TWI839813B - Electronic computing device for verifying user identity, update method of discriminant model thereof and computer program product - Google Patents

Abstract

An electronic computing device for verifying user identity, an update method of a discriminant model thereof, and a computer program product are disclosed herein. The electronic computing device simplifies the previously training data set according to a clustering-based pooling algorithm and add new training data into the previously training data set, and thereby produce an updated training data set. In addition, the electronic computing device also executes the updated discriminant model to identify whether a user is a legitimate user according to at least one piece of behavior data corresponding to the behavior characteristics of the user.

Description

Electronic computing device for verifying user identity, updating method of its discrimination model and computer program product

The present disclosure relates to an electronic computing device that uses a discriminant model to verify the identity of a user, a method for updating the discriminant model, and a computer program product. More specifically, the present disclosure relates to an electronic computing device that updates a training data set based on a clustering pooling strategy to retrain the discriminant model, a method for updating the discriminant model, and a computer program product.

In the current mode of verifying the identity of users in order to maintain the information security of electronic computing devices, there is already a two-stage verification mode. In the first stage, a verification mode based on information such as biometrics, character passwords, sliding graphics, etc. can be performed on the user to identify the initial legitimacy of the user. However, because the information required by the user to provide in the first stage of verification may be stolen and misused, the second stage can further attempt to identify the identity of the user based on the behavioral characteristics of the user when actually operating the electronic computing device, and determine whether the requirements are met. The verification mode of the second stage can be, for example, the user identification mode described in the Republic of China Patent No. I512550 (the invention name is "Method and module for identifying users of mobile devices, computer program product").

The second stage of verification can be achieved by training a discriminant model based on a machine learning framework with existing operation data of a specific user (for example, a user who should be considered legal or illegal), so that the discriminant model can be used to make judgments on future user behavior feature data. However, even the same user may have different operation behaviors in different usage scenarios, so as time goes by, the user's behavior feature data will gradually become chaotic and unreliable. Since the discriminant model cannot adapt to changes in the user's usage behavior, this will cause the error rate of the discriminant model to gradually increase. Therefore, it is obviously necessary to re-train the discriminant model.

Theoretically, in order to make the discrimination model adapt to the user's behavioral changes, all the characteristic data of the user during the use of the electronic computing device should be used as training data for retraining. However, this will not only greatly increase the time required for training, but also consume a lot of computing resources of the electronic computing device. However, if the training data is directly reduced for this reason, the discrimination accuracy of the retrained discrimination model will be reduced. In view of the above situation, how to quickly retrain the model to cope with the changes in the user's operating behavior while maintaining the discrimination accuracy is indeed a technical problem that needs to be solved in this field.

In order to at least solve the above problems, the present invention provides an electronic computing device for verifying user identity. The electronic computing device may include a memory and a processor electrically connected to the memory. The memory may be used to store a discrimination model and a training data set, wherein the training data set includes a plurality of training data. The processor may be used to run the discrimination model to determine whether a user is a legitimate user based on at least one piece of behavioral data. The at least one piece of behavioral data may correspond to the behavioral characteristics of the user. In addition, the processor can also be used to simplify an original training data set according to a clustering-based pooling algorithm, and add a plurality of new training data to the original training data set to generate the training data set, and train an original discriminant model with the training data set to generate the discriminant model.

In order to at least solve the above problems, the present invention also provides a method for updating a discriminant model. The discriminant model can be used to verify the identity of a user of an electronic computing device. The method may include the following steps: The electronic computing device simplifies an original training data set according to a pooling algorithm based on clustering, and adds a plurality of new training data to the original training data set to generate a training data set, wherein the training data set includes a plurality of training data; and The electronic computing device trains an original discriminant model with the training data set to generate the discriminant model.

In order to at least solve the above problems, the present invention also provides a computer program product. After loading the computer program product into an electronic computing device, the following instructions can be executed: Simplifying an original training data set according to a pooling algorithm based on clustering, and adding a plurality of new training data to the original training data set to generate a training data set, wherein the training data set includes a plurality of training data; and Training an original discriminant model with the training data set to generate a discriminant model for verifying the identity of the user of the electronic computing device.

In summary, the electronic computing device for verifying user identity, the method for updating the discriminant model, and the corresponding computer program product provided by the present disclosure are based on the clustering and pooling strategy to reduce the amount of data in the training data set, so that the overall training data input amount of the discriminant model will not increase significantly due to the increase in the training cycle. Because the clustering and pooling strategy reduces the amount of training data while still ensuring the representativeness of the training data, the equal error rate (EER) of the discriminant model during inference will not be significantly improved. Accordingly, the electronic computing device for verifying user identity, the method for updating the discriminant model, and the corresponding computer program product provided by the present disclosure have indeed solved the above-mentioned problems in the technical field to which the present invention belongs.

The content of the invention describes the core concept of the invention as a whole, and covers the problems that the invention can solve, the means that can be adopted, and the effects that can be achieved, so as to provide a basic understanding of the invention by those with ordinary knowledge in the technical field to which the invention belongs. However, it should be understood that the content of the invention is not intended to summarize all embodiments of the invention, but only presents the core concept of the invention in a simple form as an introduction to the subsequent detailed description. The following describes the detailed technology and implementation of the invention in conjunction with the drawings, so that those with ordinary knowledge in the technical field to which the invention belongs can understand the technical features of the invention for which protection is requested.

The following will explain the electronic computing device for verifying user identity, the method for updating the discrimination model, and the corresponding computer program product provided by the present invention through implementation methods. However, these implementation methods are not intended to limit the present invention to any environment, application, or method as described in these implementation methods. Therefore, the description of the implementation methods is only for the purpose of explaining the present invention, and is not intended to limit the scope of the present invention. It should be understood that in the following implementation methods and drawings, components that are not directly related to the present invention have been omitted and are not shown, and the size of each component and the size ratio between components are only for example, and are not intended to limit the scope of the present invention.

FIG. 1 is a schematic diagram of an electronic computing device for verifying user identity according to one or more embodiments of the present invention. The content shown in FIG. 1 is only for illustrating an embodiment of the present invention, not for limiting the present invention.

Referring to FIG. 1 , an electronic computing device 1 may basically include a memory 11 and a processor 12, and the memory 11 may be electrically connected to the processor 12. The electrical connection between the memory 11 and the processor 12 may be direct (i.e., not connected to each other through other components) or indirect (i.e., connected to each other through other components). The electronic computing device 1 may be a computing device of various types, such as but not limited to a laptop, a mobile phone, a portable electronic accessory (a watch, glasses, etc.). When a user U1 operates the electronic computing device 1, the electronic computing device 1 may verify the identity of the user U1 based on at least one piece of behavioral data (e.g., behavioral data BD1) provided by the user U1.

The memory 11 can be used to store data generated by the electronic computing device 1, data input from an external device, or data input by the user. For example, the memory 11 can be used to store a training data set 111 and a discriminant model 112. The memory 11 can include a first-level memory (also known as a main memory or an internal memory), and the processor 12 can directly read the instruction set stored in the first-level memory and execute these instruction sets when necessary. The memory 11 can optionally include a second-level memory (also known as an external memory or an auxiliary memory), and this memory can transfer the stored data to the first-level memory through a data buffer. For example, the second level memory may be, but is not limited to, a hard disk, an optical disk, etc. The storage device 11 may optionally include a third level memory, that is, a storage device that can be directly inserted into or removed from the computer, such as a portable hard disk.

The processor 12 may be a microprocessor or microcontroller with signal processing functions. A microprocessor or microcontroller is a special programmable integrated circuit that has the capabilities of computing, storage, input/output, etc., and can accept and process various coded instructions to perform various logical operations and arithmetic operations and output corresponding operation results. The processor 12 can be programmed to interpret various instructions to process data in the electronic computing device 1 and execute various operation procedures or programs.

In some embodiments, the electronic computing device 1 may further include an input element 13 and an output element 14, and both the input element 13 and the output element 14 may be electrically connected to the memory 11 and the processor 12. The input element 13 may be used to receive specific information from an external device or a user, and the output element 14 may be used to output specific information to an external device or a user. For example, the input element 13 may be a touch panel, a keyboard, a gyroscope, an altimeter, or other element or combination thereof that can be operated by the user U1 and generate corresponding data, and the output element 14 may be a display, a speaker, a vibrator, or other element or combination thereof. In some embodiments, the input element 13 and the output element 14 may be further integrated into a touch display.

FIG. 2 is a flow chart describing the discriminant model retraining and user identity verification according to one or more embodiments of the present invention. The content shown in FIG. 2 is only for illustrating the embodiments of the present invention, and is not intended to limit the present invention.

Referring to FIG. 1 and FIG. 2 at the same time, the electronic computing device 1 may perform retraining of the discrimination model and user identity verification as shown in a process 2. First, in order to allow the discrimination model 112 to learn the behavioral characteristics of a legitimate user and/or an illegitimate user, the processor 12 of the electronic computing device 1 may first collect (e.g., through the input element 13) behavioral data of the corresponding type of user (i.e., action 201).

The behavior data may be data generated by a specific component of the electronic computing device 1 in response to the user's operation behavior when the electronic computing device 1 is operated by the user. For example, the behavior data may be various data generated by the input component 13 (e.g., the aforementioned touch panel, touch display, keyboard, gyroscope, altimeter, etc.) in response to the user's operation behavior.

After collecting enough behavior data, the processor 12 may pre-process the collected behavior data (i.e., action 202) to convert it into corresponding feature data. For example, the processor 12 may extract features from the collected behavior data for items such as (but not limited to) touch trajectory, starting point/end point/speed/acceleration/duration when sliding on the screen, pressure, device tilt angle, device height, speed/acceleration/angular velocity of device movement, etc., and further convert each feature into training data in the form of a histogram. Since each feature in the histogram is represented by multiple bars of different sizes to show the distribution of the features of the user behavior data, the processor 12 is more resistant to noise and/or interference in the data when extracting features. In addition, the training data in the form of histograms is also more conducive to the efficiency of the discriminant model 112 in learning to distinguish between legitimate users and illegal users.

The training data in the form of histograms converted by the processor 12 may form a training data set 111 and be stored in the memory 11. In some embodiments, the training data in the form of histograms may be stored in the memory 11 in a format such as (but not limited to) ".csv".

After completing the preprocessing, the processor 12 may then train the discriminant model 112 with the training data in the training data set 111 (i.e., action 203). In some embodiments, the discriminant model 112 may be a machine learning model that performs data classification based on Linear Discriminant Analysis (LDA). The linear discriminant analysis performs classification operations based on a covariance matrix, such as calculating within-class variance. In other words, the processor 12 may calculate within-class variance based on a covariance matrix during the retraining phase of the discriminant model 112 or during the actual user authentication phase after the retraining is completed.

However, when the amount of behavioral data/feature data is large, the amount of computation of the covariance matrix will also become large and time-consuming. To solve this problem, in some embodiments, the discriminant model 112 of the present disclosure may adopt a lightweight linear discriminant analysis mode. FIG. 3 is a schematic diagram depicting the correlation of feature data in the form of a histogram according to one or more embodiments of the present invention. The content shown in FIG. 3 is only for illustrating the embodiments of the present invention, and is not intended to limit the present invention. Referring to FIG. 3 , since the feature data in the form of a histogram have the highest correlation at the diagonal matrix position (as indicated by the left slash in the figure), in the above-mentioned lightweight linear discriminant analysis mode, in order to save computing resources and thus shorten the training/processing time of the linear discriminant analysis, the processor 12 may choose to process only the feature data on the diagonal line, rather than the entire covariance matrix. Therefore, in some embodiments, the processor 12 may calculate the intra-class variance based on the diagonal covariance matrix when training the discriminant model 112 and actually verifying the identity of the user after completing the retraining.

Referring again to FIG. 1 and FIG. 2, since the training data will accumulate over time, it is necessary to pool the training data to improve the training efficiency. Specifically, the processor 12 can use a clustering-based pooling algorithm to reduce the amount of data in the training data set 111. The clustering-based pooling algorithm can be as follows: (1) For the training data set of the current training cycle, set a specific number of cluster centers. (2) Assign the training data of this training data set to the nearest cluster center. (3) Sum and average the positions of each training data in the same cluster to obtain the recalculated average value of this cluster, and assign the average value as the new cluster center. (4) Repeat steps (2) and (3) until each cluster center reaches convergence. (5) Replace the training data in each cluster with the cluster center to update the training data set.

The processor 12 executes the above-mentioned clustering-based pooling algorithm in detail as follows: First, the processor 12 can determine a plurality of cluster centers in the training data set 111, and divide the plurality of training data in the training data set 111 into a plurality of clusters according to the plurality of cluster centers.

For example, if the processor 12 determines 30 cluster centers, the data in the training data set 111 may be divided into 30 clusters accordingly. A specific clustering method may be to calculate the distance between each training data and each cluster center, and associate each training data with the cluster center with the smallest distance (i.e., assign it to the cluster to which the cluster center with the smallest distance belongs). The distance may be, for example, but not limited to, a Euclidean distance.

After forming the plurality of clusters, the processor 12 may sum up and average all the training data in each cluster to obtain an average data of the cluster. The processor 12 may use the average data calculated in each cluster as the representative data of the cluster (ie, action 204).

In some embodiments, regarding action 204, after calculating the average data of each cluster, the processor 12 may instead use each average data as the new group center of the corresponding cluster, and repeatedly execute the above-mentioned steps of "calculating the gap for grouping", "adding the average to calculate the average data of each group", and "updating the group center with the average data" until the next calculated average data is the same as the current group center (indicating that the group center no longer changes, in other words, the new group center shows convergence), and the last calculated average data is used as the representative data of each cluster.

Subsequently, the processor 12 can use the finally calculated average data to replace other training data in the corresponding clusters, thereby simplifying the training data set 111. In addition to simplifying the training data set 111, the processor 12 can add the training data to be added in the next training cycle to the current training data set 111 to update the training data set 111 (i.e., action 205). Then, the processor 12 can retrain the discriminant model 112 with the updated training data set 111 (i.e., perform action 203 again).

The amount of data in the training data set 111 after being processed by the clustering and pooling strategy disclosed in the present invention can be shown in Table 1 below, and the amount of data in the same training data set without being processed by the clustering and pooling strategy can be shown in Table 2 below: Training cycle Add training data Pooling training data Total training information 1 48 0 48 2 48 30 78 3 48 30 78 4 48 30 78 5 48 30 78 6 48 30 78 7 48 30 78 ＜Table 1＞ Training cycle Current training data Add training data Total training information 1 48 0 48 2 48 48 96 3 48 48 144 4 48 48 192 5 48 48 240 6 48 48 288 7 48 48 336 ＜Table 2＞

As can be seen from the example in Table 1, the processor 12 can perform multiple cycles of retraining for the discriminant model 112. Since the processor 12 will reduce the amount of data in the training data set 111 to 30 records in each round of training, the total amount of training data can be maintained at 78 records when 48 new training data are added in each round of training. On the other hand, in the example in Table 2, since there is no clustering and pooling, the amount of training data will increase by multiples in each round. Over time, it will significantly affect the retraining efficiency of the discriminant model 112.

After completing the retraining of the discriminant model 112, the processor 12 can classify the behavior data of the specific user by executing the discriminant model 112, and then verify whether the specific user is a legitimate user (i.e., action 206). Specifically, the processor 12 can convert the behavior data of the specific user (e.g., the behavior data BD1 provided by the user U1 in FIG. 1) into data in the form of a histogram according to the same mode as in the training phase, and then calculate the difference between the converted histogram data and the histogram data of the legitimate user or the illegitimate user defined during training, and verify whether the specific user is a legitimate user or an illegitimate user based on this.

If the specific user is determined to be an illegal user, the processor 12 may issue a corresponding warning message to inform the specific user that the specific user will not be able to continue to use the electronic computing device 1, and lock the electronic computing device 1 (i.e., action 207). The warning message may be, for example, the warning message A1 issued by the output element 14 in FIG. 1. On the other hand, if the user is determined to be a legal user, the user may be allowed to continue to use the electronic computing device 1 (i.e., action 208).

In some embodiments, the electronic computing device 1 may further include a transceiver (not shown) electrically connected to the memory 11 and the processor 12, and the processor 12 may notify the administrator of the electronic computing device 1 through the transceiver that an illegal user is using the device it manages. The transceiver may include a transmitter and a receiver. Taking wireless communication as an example, the transceiver may include but is not limited to: antenna, amplifier, modulator, demodulator, detector, analog to digital converter, digital to analog converter and other communication elements. Taking wired communication as an example, the transceiver may be, for example but not limited to: a gigabit Ethernet transceiver, a gigabit interface converter (GBIC), a small form-factor pluggable (SFP) transceiver, a ten gigabit small form-factor pluggable (XFP) transceiver, etc.

It should be understood that the two stages of "the electronic computing device 1 retrains the discriminant model 112" and "the electronic computing device 1 verifies the user's identity" are separated by a dotted line in FIG. 2, and these two stages can be performed independently. Specifically, in FIG. 2, the action 206 corresponding to the stage of verifying the user's identity is performed after the action 203 corresponding to the retraining stage. The purpose is only to express that the electronic computing device 1 can use the discriminant model 112 that has been retrained to verify the user's identity, but it does not limit the electronic computing device 1 to retrain actions 201 to 205 before each user verification (i.e., action 206, action 207, action 208).

FIG. 4 is a flow chart describing a method for updating a discriminant model according to one or more embodiments of the present invention. The contents shown in FIG. 4 are only for illustrating embodiments of the present invention, and are not intended to limit the present invention.

Referring to FIG. 4, a second embodiment of the present disclosure is a method 4 for updating a discriminant model. The discriminant model can be used to verify the identity of a user of an electronic computing device. Method 4 may include the following steps: The electronic computing device simplifies an original training data set according to a pooling algorithm based on clustering, and adds a plurality of new training data to the original training data set to generate a training data set (labeled as 401), wherein the training data set includes a plurality of training data; and The electronic computing device trains an original discriminant model with the training data set to generate the discriminant model (labeled as 402).

In some embodiments, when simplifying the original training data set, method 4 may also include the following steps: (A) the electronic computing device determines a plurality of group centers from a plurality of training data; (B) the electronic computing device divides the plurality of training data into a plurality of clusters based on the plurality of group centers, wherein the number of the plurality of clusters is the same as the number of the plurality of group centers; (C) the electronic computing device adds up and averages all the training data in each cluster to obtain an average data of the cluster; (D) the electronic computing device updates the plurality of group centers with the plurality of average data; (E) The electronic computing device repeatedly and sequentially performs step (B), step (C), and step (D) until the plurality of average data converges to the same as the plurality of cluster centers; and (F) The electronic computing device uses the average data of each cluster to replace all training data in the cluster, thereby simplifying the original training data set.

In some embodiments, in addition to the above steps (A) to (D), when dividing the plurality of training data in the original training data set into the plurality of clusters, method 4 may further include the following steps: (B1) the electronic computing device calculates a gap between each training data in the original training data set and each of the cluster centers; and (B2) the electronic computing device associates each of the training data in the original training data set with the cluster center with the smallest gap, thereby forming the plurality of clusters.

In some embodiments, regarding method 4, the plurality of training data may be histogram data. In addition, in some embodiments, the original training data set and the training data set have the same amount of training data.

In some embodiments, method 4 may also include the following steps: When training the original discriminant model, the electronic computing device calculates the intra-class variance based on the diagonal covariance matrix.

Each embodiment of method 4 basically corresponds to a certain embodiment of electronic computing device 1. Therefore, based on the above description of electronic computing device 1, a person with ordinary knowledge in the technical field to which the present invention belongs can fully understand and implement all corresponding embodiments of method 4, even if each embodiment of method 4 is not described in detail above.

In some embodiments, method 4 may be implemented as a computer program product. When the computer program product is read into an electronic computing device, a plurality of program instructions contained in the computer program product may execute method 4 described in the second embodiment. The computer program product may be stored in a non-transitory tangible machine-readable medium, such as (but not limited to) a read-only memory (ROM), a flash memory, a floppy disk, a hard disk, a magnetic tape, a database connected to the Internet, or any other storage medium that is well known to a person of ordinary skill in the art to which the present invention belongs and has the same function. Due to the popularity of the Internet, computer software can be stored in recording media and can also be directly transmitted and provided on the Internet without being stored on recording media. A computer program product refers to an item that contains a computer-readable program and is not limited to an external form.

The above implementations are only used to exemplify some implementation modes of the present invention and to explain the technical features of the present invention, and are not used to limit the scope and range of protection of the present invention. Any changes or equivalent arrangements that can be easily completed by a person with ordinary knowledge in the technical field to which the present invention belongs are within the scope advocated by the present invention, and the scope of protection of the present invention is subject to the scope of the patent application.

As shown below: 1: Electronic computing device 11: Memory 111: Training data set 112: Discrimination model 12: Processor 13: Input element 14: Output element 2: Process 201~208: Action 4: Method 401~402: Step A1: Warning message BD1: Behavior data U1: User

FIG. 1 is a schematic diagram of an electronic computing device for verifying user identity according to one or more embodiments of the present invention. FIG. 2 is a flowchart for retraining a discriminant model and verifying user identity according to one or more embodiments of the present invention. FIG. 3 is a schematic diagram for describing the correlation of feature data in the form of a histogram according to one or more embodiments of the present invention. FIG. 4 is a flowchart for describing a method for updating a discriminant model according to one or more embodiments of the present invention.

without.

4: Update method of discriminant model 401~402: Steps

Claims (15)

An electronic computing device for verifying user identity comprises: a memory for storing a discrimination model and a training data set, wherein the training data set comprises a plurality of training data; and a processor, electrically connected to the memory, for running the discrimination model to determine whether a user is a legitimate user based on at least one piece of behavior data, wherein the at least one piece of behavior data corresponds to the behavior characteristics of the user; wherein the processor is further used to: simplify an original training data set according to a pooling algorithm based on clustering, and add a plurality of new training data to the original training data set to generate the training data set; train an original discrimination model with the training data set to generate the discrimination model; wherein, in simplifying the original When training a data set, the processor is also used to: (A) determine a plurality of centroids in a plurality of training data; (B) divide the plurality of training data into a plurality of clusters according to the plurality of centroids, wherein the number of the plurality of clusters is the same as the number of the centroids; (C) for each cluster, sum up and average all the training data in the cluster to obtain an average data of the cluster; (D) update the plurality of centroids with the plurality of average data; (E) repeatedly and sequentially perform steps (B), (C), and (D) until the plurality of average data converges to the same as the plurality of centroids; and (F) use the average data of each cluster to replace all the training data in the cluster, thereby simplifying the original training data set. The electronic computing device as described in claim 1, wherein when the plurality of training data are divided into a plurality of clusters, the processor is also used to: (B1) calculate a gap between each training data in the original training data set and each of the cluster centers; and (B2) associate each of the training data in the original training data set with the cluster center with the smallest gap, thereby forming the plurality of clusters. An electronic computing device as described in claim 1, wherein the plurality of training data are histogram data. An electronic computing device as described in claim 1, wherein the original training data set and the training data set have the same amount of training data. The electronic computing device as described in claim 1, wherein the processor is also used to: calculate the intra-class variance based on the diagonal covariance matrix when training the original discriminant model and when making a judgment based on the at least one behavioral data. A method for updating a discriminant model, the discriminant model is used to verify the identity of a user of an electronic computing device, the method comprising the following steps: the electronic computing device simplifies an original training data set according to a pooling algorithm based on clustering, and adds a plurality of new training data to the original training data set to generate a training data set, wherein the training data set includes a plurality of training data; and the electronic computing device trains an original discriminant model with the training data set to generate the discriminant model, wherein when simplifying the original training data set, the method further comprises the following steps: (A) the electronic computing device determines a plurality of group centroids from the plurality of training data; (B) the electronic computing device According to the plurality of group centroids, the plurality of training data are divided into a plurality of clusters, wherein the number of the plurality of clusters is the same as the number of the plurality of group centroids; (C) the electronic computing device adds up and averages all the training data in each cluster to obtain an average data of the cluster; (D) the electronic computing device updates the plurality of group centroids with the plurality of average data; (E) the electronic computing device repeatedly and sequentially performs steps (B), (C), and (D) until the plurality of average data converges to the same as the plurality of group centroids; and (F) the electronic computing device replaces all the training data in the cluster with the average data of each cluster to simplify the original training data set. The method as described in claim 6, wherein when the plurality of training data in the original training data set are divided into the plurality of clusters, the method further comprises the following steps: (B1) the electronic computing device calculates a gap between each training data in the original training data set and each of the cluster centers; and (B2) the electronic computing device associates each of the training data in the original training data set with the cluster center with the smallest gap, thereby forming the plurality of clusters. The method as described in claim 6, wherein the plurality of training data are histogram data. The method as described in claim 6, wherein the original training data set and the training data set have the same amount of training data. The method as described in claim 6 further comprises the following steps: When training the original discriminant model, the electronic computing device calculates the intra-class variance based on the diagonal covariance matrix. A computer program product, after being loaded into an electronic computing device, executes the following instructions: simplifying an original training data set according to a pooling algorithm based on clustering, and adding a plurality of new training data to the original training data set to generate a training data set, wherein the training data set includes a plurality of training data; and training an original discriminant model with the training data set to generate a discriminant model for verifying the identity of a user of the electronic computing device, wherein when the electronic computing device simplifies the original training data set, the computer program product further includes the following instructions: (A) determining a plurality of group centers in the plurality of training data; (B) dividing the plurality of training data into a plurality of clusters according to the plurality of group centroids, wherein the number of the plurality of clusters is the same as the number of the plurality of group centroids; (C) for each cluster, summing up all the training data therein and averaging them to obtain an average data of the cluster; (D) updating the plurality of group centroids with the plurality of average data; (E) repeatedly and sequentially performing steps (B), (C), and (D) until the plurality of average data converge to the same as the plurality of group centroids; and (F) using the average data of each cluster to replace all the training data in the cluster, thereby simplifying the original training data set. A computer program product as described in claim 11, wherein when the electronic computing device divides the plurality of training data in the original training data set into the plurality of clusters, the computer program product further comprises the following instructions: (B1) calculating a gap between each training data in the original training data set and each of the cluster centers; and (B2) associating each of the training data in the original training data set with the cluster center with the smallest gap, thereby forming the plurality of clusters. A computer program product as described in claim 11, wherein the plurality of training data are histogram data. A computer program product as described in claim 11, wherein the original training data set and the training data set have the same amount of training data. The computer program product as described in claim 11 further comprises the following instructions: when the electronic computing device trains the original discriminant model, the intra-class variance is calculated based on the diagonal covariance matrix.