of elements of the first element sequence and a set of elements of the second element sequence,
A first directed acyclic graph is formed by providing a plurality of directed edges with a point in the lattice space as a lattice point, one lattice point as a start point, and another lattice point as an end point so as not to cause a cycle. And the steps
For all the grid points included as vertices in the directed acyclic graph, the cost is determined for each combination of the elements of the first element sequence and the elements of the second element sequence constituting each grid point. A second step for the cost of the grid points;
A route that connects two or more directed edges in succession by repeating the connection of two directed edges by matching the end point of the directed edge on the directed acyclic graph with the start point of another directed edge. age,
The total cost of the grid points included as the start point or end point of the directed side in the route is defined as the route cost.
The lattice points are sequentially processed in a topologically sorted order according to the semi-order defined by the directed acyclic graph, and the route that minimizes the route cost to the lattice point and the minimum route cost are obtained. A third step of determining a minimum cost path in the directed acyclic graph by dynamic programming;
A set of sets of elements of the first element sequence and elements of the second element sequence of the grid points included in the determined minimum cost path, and a result of associating the first element sequence with the second element sequence A fourth step to:
In the element string matching method having
In the first step,
In a partial order defined by the directed acyclic graph, in an order relationship in which the start point side of the directed edge is higher and the end point side is lower,
Configuring the directed acyclic graph so as to provide directed edges from the upper grid point to the lower grid point for all the upper grid points and the lower grid points in the order relationship; ,
In the second step,
For the purpose of associating the element strings, associating the elements of the first element string and the elements of the second element string constituting the lattice points is a negative cost when the object is met. If the cost is not positive, the cost of the positive value, if not, the value 0 is the cost of the grid point.
Mixing lattice points with negative cost and non-negative cost points,
A method for associating element strings, characterized by When the first element sequence is compared with the second element sequence to obtain an association including one or more pairs of elements of the first element sequence and elements of the second element sequence,
On a lattice space that is a Cartesian product set of a set of elements of the first element sequence and a set of elements of the second element sequence,
A first directed acyclic graph is formed by providing a plurality of directed edges with a point in the lattice space as a lattice point, one lattice point as a start point, and another lattice point as an end point so as not to cause a cycle. And the steps
For all the grid points included as vertices in the directed acyclic graph, the cost is determined for each combination of the elements of the first element sequence and the elements of the second element sequence constituting each grid point. A second step for the cost of the grid points;
A route that connects two or more directed edges in succession by repeating the connection of two directed edges by matching the end point of the directed edge on the directed acyclic graph with the start point of another directed edge. age,
The total cost of the grid points included as the start point or end point of the directed side in the route is defined as the route cost.
The lattice points are sequentially processed in a topologically sorted order according to the semi-order defined by the directed acyclic graph, and the route that minimizes the route cost to the lattice point and the minimum route cost are obtained. A third step of determining a minimum cost path in the directed acyclic graph by dynamic programming;
A set of sets of elements of the first element sequence and elements of the second element sequence of the grid points included in the determined minimum cost path, and a result of associating the first element sequence with the second element sequence A fourth step to:
In the element string matching method having
In the first step,
The number of elements in the first element row is I, the number of elements in the second element row is J, and there are a number proportional to I ² J ² according to the two values I and J. Providing a directed edge to construct the directed acyclic graph;
In the second step,
For the purpose of associating the element strings, associating the elements of the first element string and the elements of the second element string constituting the lattice points is a negative cost when the object is met. If the cost is not positive, the cost of the positive value, if not, the value 0 is the cost of the grid point.
Mixing lattice points with negative cost and non-negative cost points,
A method for associating element strings, characterized by In the third step of obtaining the minimum cost path,
When sequentially calculating the minimum path cost of the path to the grid point for each grid point in the order topologically sorted by the semi-order defined by the directed acyclic graph,
For all of the second grid points that are the starting points of the directed sides that end at the first grid point that is the target for which the minimum path cost is to be calculated,
When there is a negative or zero value in the calculated minimum path cost of the second grid point, the cost of the first grid point is added to the minimum value among the negative or zero values. The obtained value is set as the minimum path cost of the path to the first grid point, and the second grid point having the minimum path cost of the minimum value is stored as the parent grid point of the first grid point;
If the calculated minimum path cost of the second grid point is a positive value without exception, the cost of the first grid point is set as the minimum path cost of the first grid point, and the first grid point Remember the point as a starting point candidate,
After calculating the minimum path cost at all the lattice points, the lattice point having the smallest value among them is defined as the end point,
Starting from the lattice point that is the end, a backtrack procedure for repeatedly obtaining the parent lattice point from the lattice point is performed,
When the lattice point stored as the starting edge candidate in the backtrack procedure becomes the parent lattice point, the lattice point is determined as the starting edge, and the repetition is ended.
A path that connects the obtained end and start to both ends of the lattice points that appeared in the backtrack procedure with the directed side as a minimum cost path,
The element string correlation method according to claim 1 or 2. When at least one of the starting edge candidate and the terminal end is determined in the third step, only lattice points that satisfy a predetermined condition are set as objects to be determined as the starting edge candidate and the terminal end. The element string correlation method according to claim 3. When the first element sequence is compared with the second element sequence to obtain an association including one or more pairs of elements of the first element sequence and elements of the second element sequence,
On a lattice space that is a Cartesian product set of a set of elements of the first element sequence and a set of elements of the second element sequence,
A first directed acyclic graph is formed by providing a plurality of directed edges with a point in the lattice space as a lattice point, one lattice point as a start point, and another lattice point as an end point so as not to cause a cycle. Means of
For all the grid points included as vertices in the directed acyclic graph, the cost is determined for each combination of the elements of the first element sequence and the elements of the second element sequence constituting each grid point. A second means for the cost of the grid points;
A route that connects two or more directed edges in succession by repeating the connection of two directed edges by matching the end point of the directed edge on the directed acyclic graph with the start point of another directed edge. age,
The total cost of the grid points included as the start point or end point of the directed side in the route is defined as the route cost.
The lattice points are sequentially processed in a topologically sorted order according to the semi-order defined by the directed acyclic graph, and the route that minimizes the route cost to the lattice point and the minimum route cost are obtained. A third means for determining a minimum cost path in the directed acyclic graph by dynamic programming;
A set of sets of elements of the first element sequence and elements of the second element sequence of the grid points included in the determined minimum cost path, and a result of associating the first element sequence with the second element sequence A fourth means to:
In the inter-element string association device having
In the first means,
In a partial order defined by the directed acyclic graph, in an order relationship in which the start point side of the directed edge is higher and the end point side is lower,
Configuring the directed acyclic graph so as to provide directed edges from the upper grid point to the lower grid point for all the upper grid points and the lower grid points in the order relationship; ,
In the second means,
For the purpose of associating the element strings, associating the elements of the first element string and the elements of the second element string constituting the lattice points is a negative cost when the object is met. If the cost is not positive, the cost of the positive value, if not, the value 0 is the cost of the grid point.
Mixing lattice points with negative cost and non-negative cost points,
A device for associating element strings, characterized by When the first element sequence is compared with the second element sequence to obtain an association including one or more pairs of elements of the first element sequence and elements of the second element sequence,
On a lattice space that is a Cartesian product set of a set of elements of the first element sequence and a set of elements of the second element sequence,
A first directed acyclic graph is formed by providing a plurality of directed edges with a point in the lattice space as a lattice point, one lattice point as a start point, and another lattice point as an end point so as not to cause a cycle. Means of
For all the grid points included as vertices in the directed acyclic graph, the cost is determined for each combination of the elements of the first element sequence and the elements of the second element sequence constituting each grid point. A second means for the cost of the grid points;
A route that connects two or more directed edges in succession by repeating the connection of two directed edges by matching the end point of the directed edge on the directed acyclic graph with the start point of another directed edge. age,
The total cost of the grid points included as the start point or end point of the directed side in the route is defined as the route cost.
The lattice points are sequentially processed in a topologically sorted order according to the semi-order defined by the directed acyclic graph, and the route that minimizes the route cost to the lattice point and the minimum route cost are obtained. A third means for determining a minimum cost path in the directed acyclic graph by dynamic programming;
A set of sets of elements of the first element sequence and elements of the second element sequence of the grid points included in the determined minimum cost path, and a result of associating the first element sequence with the second element sequence A fourth means to:
In the inter-element string association device having
In the first means,
The number of elements in the first element row is I, the number of elements in the second element row is J, and there are a number proportional to I ² J ² according to the two values I and J. Providing a directed edge to construct the directed acyclic graph;
In the second means,
For the purpose of associating the element strings, associating the elements of the first element string and the elements of the second element string constituting the lattice points is a negative cost when the object is met. If the cost is not positive, the cost of the positive value, if not, the value 0 is the cost of the grid point.
Mixing lattice points with negative cost and non-negative cost points,
A device for associating element strings, characterized by In the third means for obtaining the minimum cost route,
When sequentially calculating the minimum path cost of the path to the grid point for each grid point in the order topologically sorted by the semi-order defined by the directed acyclic graph,
For all of the second grid points that are the starting points of the directed sides that end at the first grid point that is the target for which the minimum path cost is to be calculated,
When there is a negative or zero value in the calculated minimum path cost of the second grid point, the cost of the first grid point is added to the minimum value among the negative or zero values. The obtained value is set as the minimum path cost of the path to the first grid point, and the second grid point having the minimum path cost of the minimum value is stored as the parent grid point of the first grid point;
If the calculated minimum path cost of the second grid point is a positive value without exception, the cost of the first grid point is set as the minimum path cost of the first grid point, and the first grid point Remember the point as a starting point candidate,
After calculating the minimum path cost at all the lattice points, the lattice point having the smallest value among them is defined as the end point,
Starting from the lattice point that is the end, a backtrack procedure for repeatedly obtaining the parent lattice point from the lattice point is performed,
When the lattice point stored as the starting edge candidate in the backtrack procedure becomes the parent lattice point, the lattice point is determined as the starting edge, and the repetition is ended.
A path that connects the obtained end and start to both ends of the lattice points that appeared in the backtrack procedure with the directed side as a minimum cost path,
The element string correlation device according to claim 5 or 6. When at least one of the starting edge candidate and the terminal end is determined by the third means, only lattice points that satisfy a predetermined condition are set as objects to be determined as the starting edge candidate and the terminal end. The inter-element-string association device according to claim 7. A program for causing a computer to execute the element string correlation method according to claim 1.