JP2014016731A - Data update processing device, method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To update, when a new sequence is input, a hidden Markov model of a hierarchical structure in a manner that the computation time and memory usage are reduced.SOLUTION: The HMM of the top layer to the HMM of the bottom layer are selected for an input sequence, the input sequence is inserted into the selected HMM of the bottom layer, and weight is determined (S103). When a space for the new sequence does not exist, the selected HMM is divided into 2 HMMs, and a plurality of HMMs in the next lower layer belonging to the selected HMM, or a plurality of sequences belonging to the selected HMM are allocated to the two divided HMMs (S106). Each parameter of the two divided HMMs is estimated (S109). When it is determined that the two divided HMMs are in the bottom layer and the value based on the likelihood of the sequence to the HMM is inappropriate (S111), the sequence is re-inserted(S113).

Description

  The present invention relates to a data update processing device, method, and program, and more particularly, to a data update processing device, method, and program for updating a hidden Markov model based on an input sequence.

Hidden Markov Model (HMM) is an effective statistical method for modeling uncertain time series data. HMM is robust to noise and is used in many applications such as speaker recognition, natural language processing, and gene sequence analysis including proteins and DNA. The HMM includes an initial state probability π = {π _i }, a state transition probability A = {a _ij }, and a symbol output probability B = {b _i (v)}.

  Given a model Θ and a sequence x, these likelihoods L (x | Θ) can be calculated by the Viterbi algorithm as shown in the following equation (1).

Here, δ _t (i) indicates the maximum probability of state i at time t.

  The EM algorithm is a method for estimating the parameters of a probability model of an unobservable latent variable based on the maximum likelihood method for data having a missing value. The EM algorithm is a kind of iterative method, and the calculation proceeds by alternately repeating the E step (Expectation) and the M step (Maximization).

E step: In HMM, Baum-Welch algorithm is an efficient method of expected value calculation in E step. The Baum-Welch algorithm calculates an expected value based on the HMM parameter Θ = {π, A, B}. γ _t (i) indicates the probability of state i at time t after the sequence is given, and is calculated as in the following equation (2).

Where α _t (i) = P (x ₁ , ..., x _t , q _t = i | Θ), β _t (i) = P (x _t +1, ..., x _m | q _t = i, Θ). q _t represents an optimum state at time t. ξ _t (i, j) is the transition probability between state i at time t and state j at time t + 1, and is expressed by the following equation (3).

M step: The algorithm calculates a new model parameter ˜Θ that maximizes the likelihood based on the expected values γ _t (i), ξ _t (i, j) and the sequence x. The model parameter update formulas are the following formulas (4) to (6).

Here, x _t indicates a symbol of x at time t.

  The Hierarchical Hidden Markov Model is an extension of the HMM to represent a sequence having a hierarchical structure (Non-Patent Document 1). Hidden states are hierarchized, that is, based on a tree structure, and model parameters of each hierarchy are estimated using an EM algorithm.

Fine, S., Singer, Y. and Tishby, N. “The Hierarchical Hidden Markov Model”, Analysis and Applications, Machine Learning, Vol.32, No.1, pp.41-62 (1998).

  While the problem dealt with in the present invention is to determine an arbitrary number of models from a large number of sequence sets, the above-mentioned hierarchical HMM divides the entire sequence into various lengths to build a hierarchical model structure There is to do. Although it is possible to apply a hierarchical HMM to the problem of the present invention, a large calculation cost is required for model estimation. In particular, when new sequence data is given, it is necessary to perform model estimation using all sequences accumulated in the past.

  The present invention has been made in view of the above circumstances. When a sequence is newly input, data that can reduce the calculation time and the memory usage and update the hidden Markov model of the hierarchical structure. An object of the present invention is to provide an update processing apparatus, method, and program.

  In order to achieve the above object, a data update processing device according to the present invention belongs to at least one of a parameter of each of a plurality of hidden Markov models (HMMs) defined in a hierarchical structure, and an HMM in a lowermost layer, and Storage means for storing a plurality of sequences weighted for each of the lowest-level HMMs to which it belongs, and the likelihood of each of the input sequences from the highest-level HMM to the lowest-level HMM according to the hierarchical structure And selecting at least one lowest-layer HMM to which the input sequence belongs, and inserting the input sequence as a sequence belonging to each of the selected lowest-layer HMMs. And a sequence insertion unit for determining a weight of the sequence for each of the selected lowermost HMMs. When there is a space for a new sequence for each HMM from the topmost HMM to the bottommost HMM selected by the sequence insertion means, the parameters of the selected HMM are input. Update means for updating based on a sequence, and when there is no free space for a new sequence for each HMM from the uppermost HMM to the lowermost HMM selected by the sequence insertion means, the selected HMM Is divided into two HMMs, and a plurality of HMMs in the next lower layer belonging to the selected HMM or a plurality of sequences belonging to the selected HMM are allocated to the two divided HMMs And each parameter of the two HMMs divided by the dividing means is assigned to the HMM. An estimation means for estimating based on a sequence under the HMM, or a sequence assigned to the HMM, and two HMMs divided by the dividing means are lowermost HMMs, and belong to the lowermost HMM If the value based on the likelihood of the HMM is determined to be an inappropriate value compared to the threshold, the sequence is deleted from the sequence belonging to the lowest-order HMM, and the sequence corresponds to the sequence Update the parameters of each HMM from the lowest HMM to the highest HMM and, for the sequence, according to the hierarchical structure, the HMM based on the likelihood for each HMM from the highest HMM to the lowest HMM To select at least one lowest HMM to which the sequence belongs, and to select the selected lowest HMM. The sequence belonging to each lower layer HMM includes a sequence reinsertion unit that reinserts the sequence and obtains the weight of the sequence for each of the selected lowermost HMMs.

  The data update processing method according to the present invention includes a parameter of each of a plurality of hidden Markov models (HMMs) defined in a hierarchical structure and at least one of the lowest-layer HMMs, and each of the lowest-layer HMMs to which it belongs A data update processing method in a data update processing apparatus, comprising storage means for storing a plurality of sequences weighted with respect to, sequence insertion means, update means, division means, estimation means, and sequence reinsertion means, wherein the sequence The input means selects the HMM based on the likelihood for each HMM from the highest layer HMM to the lowest layer HMM according to the hierarchical structure with respect to the input sequence by the inserting means, and at least one to which the input sequence belongs A lowermost HMM is selected, and a sequence belonging to each of the selected lowermost HMMs And inserting the inputted sequence and determining the weight of the sequence for each of the selected lowest layer HMMs, and by the updating means, from the highest layer HMM selected by the sequence insertion means to the lowest layer If there is room for a new sequence for each of the HMMs up to the HMM, the parameters of the selected HMM are updated based on the input sequence, by the dividing means, by the sequence inserting means For each HMM from the selected top HMM to the bottom HMM, if there is no room for a new sequence, the selected HMM is divided into two HMMs and the selected HMM A plurality of HMMs in the next lower layer belonging to the group, or a group belonging to the selected HMM Are assigned to the two divided HMMs, and the parameters of the two HMMs divided by the dividing means are assigned by the estimating means to the sequences under the HMM assigned to the HMM, or to the HMM. The two HMMs estimated by the sequence re-insertion means and divided by the division means are the lowest-layer HMMs, and the likelihood of the sequence belonging to the lowest-layer HMM to the HMM If the value based on is determined to be an inappropriate value compared to the threshold value, the sequence is deleted from the sequence belonging to the lowermost layer HMM, and the lowermost layer HMM corresponding to the sequence is deleted. Update the parameters of each HMM up to the top layer HMM and According to the structure, from the top layer HMM to the bottom layer HMM, select the HMM based on the likelihood for each HMM, select at least one bottom layer HMM to which the sequence belongs, and select the bottom layer selected The sequence is reinserted as a sequence belonging to each of the HMMs, and the sequence weight for each of the selected lowest-layer HMMs is obtained.

  The program according to the present invention is a program for causing a computer to function as each unit of the data update processing device.

  As described above, according to the data update processing device, method, and program of the present invention, with respect to a plurality of hidden Markov models (HMMs) defined in a hierarchical structure, a newest input sequence is the top layer. Select the HMM from the lowest HMM to the lowest HMM, insert the input sequence into the lowest HMM, and if there is no room for a new sequence in the HMM, If an inappropriate sequence allocation occurs as a result of allocating and dividing a layer HMM or sequence, an HMM is selected from the top layer HMM to the bottom layer HMM for the sequence, and the bottom layer HMM is selected. When a new sequence is input by re-inserting, the calculation time and memory usage are reduced, and the hidden Markov model of the hierarchical structure is reduced. Can be updated Le, effect is obtained that.

It is the schematic which shows the structure of the data update processing apparatus which concerns on the 1st Embodiment of this invention. It is the figure which illustrated the hierarchical model structure. It is the figure which illustrated the update of the hierarchical model structure. It is a flowchart which shows the content of the hierarchy model update process routine in the data update processing apparatus which concerns on the 1st Embodiment of this invention. It is the schematic which shows the structure of the approximate data update processing apparatus which concerns on the 2nd Embodiment of this invention. It is a flowchart which shows the content of the hierarchical sampling process routine in the approximate data update processing apparatus which concerns on the 2nd Embodiment of this invention. It is the figure which showed the example of the sequence showing the kinetic energy of the right and left leg in motion capture data. It is the figure which showed the result of having classified the sequence by the comparison method and the method of this invention. It is the figure which showed the experimental result regarding calculation cost.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

[First Embodiment]
<Outline of the invention>
Let X be n time-series sequence data (that is, X = {x ₁ , ..., x _n }). An object of the present invention is to determine c HMMs that statistically represent the features of X. All sequences x _i (i = 1, ..., n) are considered to belong to one or more of the c models with probability w (ie weight 0 ≤ w ≤ 1) . Therefore, the problems solved by the present invention are as follows.

(Problem 1): When a time-series data set X = {x ₁ , ..., x _n } consisting of n sequences is given at regular intervals, the total likelihood Σ ⁿ _{i = 1} Σ ^c _{j = 1} Find a model Θ _j (j = 1, ..., c) such that w _{i, j} L (x _i | Θ _j ) is maximized.

  In a dynamic situation in which the learning data set for model estimation increases with time, that is, the number of sequences n increases, it is necessary to devise in order to solve the above problem. There is a need for a method that continuously learns the input sequence and presents arbitrary c models at the time when the user requests at any time. Specifically, it is necessary to satisfy the following three requirements as an ideal solution.

  Applicability: Automatically discriminate and group input sequences and estimate HMM parameters. At this time, it is assumed that there is no knowledge about each group in advance.

  Extensibility: The process for updating the model realizes a sub-linear calculation cost that is shorter than the linear time for the number of sequences.

  Immediateness: When learning a sequence, the number of models c is not given in advance, and without such prior knowledge, the model is immediately presented to the user when c models are obtained.

  In existing data learning, a method of estimating a model using all original sequence sets is the mainstream. However, under a dynamic situation where data is generated intermittently, there is a problem in that the calculation cost becomes enormous if all the past large amounts of data archived for model estimation are used. In view of this, the present invention describes a hierarchical model data update processing apparatus that can significantly reduce calculation time and memory usage, and can estimate a model with an arbitrary granularity.

<System configuration>
As shown in FIG. 1, the data update processing device 100 according to the first embodiment of the present invention includes a CPU, a RAM, and a ROM that stores a program for executing a hierarchical model update processing routine described later. It is composed of a computer equipped and functionally configured as follows. As shown in FIG. 1, the data update processing device 100 includes an input unit 10, a processing unit 20, and an output unit 30.

  The input unit 10 receives input of time series data received via a network. The input unit 10 receives an input of an arbitrary number of models as inquiry data from an input device such as a keyboard.

  The processing unit 20 includes a time series data storage unit 21, a hierarchical model data storage unit 22, and a time series data processing unit 23. The time-series data storage unit 21 and the hierarchical model data storage unit 22 are examples of storage units, and the time-series data processing unit 23 includes a sequence insertion unit, an update unit, a division unit, an estimation unit, a sequence reinsertion unit, And it is an example of a presentation means.

  The time series data storage unit 21 stores the time series data received by the input unit 10. The hierarchical model data storage unit 22 stores model parameters of a plurality of HMMs having a hierarchical structure. When time series data is received by the input unit 10, the time series data processing unit 23 updates the model parameters stored in the hierarchical model data storage unit 22. At this time, the time series data processing unit 23 updates the model parameters without accessing all the sequences stored in the time series data storage unit 21. The time-series data processing unit 23 performs a model parameter update process characterized by weighted model estimation, node division, and reinsertion processing. Although the input time-series data is stored in the disk space of the time-series data storage unit 21, it is discarded from the memory space, and the amount of memory in the data update processing device 100 can be saved.

  When the number of models c as inquiry data input from the user is received, the time-series data processing unit 23 outputs c models that express the characteristics of the time-series data to the user by the output unit 30. Output.

  Next, the principle of data update processing by the time-series data processing unit 23 will be described.

  First, the structure of the hierarchical model will be described.

  In the present invention, a model is estimated using a hierarchical structure. By using the hierarchical structure, it is possible to update the model parameters at a minimum necessary cost without accessing all past sequences stored at that time when a new sequence is inserted. This is one of the advantages of using a hierarchical structure. A second advantage is that the sequence grouping process can be performed incrementally, and it is not necessary to analyze the set of all sequences in advance. These features allow model updates to be performed at a cost that is less than linear time for the number of sequences. Furthermore, a very important third advantage is that a set of HMM parameters can be obtained at an arbitrary granularity. That is, when the user requests c models, the present invention can quickly present c model parameters. This makes it possible to respond flexibly to user requests.

<Model structure>
FIG. 2 shows an example of the model structure of the present invention. FIG. 2 shows a two-layer model structure (ie h = 2). In the l-th layer of the model structure, there are b ^hl elements (in this case, b = 4), and each element includes b subelements below it. The j-th element in the l layer holds summary information of subelements under it, and is defined as the following equation (7).

Here, n _{l; j} and Θ _{l, j} indicate the number of all sequences belonging to the subelements under the element N _{l, j and} the model parameters expressing those sequences, respectively. However, unlike the above elements, the lowest layer (ie, l = 1) holds a list of sequences in addition to n _{l, j} and Θ _{l, j} . The jth element at l = 1 is defined as follows:

Here, the sequence list D _j is a set of entries represented by a pair of (x _i , w _{i, j} ). Each entry has a pointer to the sequence x _i and x _i is N _{1. ,} two pieces of information of probability (ie, weight) belonging to _j are managed. The weights w _{i, j} are calculated when the input sequence x _i is inserted. The total sum of the weights in the list of each sequence is b (ie, b ≧ Σ _i w _{i, j} ). The hierarchical model structure is effective for presenting an arbitrary number of models requested by the user, but is also very effective for the purpose of grouping and summarizing input sequences. Handling and managing sequence summary information (i.e. model parameters) in the hierarchy is much more efficient than handling all information about the sequence, and when updating the hierarchy, By calculating the likelihood between the model managed by each element and the input sequence, sequence grouping processing can be performed immediately. Here, an example of a hierarchical structure is shown using FIG.

(Example 1): Let {x ₁ , ..., x ₆ } be a set of sequences stored in a hierarchical structure. Each element (N _2,1 , N _1,1 , N _1,2 ) holds model parameters Θ _2,1 , Θ _1,1 , Θ _1,2 respectively. The model of each element expresses the characteristics of the sequence set managed under it. Specifically, Θ _1,1 is a parameter of a model obtained by learning the sequence set {x ₁ , x ₂ , x ₆ } with weights w _1,1 , w _2,1 , w _6,1 . Similarly, Θ _1,2 is a model obtained by learning {x ₃ ,..., X ₆ } with weights w _3,2 , w _4,2 , w _5,2 , w _6,2 . And Θ _2,1 represents the characteristics of the set {x ₁ , ..., x ₆ } of all sequences.

<Presentation of model>
By using a hierarchical structure, an arbitrary number of models can be presented at an arbitrary time. Here, consider a case where the user requests c representative models. First, the algorithm extracts a sufficient number (≧ c) of elements from the structure. These elements are then integrated into a group of c sequences using likelihood. Finally, the parameters of the model of the sequence set grouped in c are re-estimated and presented to the user.

<Insert>
Next, a method for inserting the input sequence into the hierarchical structure will be described.

  Unlike the conventional data structure, the hierarchical structure proposed in the present invention is characterized in that the probability (weight) is considered for each stored entry (sequence). Therefore, the conventional insertion method cannot be used for the hierarchical structure proposed in the present invention. Therefore, the present invention proposes a new algorithm for solving this problem. In the proposed insertion algorithm, input data is inserted into a plurality of elements according to weight values. That is, unlike the conventional insertion method, the present invention needs to handle a plurality of insertion paths. In designing an insertion algorithm in the present invention, we consider an approach of depth-first search and performing insertion processing for all paths.

When an input sequence x _i is given, the algorithm performs insertion processing in the following order (1) to (3).

(1) Start from the HMM at the top layer, and descend to the bottom layer while selecting an appropriate element (HMM) according to the likelihood for the HMM in the input sequence. Here, the calculated likelihood is also used for calculating the weight of the input sequence. This weight represents the probability between the model of all elements on the insertion path (the selected HMM from the top layer to the bottom layer) and the input sequence (see equation (9)). After the algorithm has reached the element N _{1, j} of the lowermost (l = 1), a new entry _{(x i, w i, j} ), i.e. weight for N _{1, j} pointer and x _i to x _i ( That is, the weight for inserting x _i into N _{1, j} is added to the sequence list D _j in N _{1, j} .

(2) After x _i is inserted into the elements N _{1, j} , the algorithm corrects the information of each element on the insertion path. That is, if division does not occur in each element for a new input (x _i , w _{i, j} ), the model parameters of each element on the insertion path are simply updated using x _i . If there is no space for new insertions at each element (ie, Σ _i w _{i, j} ≧ b), element division occurs and the model parameters are re-estimated at the divided elements.

(3) When an element division operation occurs, if an inappropriate entry occurs in each element in the lowest layer, the algorithm re-inserts those entries into appropriate elements. In the reinsertion operation, the model structure that represents the sequence set more correctly can be constructed by performing the same processing as the insert operation and moving the sequence managed in the hierarchical structure under more appropriate elements. .

Here, an important point is mentioned. Theoretically, the sum of the weight values in the i-th sequence x _i is Σ _j w _{i, j} = 1. However, the number of elements managed in the structure becomes very large especially when dealing with large-scale data. On the other hand, the value of the weight related to other than the main insertion path is very small and can be ignored. Therefore, in the present invention, it is assumed that insertion is performed only for elements with large weights, and insertion is not performed for other elements with fine weights. Specifically, the insertion is stopped when the total value of weights exceeds a threshold value w _th (for example, w _th = 0.9) when the insertion is repeated.

Next, calculation of weights in the insertion operation will be described. Weight w _i of x _i in the lowermost layer of the j-th element N _{1, j, j} by using the likelihood of x _i, is calculated according to the following equation (9).

Note that h indicates the height of the hierarchical structure, and b _l (b _l ≦ b) in the l-th layer is the number of sibling elements on the insertion path.

<Weighted model estimation>
The present invention holds a weight for an input sequence and performs model estimation of the sequence using the weight. Therefore, in the present invention, the existing EM algorithm is improved to realize model estimation with weights. When an input sequence x and its weight w are given, the present invention calculates a weighted expected value γ _t (i) of x as shown in the following equations (10) and (11).

  In the M step, the model parameter is updated based on the above equations (4) to (6) using the weighted expected value.

(Example 2): Here, as shown in FIG. 2 will be described for an example of inserting a new sequence x _6. As a first insertion, the algorithm starts from the top and finds the most appropriate model Θ _2,1 , Θ _1,1 in each layer. Further, the weights w _6,1 are calculated using equation (9). Since element N _1,1 has a space for inserting this new entry, no element division occurs, and the entry is added to N _1,1 as it is. After adding the entry, the algorithm updates the model Θ _2,1 , Θ _1,1 on the insertion path with the entry (x ₆ , w _6,1 ). In the next process, the insertion paths Θ _2,1 and Θ _1,2 are found as the second closest model, and x ₆ is added to N _1,2 . Again, no element splitting occurs. Subsequently, weights w _6,2 are calculated. After these two insertion operation, when exceeding the sum threshold value of the weights of x ₆ (i.e. _{w 6,1 + w 6,2> w th} ), the algorithm terminates the insertion operation.

<Division operation>
Next, details of the division operation will be described. When the element N is given, the division is performed according to the following procedures (1) to (5).

(1) Two subelements are selected at random from all subelements belonging to the element N, and their models Θ ₁ and Θ ₂ are obtained.

(2) Assign each subelement belonging to N to a closer group of models Θ ₁ and Θ ₂ . Here, for allocation to the group, the total likelihood Σ _i L (x _i | Θ ₁ ) of the sequence x _i belonging to each subelement for each model Θ ₁ , Θ ₂ (or Σ _i L (x _i | Θ ₁ )) is used as a similarity index.

(3) A new model is randomly selected one by one for each group to which subelements have been allocated, and Θ ₁ and Θ ₂ are obtained.

(4) The above procedures (2) to (4) are repeated until there is no movement between the groups.

(5) For the two newly generated groups, model parameters Θ ₁ and Θ ₂ are estimated using all sequences belonging to each group. Finally, the current element N is deleted, and newly divided and generated elements N ₁ and N ₂ and their model parameters Θ ₁ and Θ ₂ are added. Further, the subelements assigned to the groups of the elements N ₁ and N ₂ that are newly divided and generated are set as the subelements that belong to the newly generated and divided elements.

  When the element N is the lowest layer element, the partial element belonging to the element N is replaced with a sequence, and the division operation is performed according to the above procedures (1) to (5). Further, for each sequence, a weight for the allocated element of the two divided elements is calculated.

(Example 3): As shown in FIG. 3, consider the example of inserting the x _7. Insert from the top layer and find the closest models Θ _2,1 and Θ _1,2 in each layer. Here, we try to insert x ₇ in the lowest element N _1,2 but there is no space for new insertion (ie Σ _i w _{i, 2} ≧ b), so the algorithm uses N _{1,2 Is} divided into two elements N _1,2 and N _1,3 and {x ₅ , x ₇ } is changed to N _1,2 for the currently managed entry set {x ₃ , x ₄ , x ₆ } , {X ₅ , x ₇ } are assigned to N _1,3 . After element splitting, Θ _1,2 is re-estimated by N _1,2 and Θ _1,3 is re-estimated by N _1,3 . Similarly, Θ _2,1 on the insertion path is also updated.

<Reinsertion operation>
The algorithm performs an insertion operation only once for each input sequence. For this reason, the value of the weight of the sequence inserted in the past may become an inappropriate value according to the update of the model structure. The problem here is the situation where the parameters of the model change drastically when the split operation occurs, and the weights of the subordinate sequences become inappropriate. A reasonable solution to this problem is to delete the past sequences that became inappropriate in those elements when division occurs in the lowermost element and perform a new insertion operation to make a sequence into a suitable element. Is to move. Here, an inappropriate sequence can be detected using a likelihood ratio test shown in the following equation (12).

Θ _i represents a model parameter estimated from x _i , and Θ _{1, j} represents a model parameter held in N _{1, j} . If the likelihood ratio ρ _i is less than or equal to a certain threshold ρ _th (ρ _th = 0.8, etc.), the algorithm deletes the current entry (x _i , w _{i, j} ) from N _{1, j} and removes this entry Insert a new one. By such reinsertion operation, the sequence can be moved to a position more suitable for the model structure.

<Operation of data update processing device>
Next, specific processing of the data update processing device 100 will be described. First, when a sequence set is input to the data update processing device 100, the data update processing device 100 stores it in the time-series data storage unit 21. Then, the data update processing device 100 constructs a hierarchical HMM based on the sequence set and stores it in the hierarchical model data storage unit 22.

  When a new sequence is input to the data update processing device 100, the data update processing device 100 executes a hierarchical model update processing routine shown in FIG.

First, in step S101, the input unit 10 accepts an input sequence x _i. In the next step S102, the time-series data processing unit 23 sets an initial value 0 to the sum w _sum of the weights of imparting the sequence x _i.

Thereafter, the time-series data processing unit 23 repeats the processes of steps S103 to S113 until the total weight w _sum becomes larger than a predetermined threshold value w _th .

In step S103, the time-series data processing unit 23 selects from the top layer to the bottom layer based on the likelihood for the element, selects an appropriate bottom layer element, and is input as a sequence belonging to the selected element. The sequence x _i is inserted, and the weight w for the selected element is calculated. When the process in step S103 is performed for the second time or later, an appropriate lowermost element is selected except for the lowermost element selected up to the previous time.

  Then, the time-series data processing unit 23 repeats steps S104 to S113 for all elements N on the insertion path composed of elements from the top layer to the bottom layer selected in step S103.

In step S104, the time-series data processing unit 23 determines whether or not the element N has a free space for a new entry. If the sum of the weights of the sequences belonging to the subelements under the element is less than the threshold value b, it is determined that the element N has a free space for a new entry. In step S105, the time-series data processing unit 23 updates the model parameter Θ of the HMM of the element N according to the above equations (10), (11) and the above equations (4) to (6) using the input sequence x _i , Return to step S103 or step S104, or end the processing routine.

On the other hand, when the sum of the weights of the sequences belonging to the subelements under the element is equal to or greater than the threshold value b, it is determined that the element N has no free space for a new entry. In step S106, time-series data The processing unit 23 divides the element N into N ₁ and N ₂ by the above dividing operation. In step S107, the time-series data processing unit 23 sets the sequence set allocated to N ₁ to X _1, and in step S108, the time-series data processing unit 23 converts the sequence set allocated to N ₂ to X _2. And

In the next step S109, the time-series data processing unit 23 updates the HMM model parameter Θ ₁ of the element N ₁ using the sequence set X ₁ and uses the sequence set X ₂ to update the HMM of the element N ₂ . Update model parameter Θ ₂ of.

In step S110, the time-series data processing unit 23 determines whether or not the elements N ₁ and N ₂ are the lowest layer elements. If the elements N ₁ and N ₂ are not the lowest layer elements, the process returns to step S103 or step S104 or ends the processing routine.

On the other hand, when the elements N ₁ and N ₂ are the lowest-layer elements, the time-series data processing unit 23 repeats steps S111 to S113 for all the sequences x _j belonging to the elements N ₁ and N ₂ .

In step S111, the time series data processing unit 23, the sequence x _j, (12) the likelihood ratio [rho _j calculated according to equation calculated likelihood ratios [rho _j is or less than the threshold value [rho _th Determine. If the calculated likelihood ratio ρ _j is larger than the threshold value ρ _th, it is determined that the weight of the sequence x _j is appropriate, and the process returns to step S103, step S104, step S111 or ends the processing routine. On the other hand, when the calculated likelihood ratio ρ _j is less than or equal to the threshold ρ _th, it is determined that the weight of the sequence x _j is inappropriate, and in step S112, the time-series data processing unit 23 determines that the sequence x _j Are removed from the sequence belonging to the element N ₁ or N _2, and the HMM model parameter Θ of each element on the path for the sequence x _j from the element N ₁ or N ₂ to the uppermost element is replaced by the sequence x Update based on the sequence set with _j removed.

In step S113, the time-series data processing unit 23 selects an appropriate lower-layer element from the uppermost layer to the lowermost layer based on the likelihood for the element, as in step S103, and a sequence belonging to the selected element. The sequence x _j is reinserted and the weight w for the selected element is calculated. Further, the same processing as the processing from step S104 to step S113 is also performed.

  And it returns to the said step S103, step S104, step S111, or a processing routine is complete | finished.

  As described above, according to the data update processing device according to the first embodiment of the present invention, with respect to a plurality of hidden Markov models (HMMs) defined in a hierarchical structure for an input new sequence, Select the HMM from the top layer HMM to the bottom layer HMM, insert the input sequence into the bottom layer HMM, and divide the HMM when there is no room for a new sequence in the HMM, If an inappropriate sequence allocation occurs as a result of allocating and dividing the lower layer HMM or sequence, select the HMM from the uppermost layer HMM to the lowermost layer HMM for the sequence, and select the lowermost layer. Re-insert into HMM to reduce computation time and memory usage without accessing all sequences when a new sequence is entered Te, it is possible to update the hidden Markov model of a hierarchical structure.

  Further, it is possible to greatly reduce the calculation time and memory usage required for the data update processing of the hierarchical model, and the model can be estimated with an arbitrary granularity in a dynamic environment.

[Second Embodiment]
Next, a second embodiment will be described. In addition, about the part which becomes the structure similar to 1st Embodiment, the same code | symbol is attached | subjected and description is abbreviate | omitted.

  In the second embodiment, the first is that the model parameter is updated using the sampling result of the sequence and that the model parameter is updated using only the newly added sequence. This is different from the embodiment.

<Outline of the invention>
In the data update processing device 100 described in the first embodiment, when a division process occurs within the structure of the hierarchical model and the model needs to be re-estimated, all sequences belonging to the elements to be divided Must be used. On the other hand, the approximate data update processing device 200 shown in FIG. 2 in the second embodiment is an improvement of the data update processing device 100 of the first embodiment, and approximate time series data processing. By performing hierarchical sampling in the unit 223, calculation time for model re-estimation can be saved.

<System configuration>
As shown in FIG. 5, the approximate data update processing device 200 according to the second embodiment

The computer includes a CPU, a RAM, and a ROM that stores a program for executing a processing routine described later, and is functionally configured as follows. As shown in FIG. 5, the approximate data update processing device 200 includes an input unit 10, a processing unit 220, and an output unit 30.

  The processing unit 220 includes a time series data storage unit 21, a hierarchical model data storage unit 22, and an approximate time series data processing unit 223. The approximate time series data processing unit 223 is an example of a sequence insertion unit, an update unit, a division unit, an estimation unit, a sequence reinsertion unit, a presentation unit, and a sampling unit.

  The principle of the update processing method performed by the approximate time series data processing unit 223 in the second embodiment will be described.

<High-speed processing>
The simplest method for estimating HMM parameters is to use all past sequences managed in a hierarchical model structure. However, using all sequences is a bottleneck under streaming conditions. Therefore, in the present embodiment, the following ideas (1) and (2) are used.

(1) When division processing occurs in a hierarchical structure and a new model needs to be re-estimated, instead of using all the sequences belonging to the elements to be divided, only a part of the sequence set is used by using a sampling approach. Is used.

(2) Incremental model estimation is performed to reduce model estimation costs. Extend the EM algorithm to update the model parameters of the sequence using only new input data.

In the hierarchical model update processing routine described in the first embodiment, the insertion operation is executed every time the input sequence x _i is received. If no element split operation occurs, use x _i to update the model. When a division operation occurs, hierarchical sampling is performed before steps S107 and S108 to extract a sample set of the sequence. In step S109, the model parameters Θ ₁ and Θ ₂ of the new element are estimated using the sample set of the sequence.

<Hierarchical sampling>
In this embodiment, a sampling algorithm using a stack is proposed. First, the element N and the number of sequences required for sampling ε (for example, ε = b × b) are stored in the stack. In the sampling algorithm, a duplicate (N _p , ε _p ) is taken out of the stack at each step, the local number of samples ε _c is determined for each subelement N _c belonging to the extracted element N _p , A new duplicate (N _c , ε _c ) is stored in the stack. Here, using the number n _p of all sequences belonging to element N _p and the number n _c of sequences belonging to each sub-element N _c , whether or not the sub-element N _c is selected as a sample is a probability n _c / n _p is determined by, on the basis of the selection result for each part element, the number of samples epsilon _c is determined.

This process is performed until the lowest layer of the hierarchical structure is reached, and a final sequence sample set is obtained. Here, if the subelement N _c is not selected as a sample (ie, ε _c = 0), all subelements under N _c are pruned.

<Incremental model estimation>
Although the weighted model estimation described in the first embodiment (see the above formulas (10) to (11)) is an important elemental technique, all input sequences are used to calculate the weighted expectation value. This is not enough in a streaming situation. Therefore, in this embodiment, a new incremental model estimation method is introduced. Given a model parameter Θ representing a sequence set {x ₁ , ... x _n } and a newly added input sequence x _{n + 1} , the new model parameter ~ Θ is obtained using the following method: It can be calculated incrementally. First, in step E, instead of calculating the expected values for all data sets, the expected values are calculated only for the new input sequence x _{n + 1} . Next, in the M step, the model parameters are efficiently updated by the following equation (13).

Here, the ^{_{N γ1 = Σ n r = 1}} Σ k j = 1 γ (r) 1 (j). Similarly, ~ a _ij and ~ b _i (v) can also be updated using new expected values. Note that this incremental model estimation approaches convergence faster than existing methods. More importantly, the computational cost of the present invention has the advantage that it does not depend on the total number of sequences.

<Operation of approximate data update processing device>
Next, the operation of the approximate data update processing device 200 according to the second embodiment will be described. First, when a sequence set is input to the approximate data update processing device 200, the approximate data update processing device 200 stores the sequence set in the time-series data storage unit 21. Then, the approximate data update processing device 200 constructs a hierarchical HMM based on the sequence set and stores it in the hierarchical model data storage unit 22.

  When a new sequence is input to the approximate data update processing device 200, the approximate data update processing device 200 executes a processing routine similar to the hierarchical model update processing routine shown in FIG.

  At this time, after the dividing operation is performed by the approximate time series data processing unit 223 in step S106, a hierarchical sampling processing routine shown in FIG. 6 is executed.

First, in step S201, the approximate time-series data processing unit 223, an element N1 generated by dividing in step S106, all sequences belonging to the number epsilon (subelements subordinate elements N ₁ sequences of the sampled (N ₁ , ε) are put in the stack.

  Then, the approximate time series data processing unit 223 repeats the processing from step S202 to step S207 until the stack becomes empty.

In step S202, the approximate time-series data processing unit 223 extracts a set (N _p , ε _p ) from the stack. In the next step S203, the approximate time-series data processing unit 223, N _p is equal to or a lowermost layer of elements, when N _p is not the lowest layer of the element, all of the underlying N _p for subelements N _c, the process is repeated from step S204~ step S206.

In step S204, the approximate time-series data processing unit 223 determines the number of samples ε _c local to the subelement Nc with the probability n _c / n _p . In step S205, the approximate time-series data processing unit 223 determines whether or not the number of samples εc determined in step S204 is greater than zero. If the number of samples ε _c is larger than 0, in step S206, the set (N _c , ε _c ) is put on the stack and the process returns to step S204 or step S202, or the process proceeds to step S208 described later. .

On the other hand, if the number of samples ε _c is equal to or smaller than 0, it is determined that the subelement N _c has not been selected as a sample, and the process returns to step S204 or step S202 or shifts to step S208 described later.

Further, in step S203, when N _p is determined to be the lowest layer of the element, in step S207, the approximate time-series data processing unit 223, from a set of sequences belonging to N _p, randomly epsilon _p Samples are selected and added to all the sequence sets X _s under N _{1, and} the process returns to step S202 or shifts to step S208 described later.

In step S208, X _s is output as a sampling result of all sequence sets under N ₁ .

Further, the approximate time series data processing unit 223 similarly executes the hierarchical sampling processing routine for the element N ₂ generated by dividing in step S106.

Then, in step S107, the approximate time-series data processing unit 223, a sampling result of all sequences set under the N _1, and X _1, in the step S108, sampling of all sequences set under the N ₂ the results, and X _2. The approximate time-series data processing unit 223 similarly executes the processes after step S109.

In step S105, the approximate time series data processing unit 223 calculates an expected value only for the input sequence x _i according to the above equations (10) and (11), and the above equation (13), Similarly to the equation (13), the HMM model parameter Θ of the element N is updated according to the equations obtained by changing the equations (4) and (5).

  As described above, according to the approximate data update processing device according to the second embodiment, when updating the model parameters of the divided elements, the update is performed using the sample set of the sequence. Memory usage can be further reduced.

  In addition, for each element on the insertion path, the calculation time and memory usage can be further reduced by updating the model parameters using only the input new sequence.

<Example>
In order to show the effectiveness of the present invention, experiments using actual data were conducted. The experiment was conducted on a Linux (registered trademark) machine equipped with 4 GB of memory and an Intel (R) Core 2 Duo 1.86 GHz CPU. The estimated HMM is set to k = 20. Mocap is a motion capture dataset that measures human movements at 120 frames per second (http://mocap.cs.cmu.edu/). FIG. 7 shows a sequence of kinetic energy of the left and right feet in the motion capture data as an example, and each sequence shows a different motion (walking, squatting, jumping, balancing). Consider using a sequence set to estimate the HMM parameters for each of the four motions. However, information on these four groups is not given in advance, and the algorithm uniquely finds similar patterns from the sequence group, groups them, and estimates parameters individually for those groups. The data used in the experiment was treated as discrete data by dividing 2D data into 100 grids. The above four types of movement (walking, squatting, jumping, balancing) were used for the learning data.

  FIG. 8 shows the classification results in MoCap. The test set includes a total of 2 × 4 sequences (# 1- # 8) belonging to the above four types of motion and two sequences (# 9and # 10) belonging to running motion that are not included in the learning data. Ten pieces were used. According to the present invention, it was possible to find an appropriate model for the first eight test sets (# 1- # 8). Interestingly, the present invention also shows that squatting and jumping motions are similar. In fact, as shown in FIG. 7, both of these sequences are movements that bend both feet at the same time, and can be said to be very similar movements. Similarly, we showed that the running motion (# 9and # 10) is similar to the walking motion. In order to verify the computation time in the learning process, the present invention is compared with the conventional HHMM. Here, the following two versions of HHMM are used for comparison. One is a method using a hierarchical structure with a complete binary tree (see HHMM (b = 2) in FIG. 9), and the other is a method using a hierarchical structure with a complete quadtree (see FIG. 9). HHMM (see b = 4). Furthermore, for the present invention, two versions were compared. One is a learning method based on streaming processing according to the present invention (see HEART in FIG. 9), and the other is a learning method based on the basic idea according to the present invention (in the case where a sampling method is not used). (See HEART (offline)). In this experiment, the calculation time in the present invention includes the time due to disk access. FIG. 9 shows the calculation cost of the HHMM and the present invention. The size of the data set (ie the total length of all sequences) was varied from 1,000 to 200,000. In this experiment, the length of the sequence was fixed at m = 100. As shown in the figure, the present invention achieves a significant increase in speed compared to the prior art.

  Note that the present invention is not limited to the above-described embodiment, and various modifications and applications are possible without departing from the gist of the present invention.

  For example, time-series data is generated in various fields such as video and music distribution, bioinformatics, and robots. The present invention is applicable to all these fields.

  In the present specification, the embodiment has been described in which the program is installed in advance. However, the program can be provided by being stored in a computer-readable recording medium.

DESCRIPTION OF SYMBOLS 10 Input part 20, 220 Processing part 21 Time series data storage part 22 Hierarchical model data storage part 23 Time series data processing part 30 Output part 100 Data update processing apparatus 200 Approximate data update processing apparatus 223 Approximate time series data processing part

Claims (8)

A plurality of hidden Markov models (HMM) defined in a hierarchical structure, and a plurality of sequences belonging to at least one of the lowest HMMs and weighted to each of the lowest HMMs Storage means for storing;
For the input sequence, according to the hierarchical structure, the HMM is selected based on the likelihood for each HMM from the highest layer HMM to the lowest layer HMM, and at least one lowest layer HMM to which the input sequence belongs A sequence insertion means for inserting the inputted sequence as a sequence belonging to each of the selected lowest-layer HMMs, and obtaining a weight of the sequence for each of the selected lowest-layer HMMs; ,
If there is room for a new sequence for each HMM from the uppermost HMM selected by the sequence insertion means to the lowermost HMM, the parameter of the selected HMM is set in the input sequence. Updating means for updating based on;
For each HMM from the topmost HMM selected by the sequence insertion means to the bottommost HMM, if there is no room for a new sequence, the selected HMM is divided into two HMMs, and A dividing unit for allocating a plurality of HMMs of a layer one layer below the selected HMM or a plurality of sequences belonging to the selected HMM to two divided HMMs;
Estimating means for estimating each parameter of the two HMMs divided by the dividing means based on a subordinate sequence of the HMM assigned to the HMM or a sequence assigned to the HMM;
The two HMMs divided by the dividing means are the lowest layer HMMs, and the value based on the likelihood for the HMM of the sequence belonging to the lowest layer HMM is an inappropriate value compared to the threshold value. If determined, the sequence is deleted from the sequence belonging to the lowest layer HMM, the parameters of each HMM from the lowest layer HMM to the highest layer HMM corresponding to the sequence are updated, and the sequence According to a hierarchical structure, selecting from the top layer HMM to the bottom layer HMM based on the likelihood for each HMM, selecting at least one bottom layer HMM to which the sequence belongs, and selecting the selected As a sequence belonging to each of the lowest HMMs, the sequence is reinserted and the selected lowest And sequence reinsertion means for determining the weight of said sequence for each of the HMM layers,
A data update processing device. When the selected HMM is divided into two HMMs by the dividing unit, each of the two divided HMMs is divided into the HMM from the divided HMM to the lowest HMM according to a hierarchical structure. A sampling means for selecting by sampling the HMM of the next lower layer or the sequence belonging to the HMM;
The data update processing device according to claim 1, wherein the estimation unit estimates each parameter of the two HMMs divided by the division unit based on a sequence under the HMM selected by the sampling unit.   The update unit updates the parameter of the selected HMM based only on the input sequence when there is a space for a new sequence for each of the HMMs selected by the sequence insertion unit. Item 3. The data update processing device according to Item 1 or 2.   The sequence insertion means adds the HMMs from the top layer HMM to the bottom layer HMM for the input sequence until the total weight of the sequence for each of the selected bottom layer HMMs exceeds a threshold value. And selecting the lowest-order HMM to which the inputted sequence belongs, and repeatedly inserting the inputted sequence as a sequence belonging to each of the selected lowest-order HMMs. 4. The data update processing device according to any one of items 3.   The determination that there is no free space for a new sequence when a total value of weights assigned to all sequences under the HMM is equal to or greater than a threshold value as a result of inserting the input sequence. The data update processing device according to any one of claims 1 to 4.   Presentation that presents each parameter of the predetermined number of HMMs based on the parameters of each of the plurality of HMMs defined in a hierarchical structure stored in the storage means when the predetermined number of HMMs are requested 6. The data update processing device according to claim 1, further comprising means. A plurality of hidden Markov models (HMM) defined in a hierarchical structure, and a plurality of sequences belonging to at least one of the lowest HMMs and weighted to each of the lowest HMMs A data update processing method in a data update processing apparatus including storage means for storing, sequence insertion means, update means, division means, estimation means, and sequence reinsertion means,
The sequence insertion means selects the HMM based on the likelihood for each HMM from the top layer HMM to the bottom layer HMM according to the hierarchical structure of the sequence input by the sequence insertion means, and at least the input sequence belongs to Select one lowermost HMM, insert the input sequence as a sequence belonging to each of the selected lowermost HMMs, and weight the sequence for each of the selected lowermost HMMs Seeking
If there is a free space for a new sequence for each HMM from the uppermost layer HMM selected by the sequence insertion unit to the lowermost layer HMM by the update unit, the parameter of the selected HMM is Update based on the sequence entered,
If there is no free space for a new sequence for each HMM from the uppermost layer HMM selected by the sequence insertion unit to the lowermost layer HMM by the dividing unit, the selected HMM is converted into two HMMs. And allocating a plurality of HMMs one layer below that belong to the selected HMM or a plurality of sequences belonging to the selected HMM to the two divided HMMs,
The estimation means estimates the parameters of each of the two HMMs divided by the dividing means based on a sequence under the HMM assigned to the HMM or a sequence assigned to the HMM,
The two HMMs divided by the dividing means by the sequence reinsertion means are the lowest HMMs, and a value based on the likelihood for the HMM of a sequence belonging to the lowest HMM is compared with a threshold value. If it is determined to be an inappropriate value, the sequence is deleted from the sequence belonging to the lowermost layer HMM, and parameters of each HMM from the lowermost layer HMM to the uppermost layer HMM corresponding to the sequence are deleted. And, for the sequence, according to the hierarchical structure, select the HMM based on the likelihood for each HMM, from the top HMM to the bottom HMM, and at least one bottom HMM to which the sequence belongs And select the sequence as a sequence belonging to each of the selected lowermost HMMs. Is inserted, data updating processing method for determining the weight of said sequence for each of the lowermost HMM said selected.   The program for functioning a computer as each means of the data update processing apparatus of any one of Claims 1-6.