TWI521361B - Method for multi-layer classifier - Google Patents

Description

Multi-level classification method

The present invention relates to a multi-level classification method, and more particularly to a classification method suitable for establishing a multi-layer discriminant analysis model and determining attribute selection and tangent points.

The classification method is very versatile. For example, in the financial industry, when the bank audits credit card users, it can discern whether the applicant will easily become a bad debt; in medical science, it can judge whether the cell organization is normal or abnormal; In marketing research, it can be judged whether such marketing methods can attract customers to purchase goods. Therefore, in the field of data mining, the possession and important part is to explore the classification method.

The classification method is a supervised learning method. The so-called supervised learning method performs data exploration in the case of knowing the target output value, and vice versa is called unsupervised learning, such as principal component analysis. (Principal component analysis) is a method of unsupervised learning. In the classification method, it is generally necessary to select an appropriate attribute to establish a classification model. For example, height and weight are used to judge whether the person is a boy or a girl, and height and weight are called attributes. When creating a classification model, the data is often divided into two groups. One group is training samples, the other group is independent test samples, and the training samples are used to establish a classification model. The independent test samples are Used to verify that this classification model is robust.

At present, two existing classification methods are common, namely Fisher linear discriminant analysis (FLD), and Classification and regression trees (CART), which are common in multivariate statistical analysis. However, the inventor of the present invention found that, based on the foregoing classification method, especially in the selection of attributes, some attributes can only discriminate specific categories and affect the accuracy of their classification application; and in the establishment of the previous classification model, due to its attributes The choices are different, or the discriminant analysis model of the desired classification is not evaluated for effectiveness, which in turn affects the accuracy of the classification.

Therefore, there is a need for a new multi-level classification method to solve the above problems.

The main object of the present invention is to provide a multi-level classification method. By using a multi-layer discriminant analysis model, one or two tangent points are searched for each layer to classify one or two categories, and each layer can use multiple layers at the same time. Attributes, and through Fisher Discriminant Analysis to find the best linear combination of these attributes.

The present invention provides a multi-level classification method for classifying a plurality of image samples in a computer recordable medium. The computer recordable medium includes a processor, an input device, and a storage device. The method includes at least:

(a) receiving a plurality of original samples;

(b) providing a plurality of attributes and performing a significant evaluation of the attributes of the original samples with a multivariate parameter;

(c) selecting at least all points and establishing a discriminant analysis model, which is one of the significant ones after the evaluation in step (b), and filtering out at least all of the points by providing a variable homogeneity analysis parameter. The plurality of original sample groups included in the saliency after the evaluation are at least one category to establish the discriminant analysis model, wherein the at least one category includes the first category (Node _A ) and the second category (Node _B ) And the third category that has not been decided (Node _N );

(d) performing a step of evaluating the performance of the model by adding such attributes to the discriminant analysis model for significant evaluation; wherein, when the attributes are added to enhance the significance of the discriminant analysis model, Discriminate the layer below the analysis model, and then filter out at least all the points by using the variable homogeneity analysis parameters. The plurality of original samples included in the discriminant analysis model added to the attributes are considered to be the first group. Category (Node _A ), second category (Node _B ), and undetermined third category (Node _N );

(e) adding a stop condition, which is to select the variable homogeneity analysis parameter. If the null hypothesis is not rejected, the discriminant analysis model stops the next layer grouping; or add these attributes in the step of evaluating the model performance. The saliency evaluation is performed by a regression analysis method. When the saliency of the discriminant analysis model cannot be improved after adding these attributes, if the null hypothesis is rejected, the discriminant analysis model stops the next layer grouping.

The invention also provides a computer recordable medium for classifying a plurality of image samples, which is to classify the image samples by establishing a multi-level classification method.

According to the multi-level classification method of the present invention, when the stop condition is added, in the last layer classification layer of the discriminant analysis model, the number of samples included in the undetermined third category (Node _N ) is zero, in other words In other words, the final result of the multi-level classification method according to the present invention must classify a plurality of original samples into a first category (Node _A ) and/or a second category (Node _B ).

According to the multi-level classification method of the present invention, the selection of the multi-variable parameters is not limited, and is preferably Wilk's lambda or Gini index; the selection of such attributes is not limited, and preferably at least one selected from the group consisting of ringPDVImax, VeinCentralVImin, VeinTDCentralVImax, TDVImax, A group consisting of CI, RMV, CI2, MCI3, and MI2. Further, there is no limitation on the selection of the variable homogeneity analysis parameters, and it is preferably Gini index, Mahalanobis distance, or Youden's Index.

On the other hand, for the significance evaluation, the p-value calculated by a F statistic is used, and the p value is used to indicate the average difference of the attributes among the categories; or one is used to measure the impurity ( The criterion of impurity; wherein the F statistic is

This impureness is

Where n is the sample size, p is the number of attributes, and Λ is Wilk's lambda; where N _L is the sample space of the first category, N _M is the sample space of the third category, and N _R is the second The sample space of the category, t _L is the Gini value of the first category, t _M is the Gini value of the third category, and t _R is the Gini value of the second category.

According to the multi-level classification method of the present invention, the step of evaluating the performance of the model may include the following four methods: adding such attributes to the same layer of the discriminant analysis model established in the step (c) to increase the discriminant analysis model The ability to distinguish in the same layer; add these attributes to the third category (Node _N ) and add a layer to create a model. This model also filters out at least everything from the homogeneity analysis parameters. The plurality of original samples determined to continue to be grouped into a first category (Node _A ), a second category (Node _B ), and an undetermined third category (Node _N ); the first category (Node _A ) is set to be undecided a category, and add a layer to the combination formed by the first category (Node _A ) plus the undetermined third category (Node _N ) to create a model. This model also uses this variable homogeneity analysis. The parameter filters out at least all points, and continues to group the remaining undetermined plurality of original samples into a first category (Node _A ), a second category (Node _B ), and an undetermined third category (Node _N ); or the second category (Node _B) is not set Prescribed category and a second category (Node _B) plus a third category of undetermined composition (Node _N) formed by adding a layer of such properties, and to create a new model, which is also variable in this analysis homogenous The parameter filters out at least all points, and continues to group the remaining undetermined plural original samples into a first category (Node _A ), a second category (Node _B ), and an undetermined third category (Node _N ).

As can be seen from the above, the present invention provides a new discriminant analysis model structure and method thereof, which is similar to a tree-like classification structure in that data is segmented from top to bottom. Different from the tree structure, each layer of the discriminant analysis model will classify some data for one or two categories, and leave the undetermined data to the next layer. In addition, each layer can select some attributes and utilize Fisher's discriminant analysis makes a linear combination.

In other words, the present invention uses the above method to establish a new multi-layer discriminant analysis model, each layer of which may only distinguish one category (Node _A or Node _B ) or both categories (Node _A and Node _B ). And leave the sample of the undetermined category (Node _N ) to the next layer for discrimination. The discriminant model analysis includes: the method of selecting the effective variable of each layer in the discriminant model and the method and criterion for finding the tangent point, and the step of evaluating the performance of the model will consider the overall performance to determine how to construct the model when adding the new attribute. And establish a stop condition to avoid excessive fit.

Therefore, according to the present invention, an attribute selection and a cut point determination method are also provided, and the discriminant analysis model considers the performance of the overall model when adding a new attribute, so as to determine how the discriminant analysis model should be established and its stopping condition, thereby greatly improving the classification. Accuracy.

2 is a schematic diagram showing the architecture of a computer recordable medium, which can be used to perform a multi-level classification method of the multi-layer discriminant analysis model of the present invention.

As shown in FIG. 2, the computer recordable medium 1 includes a display device 13, a processor 12, a memory 11, an input device 14, a storage device 15, and the like. The input device 14 can be used to input image, text, instructions and the like to the computer recordable medium. The storage device 15 is, for example, a hard disk, a CD player or a remote database connected through the Internet for storing the system program. The application 11 and the user data are used to temporarily store data or execute programs, the processor 12 is used to calculate and process data, and the display device 13 is used to display the output data.

The computer recordable media shown in FIG. 2 generally executes various applications, such as a word processing program, a drawing program, a scientific computing program, a browsing program, an email program, etc., under the operating system (Operating System). In the present embodiment, the storage device 14 stores a program for causing the computer recordable medium to perform a multi-level classification method. When the computer recordable medium is to perform this sorting method, the corresponding program is loaded into the memory 11 to cooperate with the processor 12 to execute the method. Finally, the related data of the classification result is displayed on the display device 13 or stored in a remote database through the Internet.

By means of the method of the present invention, the flow diagram can be as shown in FIG. 1a, and the multi-layer discriminant analysis model architecture established according to the present invention is as shown in FIG. 1b, which is similar to the classification tree in that the data is divided from top to bottom. However, unlike the classification tree, the multi-level classification method of this case will judge some or all of the original samples for each layer, and these identified categories (Node _A ) or Node _B ) will not. Will enter the next layer of the model, leaving only the level determined in this layer as the undetermined category (Node _N ) to add a new attribute to the next layer to discriminate it, and each layer can only be judged for one category or two For each category, you only need to find a cut point to cut the sample into two parts, one part can be classified at this level, and the other part is undecided and must be left to the next level, but if you want to judge two categories Then you need to find two tangent points, cut the data into three parts, one part is the first category (Node _A ), one part is the second category (Node _B ), and the remaining part is the undetermined third category (Node _N) ). And each time you want to add a new attribute, you will consider the performance of the overall model to decide to combine the new attributes in the original layer to make the original layer better judgment or to add a new attribute to those that have not yet The classified samples are classified. New properties are continually added to this model until the model reaches the stop condition.

Hereinafter, the multi-level classification method of the present invention and the established multi-layer discriminant analysis model architecture will be described in detail.

First, a plurality of original samples are accepted. For the plurality of original samples, an attribute must be selected from a plurality of attributes, and a multivariate parameter is used to perform a significant evaluation on the original samples. The evaluation of this significance is to provide at least one point by providing a variable homogeneity analysis parameter, and the attributes are evaluated to be significant, and then the point is used to determine which category the sample in the model belongs to (Node _A , Node _B or Node _N ) or to stay on the next layer, the better choice is the most significant after evaluation. From this we can see that it is very important to select attributes and determine these cut points. After that, the step of evaluating the performance of the model is performed on the discriminant analysis model established above, that is, by adding more attributes to the model and comparing the two models, which may include adding one to the original discriminant analysis model. The attributes are combined using Fisher linear discriminant analysis (FLD), and the other is a new layer of model.

[Attribute and multivariate parameter selection]

In the selection of attributes, ringPDVImax, VeinCentralVImin, VeinTDCentralVImax, TDVImax, CI, RMV, CI2, MCI3, and MI2 can be used; and there are two criteria for selecting multivariable parameters. One is Wilk’s lambda, which is common in multivariate statistical methods to determine whether there is a difference in the average between categories, and the other is to evaluate the purity of the Gini index on the classification tree.

Wilk’s lambda

Suppose there are g categories, p attributes, and x _k ~ N _p (μ _k , Σ), k =1, 2,..., g

Among them, H ₀ is a null hypothesis, H ₁ is an alternative hypothesis, and μ _k is the average of the class K.

Where W is the intra-group variation matrix

B is the variation matrix between groups

I system unit matrix (identity matrix)

λ _i is the eigenvalue of W ^-1 B

When H ₀ is true, Λ will obey F allocation after some conversion (Equation 2)

when When s =1, m ₁ = p , m ₂ = n - p -1, the statistic F can be simplified

Wilk’s lambda can also be converted to chi-squared

When there are few categories, the F statistic will be better than the chi-square statistic. Since the multi-layer discriminant analysis is preferably for two categories, we use the F statistic.

The present invention can compare the p-values calculated by using the aforementioned F statistic for each attribute. The smaller the p-value is, the more significant the difference between the averages of the attributes is. The p-value of each attribute is selected to be the most Significant attributes. If you want to select a new attribute in the same layer, compare the p value obtained by combining the new attribute with the original attribute, and select the variable with the smallest p value combined with the original attribute.

Gini Index

Since each time a segment is searched for a better or better attribute and a cut point, there is a segmentation criterion to evaluate the performance of this attribute and the cut point. The more common criterion is the Gini index. The Gini index is a measure of impurity, so the smaller the Gini index, the better. Each attribute is assigned a corresponding tangent to get its Gini index, so each attribute can search for an optimal corresponding point. When making a variable selection, you can select the best attribute and cut point in this segment by comparing the Gini index of each attribute with its corresponding optimal cut point.

Assuming there are now g categories, the Gini Index is defined as:

Impurity is:

Where P ( i | t ) is the proportion of category i at node t

P ( j | t ) is the proportion of category j at node t

n _L is the number of samples of the left node

n _R is the number of samples on the right node

N= n _R + n _L is the sum of all samples

Here, the multi-layer discriminant analysis model of the present invention differs from the classification tree in that the classification tree is binary-divided at each node, but in the multi-layer discriminant analysis model of the present invention, each layer must divide the data. Into two nodes, so the calculation of impureness should be changed to

The present invention can compare the purity obtained after each attribute is matched with its optimal set of cut points, and select an attribute with the least purity.

If you want to add new attributes on the same layer, you can use the new attribute and the difference score obtained by the original attribute through FLD to calculate the impurity, and find the attribute with the lowest purity after combining with the original attribute.

[cut point selection]

There are three ways to select the tangent points, namely Gini index, Mahalanobis distance, or Youden’s Index.

Gini Index

When using Gini index to select attributes, each attribute must select a set of tangent points to match to obtain its impureness, so a method is needed to select the best set of tangent points to match to get the lowest impurity, if it is in the classification tree. In that, just look for a tangent point, so the way to find the tangent point in the classification tree is to try all possible cut points and find a cut point with the lowest purity. However, in the multi-layer discriminant analysis model of the present invention, for example, it is necessary to obtain two tangent points to divide the data into three groups. In this case, it is assumed that there are N samples, and it is only necessary to test N kinds of possibilities to find a tangent point. There are N ( N -1)/2 possibilities for the tangent point. When the number of samples is large, it is very slow to find all the possible tangent points to find two tangent points. Therefore, the present invention solves the aforementioned problems and Develop a quick way to find two cut points.

First, like a general classification tree, first search for all the cut points that have the lowest purity after dividing all the data into two groups, C ₀ , and then use C ₀ to cut the data into Node _L and Node _R. In Node _L , search for a point that can be used to divide Node _L into two groups with the lowest purity, C ₁ . Similarly, in Node _R , we also search for a tangent point that can minimize the purity of Node _R into two groups, C ₂ , as shown in Figure 3.

In this way, three candidate cut points C ₀ , C ₁ , and C ₂ can be obtained, and the three candidate cut points can be used to form ( C ₀ , C ₁ ), ( C ₁ , C ₂ ) and ( C ₀ , C ₂ ). Three combinations of tangent points, compare the three types of tangent points to cut the data into three groups of impurities, select an optimal combination of tangent points, preferably to place samples of high homogeneity on the left and right sides. Therefore, when searching for C ₁ , the limit is set. In the two groups of data cut out by C ₁ , the data of the group farther away from C ₀ is higher than the other group. For the same reason, the same restrictions should be set when searching for C ₂ . That is, Gini ( t _LL )< Gini ( t _LR ), Gini ( t _RR )< Gini ( t _RL ). If you use this search algorithm, you only need to search about 2N times to find those three candidate cut points, and then compare the three combinations.

Mahalanobis distance

Another method of choice according to the present invention is the Mahalanobis distance, which differs from the Euclidean distance in that the Mahalanobis distance considers not only the difference in the center point between the categories, but also the dispersion of each category. For example, if there is a sample distance A category is the same as the center of the B category, if the A category has a large number of variances, the distribution is more scattered, the B category has a smaller number of variances, and the distribution is very concentrated. The Mahalanobis distance from the A category is smaller than the Mahalanobis distance from the B category, so it is considered that the comparison belongs to the A category.

The method of applying the Mahalanobis distance to the classification will be described in detail below. First, if there are two categories, the Mahalanobis distance of the distance A category can be calculated as: , and the Mahalanobis distance from the B category is: , where μ _A = (μ _{A 1} , μ _{A 2} , ... μ _Ap ) is the average of the class A, S _A is the covariance matrix of the class A, μ _B = (μ _{B 1} , μ _{B 2} ,...μ _Bp ) is the average of the B categories, S _B is the covariance matrix of the B categories; when D _A ( x )< D _B ( x ) belongs to the A category, and D _A ( x )> D _B ( x ) belongs to category B.

However, in the multi-layer discriminant analysis model of the present invention, the present invention divides a plurality of samples into three groups of A, B (Node _A , Node _B ) and undetermined (Node _N ), so that the original D _A ( x ) < D _B ( x ), the number of samples belonging to the A category is selected, and then a new μ _{A 1} , μ _{B 1} , S _{A 1} , S _{B 1 is} calculated using these samples which have been judged as the A category, and then these have been A sample determined to be in the A category is recalculated with a new average and the number of variances:

If D _{A 1} ( x )< D _{B 1} ( x ), it belongs to category A; and D _{A 1} ( x )> D _{B 1} ( x ), it is undecided.

Similarly, the original D _A ( x )> D _B ( x ), the number of samples belonging to the B category is selected, and then a sample of the original B class is used to calculate a new μ _{A 2} , μ _{B 2} , S _{A 2} , S _{B 2} , and then calculate the Mahalanobis distance by using the new average and the variance for the samples that have been judged as the B category.

If D _{A 2} ( x )> D _{B 2} ( x ), it belongs to the B category, and D _{A 2} ( x )< D _{B 2} ( x ) belongs to the undetermined.

It should be noted that, when the Mahalanobis distance finding point is used in the multi-layer discriminant analysis model of the present invention, the two data sub-collections are mainly used to divide the data into the categories belonging to the category A and the categories belonging to the category B. To find the cut point we want, but when the two sub-collections of data are as shown in Figure 4a, because the choice of its nodes will affect the accuracy of non-classification, in order to improve the situation, the difference in the number of samples is extremely large. The distance from the tangent point is unreliable, and the Gini index can be further used to correct the Mahalanobis distance, as shown in Figure 4b. First, use the Gini index to find a tangent point, then use the tangent point to divide the data into two sides, and compare the proportion of each category on the two sides. If the proportion of the A category on the left side is larger than the ratio on the right side, then the right side is used. The A category is removed, otherwise the A category of the left material is removed. Similarly, the B category also compares its proportion on the left and right sides, and removes the B category with a smaller proportion. Then use the remaining A categories, B categories to recalculate the average and the variance, and get a Markov distance corrected by Gini index.

Youden’s Index

First, define Youdee's Index=specificity+sensitivity-1, where specificity is the correct proportion of all A-category samples in the provided plurality of original samples, and the sensitivity is in all B-category samples in the plurality of original samples provided. Determine the correct ratio, so the higher the Youden's index, the better.

The method of searching for the pointcut is similar to using the Gini index. First search for all the possible cut points that divide the all the data into two groups and the highest cut point of the Younde's Index, C ₀ , and then use C ₀ to cut the data into Node _L and Node _R. In Node _L , search for a tangent point, C ₁ , that can divide the Node _L into two groups and the highest Younde's Index. Similarly, in Node _R , you also search for a tangent point, C ₂ , that can divide the Node _R into two groups and the highest Younde's Index. In this way, we can get three candidate cut points C ₀ , C ₁ , and C ₂ , which can be composed of ( C ₀ , C ₁ ), ( C ₁ , C ₂ ) and ( C ₀ , C ₂ ) Three kinds of tangent point combinations, compare these three types of tangent points to cut the data into three groups of Youden's Index, and choose an optimal cut point combination.

When divided into three groups, the calculation of specificity and sensitivity is to be changed because there are undetermined parts.

Specificity=(A category judges the number of samples +0.5* is not discriminated as the number of samples in the A category)/A total number of samples in the A category;

Sensitivity=(the number of samples in the B category is +0.5* the number of samples in the B category is not discriminated)/the total number of samples in the B category;

Then, select the set of cut points with the highest Youden’s index among the three sets of cut points.

[Evaluation Model Effectiveness]

In the multi-layer discriminant analysis model, each time an attribute is added to the model, the evaluation steps can be performed in the following four different schemes.

First, as shown in FIG. 5, it is assumed by the model layer have been formed of X _1, X ₁ and using the put sample into three groups, namely, Class A, B categories, and undecided samples, respectively, Node _A, Node _B , Node _N to indicate.

plan 1:

In the original layer, the new attribute X _{i is} added, and the X _{1 is} combined with the FLD to increase the difference of the original layer.

Scenario 2:

Add a property X _{1 to the} Node _N to build a model, and use this model to distinguish the samples that are not distinguishable in the original layer.

Option 3:

The Node _{A and} Node _N samples are merged and represented by Node _AN . At this time, the original X ₁ model is only used to distinguish the B category, and the attribute X _k is added to the Node _AN to build a model. To distinguish between samples that are not distinguishable in the original layer.

Option 4:

The Node _{B and} Node _N samples are merged and represented by Node _BN . At this time, the original model of X ₁ is only used to distinguish the A category, and the attribute X _p is added to the Node _BN to build a model. To distinguish between samples that are not distinguishable in the original layer.

[stop condition]

In the stopping condition of the multi-layer discriminant analysis model of the present invention, it can be divided into two types, one is to decide whether to continue to divide the undetermined sample, and the other is to decide whether to add a new attribute to the existing layer.

In deciding whether to continue to divide the undecided sample into the next division, you can use the Wilk's lambda mentioned in the attribute selection. If you do not reject the null hypothesis, it means that in the remaining samples, you can not find the significant difference between the categories. Separate the attributes, so stop continuing to split down.

As mentioned above, another stop condition is to decide whether to add a new attribute to the original layer. Since the model already has some significant attributes, if you want to add a new attribute, the whole thing to consider is not to add the new attribute. The model is not significant enough, but rather considers how much variation is additionally explained by the newly added attributes. Here, reference can be made to the partial F-test used in the forward selection method in the regression analysis method, which is to verify that the model newly added to an attribute has no significant difference from the original model. If the null hypothesis is rejected, the model that added the new attribute has no significant improvement, and this attribute is not added to the model. Its verification model is (Equation 6)

Where df _F is the degree of freedom of the full model; df _R is the degree of freedom of the reduce model; df _R β ₀ , β ₁ , β ₂ are the parameters of the variable; df _R SSR is the expansive sum of square And df _R SSE is the e residual sum of square.

In the forward selection method of discriminant analysis, the model is (Equation 7)

If you reject the null hypothesis, it means that the model does not need to join this new attribute.

If the new attribute added is significant enough, the performance of the model before and after the addition is compared using the method of evaluating the performance of the model. Conversely, if you can't improve the performance of the overall model after adding new attributes, stop adding new attributes. It should be noted that the multi-level classification method of the present invention and the established multi-layer discriminant analysis model architecture are forced to classify all the data in the last layer of the model, and no undetermined samples can be left.

According to the foregoing parameters and setting conditions, a detailed flow chart for establishing a multi-layer discriminant analysis model according to the method of the present invention is shown in FIG. 6.

First, after accepting a plurality of original samples (not shown), Wilk's lambda or Gini index is used to select a most significant attribute, and then it is checked whether the attribute has a significant difference in the ability of each category. If the null hypothesis is rejected, it means that this attribute has explanatory power. Reuse the Markov distance or Gini index as described above to find the best set of tangent points for this attribute, and divide the data into the first category (A category, Node _A ), and the second category (B category, Node _B ) and not determined. The third category (Node _N ) is a group of data, and then the performance of the model can be evaluated based on the three groups of data.

Then, when selecting the second attribute, consider where to add the second attribute. In the four scenarios mentioned above, respectively: (Scenario 1) In the original layer, find one with the original The best attributes and tangent points after the combination of variables; (Scheme 2) Find the most suitable attribute and cut point with the original undetermined sample; (Scheme 3) Treat the A category as undecided, and add the undetermined A category. The sample is to find the most suitable attribute and tangent point; and (Scheme 4) to consider the B category as undecided, and use the B category plus undetermined samples to find the most suitable attribute and cut point.

After each option is selected, Wilk’a lambda is used to verify its significance. If the scheme is not significant enough, the attribute is discarded, and then the performance of each model is evaluated by the steps mentioned above. If the performance of the scheme 1 is the best, the new attribute is added to the original layer. If the performance of scenario 2 is the best, a new layer of model is created using the remaining undetermined samples from the previous layer. If the best for scenario 3 or scenario 4 is to consider the class A or class B as undecided in the previous layer, and create a new layer model with all the remaining undetermined samples, and the model of the previous layer is converted into only one point. To judge the A category or the B category, the two categories are not judged at the same level.

If the current model already has n layers, when adding a new attribute, adding the new attribute to the original layer will have n cases, plus schemes 2, 3, and 4, a total of n+3 will be considered. Kind of situation. If the new variables in this n+3 case are not significant, the model will stop. If there is a plan to pass, select the best-performing solution and check whether the overall model of the plan has been improved by selecting one attribute. If there is no improvement, stop adding new variables. If there is improvement, continue to add new attributes to the model, and continue to add variables until the model performance is no longer improved.

In summary, the present invention provides a systematic variable selection method for a multi-layer discriminant analysis model, which can be selected by converting Wilk's lambda into F-assigned p-value or Gini index. In the decision of the cut point, methods such as Mahalanobis distance and Gini index are also provided. When determining the tangent point with the Gini index, it is very time consuming to search for all possible tangent point combinations since it is necessary to find at least all points. Therefore, the present invention also provides a method for quickly searching for the desired tangent point. When using Markov distance to determine this at least all points, we will first use the Mahalanobis distance to divide all samples into A-class and B-classes, and then use the two sets of samples to find two Markov distance cut points, but because First, the data is divided into two groups by Mahalanobis. The difference in the number of samples between the two groups is usually very large, and the difference in the number of samples between the categories will cause the Mahalanobis distance to find the tangent point unreliable, so the present invention provides Use the Gini index to correct the Mahalanobis distance to solve this problem. Each time a new attribute is added to the model, not only the performance of one layer is considered, but the performance of the overall model is considered before deciding where to add the new attribute. In the stop condition of the model, the use of Wilk’s lambda is also provided to prevent over-adaptation of the model, thus greatly improving the accuracy of the classification.

[Example 1]

In this embodiment, a data of 100, 2 categories, 5 attributes (X ₁ , X ₂ , ..., X ₅ ) is provided, wherein each attribute obeys N(0, 1), its category The scatter plot is shown in Figure 7b, and its default model is shown in Figure 7a. Among them, the first layer will be explained by X ₁ , and the unclassified part will be left to the next layer to explain to X ₂ .

The results obtained by the multi-layer discriminant analysis are shown in Fig. 7c. Since the multi-layer discriminant analysis model uses the Gini index and the Mahalanobis distance to find the tangent point, the two methods are put on the results of the multi-layer discriminant analysis. . As for the results obtained via CART, it is as shown in Figure 7d. Multi-level discriminant analysis using Cini index to find points can be compared with CART, which is the same as the criteria for finding tangent points.

In the multilayer discriminant analysis, the separation of the first layer category 1 and category 0, Type 0 0 contains 24 categories with Category 1 and 0 X _1, Class 1 contains three categories category 0 and 35 1. However, as shown in Figure 7d, in CART, category _{1 is} divided by X ₁ in the first layer, including 3 categories 0 and 35 categories 1 , and the second layer is assigned category 1 by X ₂ . Contains 24 categories 0 and 0 categories 1, so the results are the same for both methods. However, the structure of the multi-level discriminant analysis will use the ability to distinguish between two categories (category 0 and category 1) in one layer, but in CART, only one category can be identified in one layer, and the same layer can be used in the next layer. One attribute identifies another category.

The results of the various methods are presented in Table 1. As can be seen from Table 1, the results obtained using the Gini index for multi-layer discriminant analysis are as good as CART.

[Embodiment 2]

In the present embodiment, a data of 200, 2 categories, 10 attributes (X ₁ , X ₂ , ..., X ₁₀ ) is provided, wherein each attribute obeys N(0, 1). The default model is shown in Figure 8a. Among them, the first layer will be selected into X ₁ and X _{2 will be} combined into one FLD model. Those those whose first layer cannot be classified will be left to the second layer to be explained by the FLD model of X ₃ and X ₄ combination.

The results obtained by multi-layer discriminant analysis are shown in Figure 8b, and the results obtained by CART are shown in Figure 8c.

The results of the method according to the present embodiment are presented in Table 2. This multi-level discriminant analysis is better than CART and FLD, regardless of whether the Gini index or the Mahalanobis distance is used to find the cut point.

[Example 3]

In the present embodiment, a data of 1000, 2 categories, 5 attributes (X ₁ , X ₂ , ..., X ₅ ) is provided, wherein each attribute obeys N(0, 1), its category The scatter plot is shown in Figure 9b, and the default model is shown in Figure 9a. The first layer will be explained by X ₁ , and X ₁ has only the ability to classify category 0, and the remaining unclassifiable parts are left to the next layer for X ₂ to explain.

The results obtained by multi-layer discriminant analysis are shown in Figure 9c, and the results obtained by CART are shown in Figure 9d. Since the preset model can be regarded as a univariate tree structure, in this case, the multi-level discriminant analysis uses the Gini index when the result of the tangent point criterion is the same as that obtained by CART.

The results of the method according to the present embodiment are presented in Table 3. The results obtained by the multi-level discriminant analysis using the Gini index are as good as the CART.

[Example 4]

In the present embodiment, a data of 1000, 2 categories, 5 attributes (X ₁ , X ₂ , ..., X ₅ ) is provided, wherein each attribute obeys N(0, 1). The default model is shown in Figure 10a. The first layer will be explained by X ₁ , and X ₁ has only the ability to classify category 0, and the remaining unclassifiable parts are left to the next layer to explain X ₂ and X ₃ .

The results obtained by the multi-layer discriminant analysis are shown in Fig. 10b, and the results obtained by CART are shown in Fig. 10c.

The results of the method according to the present embodiment are presented in Table 4, and the results obtained by the multi-dimensional discriminant analysis using the Gini index are the best.

[Example 5]

In this embodiment, the quantitative properties of some tumor images are obtained by ultrasonic scanning, and then a discriminant model is constructed through these attributes, wherein there are 160 tumor image samples, 108 are represented by category 0, and 52 are Category 1 represents.

Firstly, the five attributes of CI, EI, MI, HI, and ringPDVImax are provided for analysis. If the five attributes are directly combined using Fisher's discriminant analysis, the accuracy rate is 0.793, and the accuracy of using multi-level discriminant analysis is 0.8. In addition, multi-level discriminant analysis uses only four of these variables, as shown in Figure 11a, and the accuracy obtained is higher than the traditional Fisher discriminant analysis.

In addition to the above five attributes, other attributes can be added together for analysis according to this embodiment. Multilayer discriminant analysis using Gini index to determine the tangent results is shown in Figure 11b, with an accuracy of 0.906. Multi-layer discriminant analysis using the Youden's index legal cut-off results is shown in Figure 11c, with an accuracy of 0.8012. The results obtained by CART are shown in Figure 11d with an accuracy of 0.868. FLD uses the nine attributes of ringPDVImax, VeinCentralVImin, VeinTDCentralVImax, TDVImax, CI, RMV, CI2, MCI3, and MI2, and the accuracy is 0.843. As shown in Table 5, the multi-layer discriminant analysis yields the best accuracy.

Furthermore, the above-mentioned execution steps of the present invention can be written in a computer language for execution, and the written software program can be stored in any recording medium that can be recognized and interpreted by the micro processing unit, or an article and device containing the recording medium. It is not limited to any form, and the article can be a hard disk, a floppy disk, a compact disc, a ZIP, an MO, an IC chip, a random access memory (RAM), or any other person familiar with the art. Media items. Since the multi-level classification method of the present invention has been disclosed as before, anyone who is familiar with the computer language knows how to write a software program after reading the specification of the present invention, so the details of the software program are not described here.

The above-mentioned embodiments are merely examples for convenience of description, and the scope of the claims is intended to be limited to the above embodiments.

1‧‧‧Computer recordable media

11‧‧‧ memory

12‧‧‧ Processor

13‧‧‧Display device

14‧‧‧ Input device

15‧‧‧Storage device

Figure 1a is a flow chart of the multilayer discriminant analysis of the present invention.

Figure 1b is a schematic diagram of a multi-layer discriminant analysis model architecture established in accordance with the method of the present invention.

2 is a schematic diagram showing the architecture of a computer recordable medium.

FIG. 3 is a schematic diagram of a search Gini index cut point according to a preferred embodiment of the present invention.

4a-4b are schematic diagrams of correcting Mahalanobis distance using Gini index in accordance with a preferred embodiment of the present invention.

Figure 5 is a schematic illustration of four modes of a comparative model of the present invention.

Figure 6 is a detailed flow chart of the multi-layer discriminant analysis model of the present invention.

7a-7d are schematic views of Embodiment 1 of the present invention.

8a-8c are schematic views of Embodiment 2 of the present invention.

9a-9d are schematic views of Embodiment 3 of the present invention.

10a-10c are schematic views of Embodiment 4 of the present invention.

11a-11d are schematic views of Embodiment 5 of the present invention.

(The figure is a flow chart, so there is no component symbol)

Claims (22)

A multi-level classification method for classifying a plurality of image samples in a computer recordable medium, the computer recordable medium comprising a processor, an input device, and a storage device, the method comprising at least the following steps: (a Receiving a plurality of original samples; (b) providing a plurality of attributes, and performing a significant evaluation of the original samples from the attributes by a multivariate parameter; (c) selecting at least all points and establishing a discriminant analysis model, It is one of the significant ones after the evaluation in the step (b), and the at least one point is selected by providing a variable homogeneity analysis parameter, and the plurality of points included in the attribute are evaluated after the attribute is evaluated. The original samples are grouped into at least one category in this layer to establish the discriminant analysis model, wherein the at least one category includes a first category (Node _A ), a second category (Node _B ), and an undetermined third category ( Node _N); (d) performing a step of evaluating the effectiveness of the model, which is added to the system in the plurality of discriminant analysis model assessment significant attributes; wherein, when there is added to the at least one property enhancing When significant discriminant analysis model, the third category of undecided (Node _N) of the plurality of original sample will enter the discriminant analysis model under layer, then the homogeneous analysis parameter variable at least all selected points, the determination The plurality of original samples included in the analytic model after adding the attributes to the analysis model are then grouped into a first category (Node _A ), a second category (Node _B ), and an undetermined third category (Node). _And (e) adding a stop condition for selecting the variable homogeneity analysis parameter, and if the null hypothesis is not rejected, the discriminant analysis model stops the next layer grouping; or in the step of evaluating the performance of the model Adding these attributes to the saliency analysis by a regression analysis method, when the attributes are added, the saliency of the discriminant analysis model cannot be improved. If the null hypothesis is rejected, the discriminant analysis model stops the next layer grouping. The multi-level classification method according to claim 1, wherein when the stop condition is added, in the last layer classification layer of the discriminant analysis model, the undetermined third category (Node _N ) is included The number of samples is zero. The multi-level classification method according to claim 1, wherein the multivariate parameter is Wilk’s lambda or Gini index. The multi-level classification method as described in claim 1, wherein the significance evaluation calculation is a p-value calculated by a F-statistic, and the p-value indicates an average significance of the differences between the categories; or Judging by a measure of impureness; wherein the F statistic is The impureness is Where n is the sample size, p is the number of attributes, and Λ is Wilk's lambda; where N _L is the sample space of the first category, N _M is the sample space of the third category, and N _R is the second The sample space of the category, t _L is the Gini value of the first category, t _M is the Gini value of the third category, and t _R is the Gini value of the second category. The multi-level classification method according to claim 1, wherein the attributes are at least one selected from the group consisting of ringPDVImax, VeinCentralVImin, VeinTDCentralVImax, TDVImax, CI, RMV, CI2, MCI3, and MI2. The multi-level classification method according to claim 1, wherein the variable homogeneity analysis parameter is Gini index, Mahalanobis distance, or Youden’s Index. The multi-level classification method according to claim 1, wherein the step of evaluating the performance of the model comprises: adding the attributes to the same layer of the discriminant analysis model established in step (c) to increase the discrimination Analyze the difference in the original layer of the model. The multi-level classification method according to claim 1, wherein the step of evaluating the performance of the model comprises: adding the attributes to the third category (Node _N ) and adding a layer to establish a model, the model At least all the points are also filtered by the variable homogeneity analysis parameter, and the remaining undetermined plurality of original samples are further grouped into a first category (Node _A ), a second category (Node _B ), and an undetermined third category ( Node _N ). The multi-level classification method as described in claim 1, wherein the step of evaluating the performance of the model comprises: setting the first category (Node _A ) to an undetermined category, and adding the first category (Node _A ) Adding the at least one attribute to the combination formed by the undetermined third category (Node _N ) and adding a layer to establish a model, the model also filters at least all points with the variable homogeneity analysis parameter, and the remaining undetermined The plurality of original samples continue to be grouped into a first category (Node _A ), a second category (Node _B ), and an undetermined third category (Node _N ). The multi-level classification method described in claim 1, wherein the step of evaluating the performance of the model comprises: setting the second category (Node _B ) to an undetermined category, and adding the second category (Node _B ) Adding these attributes to the combination formed by the undetermined third category (Node _N ) and adding a layer to establish a model, the model also filters out at least all points with the variable homogeneity analysis parameters, and the remaining undetermined The plurality of original samples continue to be grouped into a first category (Node _A ), a second category (Node _B ), and an undetermined third category (Node _N ). The multi-level classification method described in claim 1, wherein the regression analysis method comprises a partial F-test used by the forward selection method. A non-transitory computer recordable medium for classifying a plurality of image samples, wherein the image samples are classified by establishing a multi-level classification method, the multi-level classification method comprising at least the following steps: (a) receiving a plurality of image samples (b) providing a plurality of attributes, and performing a significant evaluation of the original samples from the attributes by a multivariate parameter; (c) selecting at least all points and establishing a discriminant analysis model, One of the significant ones after the evaluation in step (b) is to screen out the at least all points by providing a variable homogeneity analysis parameter, and the plurality of original samples included in the attribute are evaluated after the attribute is evaluated. Grouping into at least one category in a layer to establish the discriminant analysis model, wherein the at least one category comprises a first category (Node _A ), a second category (Node _B ), and an undetermined third category (Node _N ); (d) performing a step of evaluating the performance of the model by adding the attributes to the discriminant analysis model for significant evaluation; wherein, when the attributes are added, the discriminant analysis model is enhanced Sexual, a third category of undecided (Node _N) of the plurality of original sample will enter the discriminant analysis model under layer, then the homogeneous analysis parameter variable at least all selected points, the discriminant analysis is added to the model The plurality of original samples included in the saliency after the attribute evaluation are then grouped into a first category (Node _A ), a second category (Node _B ), and an undetermined third category (Node _N ); and e) adding a stop condition, which is to select the variable homogeneity analysis parameter, if the null hypothesis is not rejected, the discriminant analysis model stops the next layer grouping; or add the attributes in the step of evaluating the model performance A regression analysis performs a significant evaluation. When the saliency of the discriminant analysis model cannot be improved after adding these attributes, if the null hypothesis is rejected, the discriminant analysis model stops the next layer grouping. The computer recordable medium according to claim 12, wherein, when the stop condition is added, in the last layer classification layer of the discriminant analysis model, the undetermined third category (Node _N ) is included The number of samples is zero. The computer recordable medium of claim 12, wherein the multivariate parameter is Wilk’s lambda or Gini index. The computer-recordable medium according to claim 12, wherein the significance evaluation calculation is a p-value calculated by a F statistic, and the p-value indicates an average difference of the attributes among the categories; or Judging by a measure of impureness; wherein the F statistic is The impureness is Where n is the sample size, p is the number of attributes, and Λ is Wilk's lambda; where N _L is the sample space of the first category, N _M is the sample space of the third category, and N _R is the second The sample space of the category, t _L is the Gini value of the first category, t _M is the Gini value of the third category, and t _R is the Gini value of the second category. The computer recordable medium of claim 12, wherein the attributes are at least one selected from the group consisting of ringPDVImax, VeinCentralVImin, VeinTDCentralVImax, TDVImax, CI, RMV, CI2, MCI3, and MI2. The computer recordable medium according to claim 12, wherein the variable homogeneity analysis parameter is Gini index, Mahalanobis distance, or Youden’s Index. The computer recordable medium according to claim 12, wherein the step of evaluating the performance of the model comprises: adding the attributes to the same layer of the discriminant analysis model established in step (c) to increase the discrimination. Analyze the difference in the original layer of the model. The computer recordable medium according to claim 12, wherein the step of evaluating the performance of the model comprises: adding the attributes to the third category (Node _N ) and adding a layer to establish a model, the model At least all the points are also filtered by the variable homogeneity analysis parameter, and the remaining undetermined plurality of original samples are further grouped into a first category (Node _A ), a second category (Node _B ), and an undetermined third category ( Node _N ). The computer recordable medium according to claim 12, wherein the step of evaluating the performance of the model comprises: setting the first category (Node _A ) to an undetermined category, and adding the first category (Node _A ) Adding these attributes to the combination formed by the undetermined third category (Node _N ) and adding a layer to establish a model, the model also filters out at least all points with the variable homogeneity analysis parameters, and the remaining undetermined The plurality of original samples continue to be grouped into a first category (Node _A ), a second category (Node _B ), and an undetermined third category (Node _N ). The computer recordable medium according to claim 12, wherein the step of evaluating the performance of the model comprises: setting the second category (Node _B ) to an undetermined category, and adding the second category (Node _B ) Adding these attributes to the combination formed by the undetermined third category (Node _N ) and adding a layer to establish a model, the model also filters out at least all points with the variable homogeneity analysis parameters, and the remaining undetermined The plurality of original samples continue to be grouped into a first category (Node _A ), a second category (Node _B ), and an undetermined third category (Node _N ). The computer recordable medium according to claim 12, wherein the regression analysis method comprises a partial F-test used by the forward selection method.