JPH10260988A - Clustering method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To hierarchically classify many examples by inputting an example set that consists of observation values of plural observation items as an initial example set and sequentially dividing an example set into two so that the reduction of fluctuation in example sets may become maximum. SOLUTION: An initial example set is inputted as a first input data (step S1), and an example set is inputted as confirmation processing of an end condition (step S2). Here, when the number of examples of the initial example set is not less than a previously defined number K (step S2A) and when observation values that do not coincide among examples of the initial example set are included (step S2B), an optimum observation item and a division threshold are calculated from an inputted example set (step S3). When the value of the optimum observation item of each inputted example is larger than the division threshold, it is classified to a group 1. When it is not, it is classified to a group 2 (step S4) and a tree diagram is generated (step S5A).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a clustering method belonging to a hierarchical classification method.

More specifically, the present invention is suitable for information processing such as voice recognition processing or information search processing.
It relates to a clustering method.

[0003]

2. Description of the Related Art Clustering is one of statistical classification methods, and is widely used in research requiring classification such as social science and biology. On the other hand, it is widely used in industry, mainly in the information processing field such as a speech recognition device and an information retrieval device.

There are various clustering techniques. The summary is detailed in "Statistics Dictionary" (Hiroshi Takenaka, Toyo Keizai Shimpo), etc., but it is roughly divided as follows.

[0005] The first is a method called a division classification method, which divides a set of cases (a classification target is referred to as a case) into subsets without overlapping.

The second is a method called a hierarchical classification method, which classifies a set of cases into upper and lower layers.

[0007] Among these classification methods, a conventional representative hierarchical classification method is an agglomerative clustering method. In this cohesive clustering method, the data used for input is
It is the table which measured the observation value of the observation item about each case. For example, Table 1 shown below is a table in which observation values of two observation items are measured for each of six cases.

[0008]

[Table 1]

Using such a table 1, a hierarchical classification of cases is created in the following procedure.

[0010] 1. The similarity between cases is calculated based on the table of observation values. In this case, ₆ C ₂ = 15 distances are obtained.

2. The following operation is repeated until the number of clusters becomes one.

3. Merge the two clusters (or cases) with the minimum distance to create a new cluster.

4. Recalculate the distance between clusters (or cases).

[0014]

However, in the above-described conventional representative hierarchical classification method, the number of distances between cases obviously increases almost in proportion to the square of the number of cases. That is, when the number of cases is N, the number of storage areas (devices) for storing distances increases in proportion to N ² .

For this reason, when the number of cases increases, there is a problem that the storage area for storing the distance is insufficient, and it becomes difficult to execute clustering. In addition, since the number of calculations for finding the minimum distance increases, there is also a problem that a long execution time is required.

In order to avoid such a problem, techniques such as limiting the number of target cases or combining with a non-hierarchical technique have been employed.

Accordingly, an object of the present invention is to provide
An object of the present invention is to provide a clustering method capable of classifying a large number of cases hierarchically without using a conventionally employed method.

[0018]

In order to achieve the above object, in the clustering method according to the present invention, a case set including observation values of a plurality of observation items is input as an initial case set, and a variation in the case set is input. The case set is sequentially divided into two so that the decrease is maximized.

Here, by compressing the storage area necessary for storing the observation values to form the case set, the storage area required for processing can be reduced.

Further, by arranging the observation items in descending order of the value of variation in the initial case set, it is possible to reduce the required number of operations. Similarly,
It is also possible to reduce the number of operations by dividing the frequency between the observation values into two.

[0021]

In DETAILED DESCRIPTION OF THE INVENTION The clustering method detailed below Summary embodiment, based on a table of observations case, sequentially bisects case set to maximize the reduction of fluctuations in the case set We use the technique of doing.

Here, it is also possible to compress the table of observation values to reduce the storage area required for processing.

In the above method, the number of calculations can be reduced by arranging the observation items in descending order of the value of the variation of the initial case set.

Further, in the above method, it is also possible to reduce the number of calculations by dividing the frequency between observation values into two.

In other words, the clustering method according to the present invention has the following features.

Sequential bisection: First, a set of cases is made into one cluster. Next, this is sequentially divided into two. In other words, the reverse method is used in which the conventional aggregation method merges the cases and finally creates one cluster.

No use of distance: The distance between cases is not used. In the clustering method to which the present invention is applied, clustering of cases is performed based on data of observed values of cases. Now, assuming that the number of cases is N and the number of observation items is M, the required size of the storage area is proportional to N × M.
In a general clustering problem, M can be regarded as a small constant, and is therefore proportional to N.

For this reason, the storage area required conventionally is greatly reduced, and the time required for processing is also greatly reduced.

Explain the characteristics of clusters: The hierarchy obtained by executing the clustering method according to the present invention is a binary tree. The root node of the binary tree is the largest cluster covering the entire case set. A case set is stored in the leaf node. Each node inside corresponds to an observation item, from which two branches emerge downward. Each case is classified under the left branch if the observed value of the observation item corresponding to the node exceeds the threshold, and otherwise classified under the right branch.

By this feature, the reason why the case set is classified into a certain cluster can be known by tracing the binary tree from the root to the case. That is, it is possible to know the magnitude of the frequency of the observation item appearing on the way.
Such a feature is not present in the conventional cohesive clustering method, but is unique to the clustering method to which the present invention is applied.

Hereinafter, such a clustering method will be specifically described.

Embodiment 1 First, the structure of input data required for the processing of the present clustering method, and words and mathematical expressions used for the processing of the present clustering method will be described.

(1) Case Set Data input to a clustering apparatus (see FIG. 1) for executing the present clustering method is data representing a set of cases. Here, the case includes observation values of a plurality of observation items. Observed values are numerical values.

Table 1 shown in the section of the prior art shows an example of a case set. In Table 1, there are six examples,
To f are given. In addition, there are two observation items, and numbers 1 and 2 are given respectively.

Hereinafter, this table is input as an initial case set to a clustering apparatus (to be described in detail later with reference to FIG. 1), and the present clustering method is executed.

(2) Array type memory Two types of reference are made to the elements of the array in the text.

The j-th element of the array type memory A is represented by A [j]
To refer to. It is a reference to one element. Since an array is a set of elements, the terms array and set are used interchangeably below.

From the s-th element of the array A to the e-th element (s ≦
The elements up to e) are referred to by A [s, e]. That is,
Subset reference.

The sequence A

[0040]

[Outside 1]

Is represented by

The number of elements of the array A [s, e] is | A [s,
e] |.

(3) Observation Value Set Assume that the observation item i of the case set has n observation values. This set of observation values is stored in an n-dimensional array (memory).
This array is represented by X ⁽ⁱ⁾ . The suffix (i) above indicates that this array is for item (i).

According to the promise in the previous section, all observation values of the observation item i are X ⁽ⁱ⁾ [1, n].

In the case of Table 1

[0046]

[Outside 2]

Is as follows.

(4) Variation of Observed Value Set Assume that an observed value set X ⁽ⁱ⁾ [1, n] is given. The variation of this set of observations is calculated by the following equation.

[0049]

(Equation 1)

If the set of observations is clustered around the mean, the variation will be small. That is, the fluctuation is an indicator of the degree of unity of the observation value set.

For example, when the fluctuations of the observation items 1 and 2 in Table 1 are calculated, the following is obtained. First, for observation item 1, t (X ⁽¹⁾ [1,6]) = (1-2) ² × 2 + (2-
2) ² × 2 + (3-2) ² × 2 = 4

On the other hand, the average value of the observation values of observation item 2 is 2, and t (X ⁽²⁾ [1,6]) = (1-2) ² × 3 +
(3-2) ² × 3 = 6. That is, it can be seen that the observation value set of observation item 2 is less organized.

(5) Observation Value Set Bisection It is assumed that an observation value set X ⁽ⁱ⁾ [1, n] is given. Dividing this array by the p-th element indicates the following operation.

First, the elements of X ⁽ⁱ⁾ [1, n] are rearranged in ascending order. That is, the array X ⁽ⁱ⁾ [1, n] is arranged in ascending order.

Next, X ⁽ⁱ⁾ [1, n] is changed to X ⁽ⁱ⁾ [1, p].
And X ⁽ⁱ⁾ [p + 1, n] (1 ≦ p <n).

For example, X ⁽¹⁾ [1,6] = {1,1,
The result of the bisection with the second element of 2,2,3,3｝
X ⁽¹⁾ [1,2] = {1,1}, X ⁽¹⁾ [3,6] =
{2,2,3,3} are obtained.

X ⁽²⁾ [1,6] = {1,1,1,
As a result of bisecting by the third element of 3,3,3｝, X
⁽²⁾ [1,3] = {1,1,1}, X ⁽²⁾ [4,6] =
Get {3,3,3} (note that the elements are arranged in ascending order).

(6) Reduction of Fluctuation Observation value set X ⁽ⁱ⁾ [1, n] is converted to X ⁽ⁱ⁾ [1, p] and X
⁽ⁱ⁾ Divide into two [p + 1, n]. For this result,
t (X ⁽ⁱ⁾ [1, n]) (variation of the observed value set before division), t (X ⁽ⁱ⁾ [1, p]) (variation of the divided subset 1), t (X ^{(i )} [P + 1, n]) (variation of the divided subset 2) can be calculated.

Using these, the fluctuation reduction b (X ⁽ⁱ⁾ [1, n], p) occurring in the two divisions by p can be calculated by the following equation.

[0060]

(Equation 2)

It is shown that the smaller the fluctuation, the better the unity of the two subsets obtained by the division.

[0062] (7) The variation reduced calculus observations set ^{X (i) [1, n} ] of the variation reduction of all possible two-piece ^{b (X (i) [1} , n], p) (1 ≦ A method for efficiently finding p <n) will be described.

Equation (2) is obtained by subtracting the variation of the subset from the total variation of the set. According to statistics (for example, Haruo Yanai et al. "Multivariate Analysis Handbook"
7), which is consistent with the variation between subsets. That is,

[0064]

(Equation 3)

Is as follows.

In equation (3),

[0067]

[Outside 3]

It is only necessary to calculate once at first.
Also,

[0069]

[Outside 4]

Can be efficiently calculated using the recurrence formula shown below. Since the observation item i is clear, the suffix (i) is omitted.

[0071]

(Equation 4)

Next, a hardware configuration for executing the present clustering method will be described with reference to FIG. In FIG. 1, an input device 2 inputs an initial case set. Numeral 4 denotes an arithmetic unit which executes the clustering method according to the processing procedure shown in FIG. Reference numeral 6 denotes a ROM which stores the flowchart shown in FIG. 2 in the form of a program. A RAM 8 is used as a work area in addition to the array type memory. Reference numeral 10 denotes an output device for outputting a calculation result.

Next, processing steps in the present clustering method will be described with reference to the flowchart shown in FIG.

(1) Step S1 (Input Process of Initial Case Set) Here, the initial case set illustrated in Table 1 is input as the first input data.

(2) Step S2 (End Condition Confirmation Process) In this step, a set of cases is input. First, an initial case set, that is, Table 1 is input via step S1. The processing in step S2 includes step S2A and step S2B as described below.

If the number of cases in the initial case set is not less than a predetermined number (represented by K; here, K = 2) (step S2A), the process proceeds to the next step S2B.

Next, when there is a case where the observed values do not match between the cases in the initial case set (step S2).
B), and proceed to the next step S3.

As described above, there are six cases in the initial case set (Table 1). In addition, since the values in Table 1 do not match, the process proceeds to the next processing step S3.

The input case set is passed to the processing step S3.

When the initial case set is equal to or less than a predetermined number K, or when all the observation values match among the cases in the initial case set, that is, when the initial case set cannot be further divided. In this case, all the processes are terminated.

(3) Step S3 (Optimal Observation Item Selection Processing) The number of cases received is n. That is, all observation items have n observation values. Here, the following processing is performed.

1. The following processing is performed for each observation item i.

2. X ⁽ⁱ⁾ Rearrange the elements of [1, n] in ascending order of value.

3. Perform all possible bisections of X ⁽ⁱ⁾ [1, n] and reduce the variation b (X ⁽ⁱ⁾ [1,
n], p) is recorded (1 ≦ p <n).

[0085] From the results reported, we obtain the observation item i _b and the division point p _b to provide maximum fluctuation decreases. These are called optimal observation items and optimal division points.

Further,

[0087]

[Outside 5]

Is calculated.

The next stage, “Case set processing step S
4 ”includes: 1. Input case set Optimal observation items 3. Pass the split threshold.

The operation of this processing step when Table 1 is input is as follows. Here, the fluctuation reduction obtained in all the two divisions of the observation items 1 and 2 is as shown in Table 2 below.

[0091]

[Table 2]

The way of reading Table 2 is as follows. The variation reduction of the split into two by the p = third element of the observation item 2 is 6.0. The meaning is as follows.

That is, the observation value set X ⁽²⁾ [1,6] of the observation item 2 in Table 1 is arranged in ascending order, and {1,1,1,3,
Create 3,3｝. When the second division is performed using the third element of this set, {1,1,1} and {3,3,3} are obtained. From this, the fluctuation b ([X ⁽²⁾ [1, 6],
3]) = 6.0 is obtained.

Further, it can be seen from Table 2 that the maximum variation was reduced in this case. As a result, six input cases, observation item number 2 and division threshold 2 (that is, a value calculated by (1 + 3) / 2) are passed to the next “case set division processing step S4”.

(4) Step S4 (case set division processing) The case set, the optimum observation item, and the division threshold are received from the previous step, and the following processing is performed.

When the value of the optimal observation item of each input case is
If it is larger than the division threshold, it is classified into group 1. Otherwise, it is classified into group 2. The two case sets are passed to the next processing step.

The current case set is Table 1 itself. When this is divided into two groups using the optimum observation item 2 and its division threshold value 2, the following table 3 and table 4 are obtained. These Tables 3 and 4 are passed to the next processing step.

[0098]

[Table 3]

[0099]

[Table 4]

(5) Step S5 (Process for creating a tree diagram)
Here, the following processing is executed.

1. A node is created (a node corresponding to the case set before being divided into two), and two branches are generated below the node (step S5A). Below the left branch, a case set of group 1 is associated. A case set of group 2 is associated below the right branch.

2. The process from step S2 to step S5 (the portion surrounded by the dashed line in FIG. 2) is recursively executed using the case set belonging to group 1 (step S5B).

3. The processing from step S2 to step S5 (portion surrounded by the dashed line in FIG. 2) is recursively executed using the case set belonging to group 2 (step S5C).

In step S2, if the number of cases to be subjected to each recursive process is equal to or less than a predetermined number K (step S2A), or if each observation value is different between the cases to be subjected to each recursive process. If all match (step S
In 2B), no further division is possible, so the recursive processing ends, and the process proceeds to the next step.

This will be described with an actual example. When the initial case set of Table 1 is used, Step S5 includes Tables 3 and 4
Is input. Then, a tree diagram 1 shown in FIG. 3 is obtained.

Next, in step S2, a recursive process using the case shown in Table 3, that is, {b, e, f} as group 1, is started.

In this case set, the optimal observation item is 1, the optimal division point is 1, and the division threshold is 2. By using this to divide into two, {e, f}, {b} are obtained, and a tree diagram 2 shown in FIG. 4 is obtained.

Next, recursive processing (step S5B) is started again with {e, f} as group 1, but the number of cases is 2
Since ≦ 2, this recursive processing is terminated (step S2A),
Proceed to the next step. That is, the next recursive processing (step S5C) is performed with {b} as group 2, but since the number of cases is 1 ≦ 2, this recursive processing is terminated. Thus, the recursive processing using {b, e, f} as group 1 (step S5B) is completed.

Next, recursive processing (step S5C) is performed with {a, c, d} as group 2. As a result of the same processing as before, a tree diagram 3 shown in FIG. 5 is obtained. This stops the entire process.

(Effects of First Embodiment) As described above, according to the first embodiment, a tree diagram for classifying cases can be obtained. Moreover, there is no need to perform an operation for obtaining a distance matrix from the case set. As described above, when the number of cases is N, the size of the distance matrix is N ² .

On the other hand, the size of the storage area required in the first embodiment is N × M, where M is the number of observation items. Generally, since M << N, the first embodiment requires a smaller storage device. In addition, since the processing is performed in a smaller storage device, the execution time is shortened.

Further, the characteristics of each cluster can be explicitly known from FIG. For example, the cluster having the case {e, f} indicates that the observation item 2 has a frequency of 2 or more and the observation item 1
Is more than 2 ".

The above is the description of the first embodiment.

The processing procedure described above for the other embodiments is effective when (a) the same value hardly appears in the observation value of a certain observation item, and (b) the number of observation items is smaller than the number of cases. . However, in the case of an observation value that does not satisfy the above properties, it is more efficient to use the following method (Table 1 shows the same value, so processing is performed by the method described below). Is more efficient).

The following is a specific example of a method considering the clustering problem of a document set as such an example.

One method of clustering a document set by applying the present invention is as follows. Investigate different words in the whole document set. Then, these words are used as observation items, and their appearance frequencies are used as observation values. For example, when such a table is created for a certain news article set, the following table 5 is obtained.

[0117]

[Table 5]

The following can be seen from Table 5.

(A) The number of observation items (words) becomes enormous, and the table becomes enormous.

(B) The majority of observed values (frequency) are 0, the next is 1, the next is 2 and so on.

Further, in the case of data having such properties,
I _b and p _b giving the maximum b (X ⁽ⁱ⁾ [1, n], p) in “optimal observation item selection processing step S3” described above.
There are the following problems to ask for.

The problem α . As the number of observation items i increases, the number of evaluations of the two divisions increases accordingly, and the processing time increases.

The problem β . For an observation item i

[0124]

[Outside 6]

However, there is much waste. For example, the observation value of the observation item "airplane" in Table 5 (targets the visible area, and the same applies to the following)

[0126]

[Outside 7]

[0127] Three divisions are required. However, all that is required is an evaluation of the bisection between 0 and 1. This evaluation is useless, since a bisection between 0 and 0 does not give the maximum variation reduction.

The following specifically describes a method for solving the problem that the table becomes enormous and the two problems that occur in the two-partitioning.

Embodiment 2 As described above, the table of cases created based on language data (for example, Table 5) becomes huge. However, since the portion having the frequency of 0 occupies the majority, the compression can be performed significantly.

That is, in each case (article), a word whose frequency is not 0 and only the frequency are stored in a storage device (referred to as a word frequency list table). In addition, a list of all words (observation items) is created. Table 6 below shows a word frequency list table corresponding to Table 5.

[0131]

[Table 6]

A list of all words corresponding to Table 6 is {airplane, president, treaty}. Observation item numbers follow the order of this word list. "President" is the second observation item.

The two divisions are performed focusing on a certain word. What is needed is the frequency of occurrence of the word in each article.
This can be determined immediately if there is a word frequency list table and an all word list. That is, if the word frequency list table and the all word list are used, processing equivalent to that of Table 5 can be realized without using a huge table.

(Effects of the Second Embodiment) As described above, according to the present embodiment, an enormous table is not used, and the processing therefor becomes unnecessary.

Embodiment 3 When the number of observation items i increases, the number of two-part evaluations in the “optimal observation item selection processing step S3” increases, and the processing time increases. Here, a method of finding the optimal observation item and the division point only by evaluating the two divisions for only a part i will be described. In other words, a method that does not evaluate useless observation items will be described. This utilizes the nature of "fluctuations".

First, the basic characteristics related to the fluctuation reduction will be described. Observation set X consisting of n elements
⁽ⁱ⁾ Consider [1, n]. The variation of this set of observations is t
(X ⁽ⁱ⁾ [1, n]). X at any point p
⁽ⁱ⁾ Dividing [1, n] reduces fluctuation b (X
⁽ⁱ⁾ [1, n], p) occurs. It is known that there is a relationship represented by equation (7) between them (for example, the above-mentioned “Multivariate Analysis Handbook”).

[0137]

(Equation 5)

This inequality indicates that there is a non-negative fluctuation decrease when the set is divided, and that the maximum value of the fluctuation decrease is the fluctuation of the original set at most.

Here, the initial case set X ⁽ⁱ⁾ [1, N],
It is assumed that (1 ≦ i ≦ M) and (n ≦ N) are given. The observation items of this set are rearranged in descending order of the variation t (X ⁽ⁱ⁾ [1, N]). That is, the following relationship is established.

[0140]

(Equation 6)

"Optimal observation item selection processing step S3"
Then, the optimal division points are obtained in order from the first observation item rearranged. Here, it can be proved that the following rules hold.

As a result of dividing the observation value set X ⁽ⁱ⁾ [1, n] into two,

[0143]

[Outside 8]

It is assumed that if

[0145]

(Equation 7)

If the condition is satisfied, it is not necessary to evaluate the observation items after (i + 1) in two. The optimal observation items obtained up to that point and the optimal division point are the solutions to be found.

[0147]

(Equation 8)

It is sufficient to show that the following holds.

Since equation (7) holds,

[0150]

[Outside 9]

[0151]

[0152]

(Equation 9)

Is established. Observation items are arranged in order of size

[0154]

(Equation 10)

Is as follows. if

[0156]

[Equation 11]

If the following holds,

[0158]

(Equation 12)

As a result, the theme was proved.

This will be described with a specific example. According to the above-described calculation of “fluctuation of observation value set”, the fluctuation of observation item 1 in Table 1 is 4 and the fluctuation of observation item 2 is 6.
When the observation items are rearranged in descending order of fluctuation, the order becomes 2,1.

Next, the optimum bisecting of each observation item is calculated. First, the optimum two-partitioning of the observation item 2 and its fluctuation reduction are obtained. It can be seen from Table 2 that p = 3 is 6.0. Incidentally, the fluctuation decrease 6.0 is larger than the fluctuation 4 of the next observation item 1. That is, the conditions of the above rule are satisfied. Therefore, it is not necessary to evaluate the observation item 1 in two parts, and the calculation can be greatly reduced.

The operation of "optimal observation item selection processing step S3" using the above method is as follows. First,
It is premised that the variation of the observation items in the initial case set is calculated, and the observation items are arranged in descending order of the variation.

1. The following processing is performed for each observation item i.

[0164] 2. X ⁽ⁱ⁾ Rearrange the elements of [1, n] in ascending order of value.

[0165] 3. Perform all possible bisections of X ⁽ⁱ⁾ [1, n],

[0166]

[Outside 10]

Is recorded.

4. if

[0169]

[Outside 11]

If it is, the process ends.

[0171] from the solution, and the observation item i _b which gives the maximum variation reduction, obtaining the optimal dividing point p _b.

Further,

[0173]

[Outside 12]

Is calculated.

The data to be passed to the next processing step is the same as in the case of the above-mentioned "processing step S3 for the optimum observation item".

Embodiment 4 Here, a method for solving the above-mentioned two-partition problem β will be described.

As described above, the division into two for a certain observation item may be performed at different frequencies. For this purpose, it is convenient to store the observation value set for each frequency, instead of storing it in an array as it is. Hereinafter, a method for realizing the above will be described.

It is assumed that a certain observation item i has k ⁽ⁱ⁾ kinds of frequencies. This is added to the array f ⁽ⁱ⁾ [j],
(1 ≦ j ≦ k ⁽ⁱ⁾ ). For example, from Table 5, the word "President (i = 2)" has three frequencies, 0, 1, and 2. Therefore, f ⁽²⁾ [1] = 0, f ⁽²⁾ [2] = 1,
f ⁽²⁾ [3] = 2.

Next, a list of observation value sets having the j-th frequency is stored in the array element E ⁽ⁱ⁾ [j]. For example, if the word is “President” (i = 2), the elements having 0, which is the first frequency, are enumerated and E ⁽²⁾ [1] = {0,
0 °. Similarly, E ⁽²⁾ [2] = {1}, E
⁽²⁾ [3] = {2}. In the following, since it is clear that attention is paid to the word i, the suffix (i) is omitted.

Since E [j] contains a list of observation value sets, E is an array of arrays. Therefore, the element reference method is different from the above-described “array type memory”. The changes are described below.

(A) | E [j] | indicates the number of elements in the set stored in the array E [j].

(B) E [s, e] is obtained from the array E [s] by E
Represents the union of each set of observations up to [e].

(C) The average of the elements of E is calculated according to the following equation.

[0184]

(Equation 13)

Next, the division into two using the frequency will be described. The set of all observations for observation item i is changed to X as before.
[1, n]. This matches E [1, k].
The bisection by the p-th frequency of the observation set E [1, k] is
Divided into E [1, p] and E [p + 1, k] (1 ≦ p <k)
It is to be.

Further, the fluctuation reduction caused by the two divisions can be calculated as follows.

[0187]

[Equation 14]

Based on the above data and calculation formula, the frequency can be divided into two. In this case, the processing of the “optimal observation item selection processing step S3” is as follows.

1. The following processing is performed for each observation item i.

2. X ⁽ⁱ⁾ [1, n] data is stored in the array memory E ⁽ⁱ⁾ [1, k ⁽ⁱ⁾ ].

[0191] 3. E ⁽ⁱ⁾ Performs all possible bisections of [1, k ⁽ⁱ⁾ ] and then reduces the variation b (E
⁽ⁱ⁾ [1, k ⁽ⁱ⁾ ], p) is recorded (1 ≦ p <k
⁽ⁱ⁾ ).

Find i _b and p _b that give the maximum fluctuation reduction. Also

[0193]

[Outside 13]

Is obtained. The data to be passed to the next process is the same as in step S3.

In this method, since the two divisions are evaluated between different frequencies, the number of evaluations is greatly reduced if the number of types of frequencies is small. In the case of Table 1 shown first, there are few types of frequencies.
For example, for the observation item 2 in this table, only one evaluation between 1 and 3 is required. On the other hand, the previous method requires five evaluations.

In addition,

[0197]

[Outside 14]

Can be efficiently calculated by the following recurrence formula.

[0199]

(Equation 15)

(Effects of Embodiments 3 and 4) The arrangement of observation items in Embodiment 3 is effective when the observation items in the initial case set vary greatly.

The two divisions between frequencies in Embodiment 4 are as follows:
This is effective when the same frequency appears many times.

Further, since language data has both properties, processing efficiency can be greatly improved by applying both methods.

[0203]

As described above, according to the present invention, it is possible to realize a clustering method having the ability to classify a large number of cases in a hierarchical manner, without using a conventionally employed method. As a result, according to the present invention, when a set of cases is given, these can be clustered at high speed in the form of a tree diagram.

That is, in the conventional clustering method, it is necessary to temporarily convert a case set into a distance matrix between cases, but according to the present invention, this is not necessary. Therefore, clustering can be performed with a smaller memory.

Furthermore, a method for improving the processing efficiency peculiar to the present invention can be adopted depending on the nature of the frequency in the case set. The method according to the present invention is particularly effective in clustering data with a large number of observation items and sparse data in which most of the observation values are zero. Typical data that corresponds to this is, for example, language data that is important in application.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a hardware configuration for implementing the present invention.

FIG. 2 is a flowchart illustrating an example of an embodiment of the present invention.

FIG. 3 is an explanatory diagram showing an example of a tree diagram obtained as a result of the processing according to FIG. 2;

FIG. 4 is an explanatory diagram showing an example of a tree diagram obtained as a result of the processing according to FIG. 2;

FIG. 5 is an explanatory diagram showing an example of a tree diagram obtained as a result of the processing according to FIG. 2;

Claims (4)

[Claims] 1. A case set consisting of observation values of a plurality of observation items is input as an initial case set, and the case set is divided into two successively so that the variation in the case set is maximized. Clustering method to use. 2. The clustering method according to claim 1, wherein the case set is formed by compressing a storage area necessary for storing the observation value. 3. The clustering method according to claim 1, wherein the observation items are arranged in descending order of a variation value in the initial case set. 4. The clustering method according to claim 1, wherein the frequency of the observed value is divided into two.