CN117609811A - ECG data clustering method based on non-parametric spherical variational autoencoder - Google Patents

ECG data clustering method based on non-parametric spherical variational autoencoder Download PDF

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CN117609811A
CN117609811A CN202311662145.3A CN202311662145A CN117609811A CN 117609811 A CN117609811 A CN 117609811A CN 202311662145 A CN202311662145 A CN 202311662145A CN 117609811 A CN117609811 A CN 117609811A
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范文涛
苏伟峰
王田
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Beijing Normal University HKBU United International College
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Abstract

The invention relates to the field of machine learning and medical data analysis, in particular to an ECG data clustering method based on a non-parametric spherical variation self-encoder. The technical problems to be solved by the technical proposal are as follows: aiming at the data clustering and analyzing method, the problems of improving the identification accuracy and the prediction capability of heart diseases are solved. The method is an end-to-end electrocardiogram data clustering method based on a depth variation self-encoder, and adopts a Bayesian non-parametric model framework based on a Pitman-Yor process mixing model to construct an infinite mixing model based on von Mises-Fisher (VMF) probability distribution. The beneficial effects of this technical scheme are: by combining the advantages of deep learning and Bayesian non-parametric model, a more efficient, accurate and flexible solution is provided for the cluster analysis of electrocardiographic data.

Description

ECG data clustering method based on nonparametric spherical variation self-encoder
Technical Field
The invention relates to the field of machine learning and medical data analysis, in particular to an Electrocardiogram (ECG) data processing and analysis, and particularly relates to an ECG data clustering method based on a non-parametric spherical variation self-encoder.
Background
In the prior art, electrocardiographic data analysis typically relies on traditional machine learning methods and basic statistical models, such as simple classification algorithms, time series analysis, and basic clustering techniques. However, these methods present challenges in processing large-scale or complex electrocardiographic data, particularly in accurately identifying and classifying diverse cardiac conditions. In contrast, variational self-Encoder (VAE), which is an advanced depth generation model, has demonstrated excellent data generation and feature extraction capabilities in the image and speech processing fields, but has still been relatively limited in its application to electrocardiographic data analysis.
Therefore, the ECG data clustering method based on the nonparametric spherical variation self-encoder can more effectively cope with complex and large-scale electrocardiogram data analysis tasks.
Disclosure of Invention
In order to achieve the above purpose, the invention adopts the technical scheme that: by combining the advantages of deep learning and Bayesian non-parametric model, a more efficient, accurate and flexible solution is provided for the cluster analysis of electrocardiographic data.
Further, the method is an end-to-end electrocardiogram data clustering method based on depth variation self-encoder, and adopts a Bayesian non-parametric model framework based on a Pitman-Yor process mixed model to construct an infinite mixed model based on VMF probability distribution, and the method comprises the following steps: step 1) collecting an ECG dataset, step 2) modeling an ECG data model using a spherical non-parametric spherical variation self-encoder.
Further, the VMF hybrid model includes a probability decoder that also obeys the VMF probability distribution, a depth generation model, and a hypersphere potential space-based depth generation model.
The beneficial effects after this technical scheme improves are: the strong feature extraction capability of the variation self-encoder and the flexibility of the non-parametric model are combined, so that the accuracy and the efficiency of clustering are improved. The model architecture of the variational self-encoder is constructed based on a Bayesian non-parametric method of a Pitman-Yor process mixed model, so that the model is allowed to automatically adjust the complexity of potential space, and the number of clusters is dynamically adjusted according to the characteristics of data. The VMF probability distribution provides a clustering mechanism that is more efficient over specific data types than traditional gaussian distributions.
Further, step 1) collects an ECG data set: in addition, anotherFor the collected data set containing N ECG data, wherein each data +.>Is a D-dimensional ECG data vector.
Further, step 2) models the ECG data model using a spherical non-parametric spherical variational self-encoder: a non-parametric hybrid model consisting of an infinite number of VMF distributions, defined as follows:
wherein,π k is the mixing coefficient of cluster k and satisfies the condition pi k > 0 and->
Further, the mixing coefficient pi k Is constructed based on a Pitman-Yor process mixture model using a Stick-break representation method, the mixture model, the mixture coefficient pi k Is represented as follows:
wherein the method comprises the steps ofObeying Beta distribution, the expression form is as follows:
wherein p is b (. Cndot.) Beta distribution, ζ k Is a discount parameter in a Pitman-Yor process model and satisfies the condition 0.ltoreq.ζ k ≤1，ξ k Satisfy condition ζ for density parameter k ＞-ζ k 。
Further, the bayesian non-parametric model is a non-parametric VMF mixture model that is potentially space-priori compliant, where k is chosen,potential representation of->From this potential distribution, a sample can be taken, as follows:
wherein,for VMF distribution, < >>And kappa (kappa) k The position parameter and the concentration parameter of the kth VMF probability distribution in the non-parameter VMF mixed model are respectively the function I D/2 (kappa) is a modified first class D/2 Bessel function.
Further, a probability decoder also obeys the VMF probability distributionTo generateSample->The following formula is shown:
wherein the parameters areAnd kappa (kappa) x By training an input to +.>
Further, the depth generation model is defined as follows:
the lower variation bound of the objective function of the depth generation model can be obtained by the following formula:
wherein E [. Cndot.]Indicating that a calculation is desired,for true posterior distribution->Is a near variational posterior of (c).
Further, the objective function of the depth generation model based on the hypersphere potential space can be redefined as:
wherein,for posterior of variation->And->KL divergence between.
Further, based on an infinite mixed model of VMF probability distribution, by calculationPosterior on variationIs->Data +.>Assigning to the cluster with the highest probability completes the clustering.
The beneficial effects of the invention are as follows:
1. the invention provides an end-to-end ECG data clustering method based on a depth variation self-encoder. The method realizes direct conversion from the original data input to the clustering output by utilizing the deep learning technology, thereby greatly simplifying the data processing flow.
2. The application of the Bayes non-parametric hybrid model is that the proposed method adopts the Bayes non-parametric hybrid model as the prior distribution of the potential space. One key advantage of this model is that it can automatically adjust the number of clusters, avoiding the limitation of manually setting the number of clusters in conventional clustering methods. This feature makes the model more flexible and able to accommodate data sets of various sizes and complexities.
3. VMF probability distribution is adopted to improve clustering performance, namely in a non-parametric hybrid model, the invention adopts VMF probability distribution as basic distribution instead of traditional Gaussian distribution. VMF distribution is particularly useful for processing data distributed on high-dimensional spheres, which makes it exhibit better clustering performance when processing normalized high-dimensional data, such as electrocardiographic data. In addition, the VMF distribution also helps to alleviate the overfitting problem and improve the generalization ability of the model.
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FIG. 1 is a flow chart of ECG data clustering based on a non-parametric spherical variation self-encoder model of the present invention.
FIG. 2 is a diagram of a Pitman-Yor process mixture model based on the Stick-break representation method of the present invention.
Fig. 3 is a diagram of an infinite VMF blend model in accordance with the invention.
Fig. 4 is a diagram of a sample generation process of the self-encoder based on a non-parametric spherical variation in accordance with the present invention.
Detailed Description
In order that those skilled in the art may better understand the technical solutions of the present invention, the following detailed description of the present invention with reference to the accompanying drawings is provided for exemplary and explanatory purposes only and should not be construed as limiting the scope of the present invention.
The invention provides an Electrocardiogram (ECG) data clustering method based on a non-parametric spherical variation self-encoder, and the validity of the method is verified on a public ECG5000 data set. The data set includes 5000 time series data of length 140, each representing a heartbeat cycle. The dataset is divided into five categories: one normal class (N) and four abnormal classes (R-on-T ventricular premature beat (R-on-T PVC), ventricular premature beat (PVC), supraventricular premature beat or ectopic beat (SP or EB), and Unclassified Beat (UB)). The raw data set is divided into training and testing sets, each set containing all classes of data. Notably, there is a significant imbalance in the number of these categories, with normal data being the majority. The model of the invention adopts complete unsupervised learning and does not depend on label data, so that the training set and the testing set are combined into a whole for analysis.
Meanwhile, the invention uses Windows 10 operating system and Python programming language, and PyTorch machine learning library. The clustering effect is measured by governor-type cluster Accuracy (ACC). Model training is carried out by adopting an Adam optimizer, the learning rate is set to be 0.003, the dropout rate is set to be 0.2, the training process comprises 200 epochs, and the batch size is set to be 32, so that gradient calculation and weight updating are carried out. The dimension of the potential space is set to 5 dimensions.
Detailed description as shown in fig. 1-4, the ECG data clustering method based on the non-parametric spherical variation self-encoder adopts a bayesian non-parametric model framework (fig. 2) based on a Pitman-Yor process mixed model to construct an infinite mixed model (fig. 3) with von Mises-Fisher (VMF) probability distribution as the prior distribution of the variation self-encoder hidden space. Since the VMF distribution is defined on the unit hypersphere, such a non-parametric spherical-shaped variation self-encoder based on the VMF distribution is referred to as a non-parametric spherical-shaped variation self-encoder. The VMF hybrid model we construct is formed from a weighted combination of multiple VMF probability distributions. Under this approach, it is assumed that each D-dimensional electrocardiographic data vector x is generated by some random process, accompanied by a corresponding, non-directly observable potential representation z. This potential representation z may be regarded as a potential embedding (or encoding) of the data vector x after processing by the encoder. Furthermore, we assume that the potential representation z is derived from an infinite VMF blend model based on the Pitman-Yor process blend model. By assuming that the potential representation z follows an infinite VMF mixed model distribution, we can cluster the potential representation z of the ECG data in potential space instead of directly clustering the raw data x. Due to the non-parametric model framework based on the Pitman-Yor process mixture model, the number of categories in the potential space can be automatically adjusted as the data volume increases. The specific embodiment comprises the following steps:
step 1) collecting ECG data setsFor the collected data set containing N ECG data, wherein each data +.>Is a D-dimensional ECG data vector.
Step 2) modeling ECG data model Using spherical nonparametric spherical variators from encoder by first lettingFor observing the representation of data X in potential space, therefore +.>Called +.>Potential representations (or encodings) of (a) are provided. Assume that each potential representation +>Obeys a non-parametric hybrid model consisting of infinite VMF distributions. In the depth generation model we construct, for generating samples from the kth cluster +.>The choice of cluster k obeys a parameter of +.>Class distribution (Categorical Distribution) defined as follows:
wherein,π k is a mixed coefficient of the cluster k (i.e., a priori probability of the cluster k), and satisfies the condition pi k > 0 and
in the present method, as shown in FIG. 2, the mixing coefficient pi k Is constructed based on a Pitman-Yor process mixture model using a Stick-break representation method. In the Pitman-Yor process mixing model based on Stick-break representation method, the mixing coefficient pi k Is represented as follows:
wherein,obeying Beta distribution, the expression form is as follows:
wherein p is b (. Cndot.) Beta distribution, ζ k Is a Discount (discovery) parameter in the Pitman-Yor process model and satisfies the condition 0 ζ k ≤1，ξ k Satisfy condition ζ for density parameter k ＞-ζ k 。
Since the potential space we set is a priori compliant with the non-parametric VMF mixture model, in the case of k being selected,potential representation of->From this potential distribution, a sample can be taken, as follows:
wherein,for VMF distribution, < >>And kappa (kappa) k Respectively, in a non-parametric VMF hybrid model.
As shown in FIG. 3, the position parameter and concentration parameter of the kth VMF probability distribution, function I D/2 (kappa) is a modified first class D/2 Bessel function. When potentially representingAfter sampling from cluster k, we can go through a probability decoder that also obeys the VMF probability distribution>Sample de-generation->The following formula is shown:
wherein the parameters areAnd kappa (kappa) x By training an input to +.>Neural network of parameter lambda->Automatic deriving
Wherein the neural networkCan be set into any network class according to different application scenesIn the present invention, we use long short term memory network (LSTM).
According to the samples described aboveOur depth generation model is defined as follows:
similar to a common variational self-encoder, according to the variational inference idea, the objective function of our depth generation model isThe lower variation bound (also known as the evidence, ELBO) of (a) can be obtained by:
wherein E [. Cndot.]Indicating that a calculation is desired,for true posterior distribution->According to the Mean-Field Theory (variational posterior), variational posterior ++>Can be further factorized into:
wherein,is a probability encoderAnd obeys VMF distribution:
wherein the parameters areAnd κ' may be input by training an input +.>Deep neural network of parameter phi>Automatic deriving
AND decoderSimilarly, encoder->LSTM neural networks are also selected.
According to the definition above, the proposed objective function of the hypersphere potential space based depth generation model can be redefined as:
wherein,for posterior of variation->And->KL divergence between. We updated and optimized the objective function ELBO by using a random gradient-varying decibel leaf (Stochastic Gradient Variational Bayes, SGVB) estimation method and an ADAM optimizer.
As shown in fig. 4, by calculationPosterior about variation->Is->Data +.>Assigning to the cluster with the highest probability completes the clustering.
Comparative example
In the most relevant prior art [1], a data clustering method combining a variational self-encoder and a Gaussian mixture model is proposed. This approach assumes that the potential representation of each data vector is subject to a gaussian mixture model and translates the clustering problem of the raw data into a cluster analysis of the potential representation. The method carries out model training by random gradient variation decibel phyllos. However, one limitation of this approach is that the number of categories needs to be manually set in advance, which limits its flexibility and adaptability to some extent. In contrast, the method of the present invention is more effective in dealing with complex and large-scale electrocardiographic data analysis tasks.
[1]Z.Jiang,Y.Zheng,H.Tan,B.Tang,and H.Zhou,“Variational deep embedding:An unsupervised and generative approach to clustering,”in Proceedings of the International Joint Conference on Artificial Intelligence(IJCAI),2017,pp.1965–1972.
Under the technical conditions proposed in the prior art [1], the present invention proposes a new solution.
First, the clustering model in prior art [1] assumes that the potential representation of each data vector follows a gaussian mixture model. However, recent studies have shown that in a depth-self encoder based clustering model, clustering performance can be significantly improved if the underlying representation of the raw data is L2 normalized. The L2 normalized data corresponds to points located on a unit hypersphere, commonly referred to as sphere data. In addition, L2 normalization can introduce regularization in data modeling, and limit the representation space on a unit hypersphere, so that model overfitting is effectively prevented. For spherical data, von Mises-Fisher (VMF) distributions, whose probability densities are defined on a unit hypersphere, are more suitable as modeling tools for such data than gaussian distributions. Thus, the present invention employs a priori distribution based on the VMF hybrid model to construct a spherical variational self-encoder to optimize modeling of the potential representation.
Secondly, the gaussian mixture model mentioned in the prior art [1] is a finite mixture model in which the number of mixture components (i.e., the number of clusters in a cluster) needs to be set in advance. In contrast, the VMF hybrid model in the present invention is a Bayes non-parametric hybrid model constructed based on the Pitman-Yor process. In the clustering problem, bayesian non-parametric hybrid model hypothesis data is generated from a hybrid model consisting of an infinite number of probability distributions, and the number of hybrid components (i.e., the number of clusters) is automatically determined during model training. The method enhances the flexibility and adaptability of the model, allows the model to reflect the potential structure of the data more accurately, and improves the clustering effect.
To evaluate the effectiveness of the method of the present invention, we compared it to two conventional clustering methods: k-means and Gaussian Mixture Model (GMM), and a variance self-encoder clustering method [1] (abbreviated as VaDE) based on Gaussian mixture model. 10 repeated experiments were performed for each method, and the average ACC value was taken as an index for performance comparison. The experimental results are shown in table 1. From the comparison result, the invention is excellent in ECG data clustering, and compared with the prior art, the invention realizes higher ACC value and shows the superiority.
TABLE 1
In summary, in the clustering problem, the Bayesian non-parametric hybrid model hypothesis data is generated by a hybrid model composed of infinite probability distributions, and the number of hybrid components is automatically determined in the model training process. The method enhances the flexibility and adaptability of the model, allows the model to reflect the potential structure of the data more accurately, and improves the clustering effect. A more efficient, accurate and flexible solution is provided for cluster analysis of electrocardiographic data.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to facilitate an understanding of the method of the present invention and its core ideas. The foregoing is merely illustrative of the preferred embodiments of the invention, and it is noted that there is virtually no limit to the specific structure which may be imposed by those skilled in the art without departing from the spirit of the invention, and that modifications, adaptations, or variations of the foregoing features may be combined in a suitable manner; such modifications, variations and combinations, or the direct application of the inventive concepts and aspects to other applications without modification, are contemplated as falling within the scope of the present invention.

Claims (9)

1. The ECG data clustering method based on the nonparametric spherical variation self-encoder is characterized by comprising the following steps of: the method is based on a non-parametric spherical variation self-encoder model, and adopts a Bayes non-parametric model framework based on a Pitman-Yor process mixed model to construct an infinite mixed model based on VMF probability distribution; the method comprises the following steps: step 1) collecting an ECG data set, and step 2) modeling the ECG data model by using a spherical non-parametric spherical variation self-encoder, wherein the VMF hybrid model comprises a probability decoder which also obeys VMF probability distribution, a depth generation model and a depth generation model based on hypersphere potential space.
2. The non-parametric spherical variation self-encoder-based ECG data clustering method of claim 1, wherein: step 1) of collecting an ECG data set, andfor the collected data set containing N ECG data, wherein each data +.>Is a D-dimensional ECG data vector.
3. The non-parametric spherical variation self-encoder-based ECG data clustering method of claim 2, wherein: step 2) uses the spherical nonparametric spherical variation self-encoder to model the ECG data model, and a nonparametric mixed model consisting of infinite VMF distributions is defined as follows:
wherein,π k is the mixing coefficient of cluster k and satisfies the condition pi k > 0 and->
4. The non-parametric spherical variation self-encoder-based ECG data clustering method of claim 3, wherein: the mixing coefficient pi k Is constructed based on a Pitman-Yor process mixture model using a Stick-break representation method, the mixture model, the mixture coefficient pi k Is represented as follows:
wherein the method comprises the steps ofObeying Beta distribution, the expression form is as follows:
wherein p is b (. Cndot.) Beta distribution, ζ k Is a discount parameter in a Pitman-Yor process model and satisfies the condition 0.ltoreq.ζ k ≤1，ξ k Satisfy condition ζ for density parameter k ＞-ζ k 。
5. The non-parametric spherical variation self-encoder-based ECG data clustering method of claim 1, wherein: the bayesian non-parametric model is a non-parametric VMF mixture model that is potentially space-priori compliant, where k is chosen,potential representation of->From this potential distribution, a sample can be taken, as follows:
wherein,for VMF distribution, < >>And kappa (kappa) k The position parameter and the concentration parameter of the kth VMF probability distribution in the non-parameter VMF mixed model are respectively the function I D/2 (kappa) is a modified first class D/2 Bessel function.
6. The non-parametric spherical variation self-encoder-based ECG data clustering method of claim 1, wherein: said one probability decoder also obeys the VMF probability distributionSample de-generation->The following formula is shown:
wherein the parameters areAnd kappa (kappa) x By training an input to +.>
7. The non-parametric spherical variation self-encoder-based ECG data clustering method of claim 1, wherein: the depth generation model is defined as follows:
the lower variation bound of the objective function of the depth generation model can be obtained by the following formula:
wherein E [. Cndot.]Indicating that a calculation is desired,for true posterior distribution->Is a near variational posterior of (c).
8. The non-parametric spherical variation self-encoder-based ECG data clustering method of claim 7, wherein: the objective function of the depth generation model based on the hypersphere potential space can be redefined as follows:
wherein,for posterior of variation->And->KL divergence between.
9. Root of Chinese characterThe non-parametric spherical variation self-encoder-based ECG data clustering method of claim 8, wherein: the infinite mixing model based on VMF probability distribution is obtained by calculationPosterior about variation->Is not limited by the desire of (a)Data +.>Assigning to the cluster with the highest probability completes the clustering.
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