CN109119158A - A kind of RdR scatter plot recognition methods based on sparse kernel principle component analysis - Google Patents
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Abstract
本发明公开一种基于稀疏核主分量分析的RdR散点图识别方法，包括步骤1）获取心电信号，对心电信号进行滤波去噪处理，提取R波峰值位置；步骤2）使用心搏间期绘制RdR散点图；步骤3）对RdR散点图进行缩放，并对图像数据进行归一化处理；步骤4）对获得的散点图样本进行标记；步骤5）对样本进行采样；步骤6）设置参数；步骤7）分别对每类样本求解近似基、特征值、特征向量；步骤8）计算每个测试样本的SPE，与实际类别比较，若满足要求则步骤9，否则返回步骤6重新设置参数训练；步骤9）获得参数，算法结束。本发明利用稀疏核主分量分析方法来进行RdR散点图的分类识别，具有令人满意的分类效果。
The invention discloses an RdR scatter diagram identification method based on sparse kernel principal component analysis, which includes step 1) obtaining an electrocardiogram signal, filtering and denoising the electrocardiogram signal, and extracting the peak position of the R wave; step 2) using the heartbeat Draw the RdR scatter plot at intervals; step 3) zoom the RdR scatter plot and normalize the image data; step 4) mark the obtained scatter plot samples; step 5) sample the samples; Step 6) Set parameters; Step 7) Solve the approximate basis, eigenvalue, and eigenvector for each type of sample respectively; Step 8) Calculate the SPE of each test sample, compare it with the actual category, if it meets the requirements, go to Step 9, otherwise return to Step 9 6. Reset the parameter training; Step 9) Obtain the parameters, and the algorithm ends. The invention utilizes the sparse kernel principal component analysis method to carry out the classification and identification of the RdR scatter diagram, and has a satisfactory classification effect.
Description
技术领域technical field
本发明涉及一种基于稀疏核主分量分析的RdR散点图识别方法，属于智能医疗技术领域。The invention relates to an RdR scatter diagram identification method based on sparse kernel principal component analysis, and belongs to the technical field of intelligent medical treatment.
背景技术Background technique
心率变异是指心动间期之间的时间变异数，其研究对象是心动间期。人的心率不是一成不变的，两次心搏之间存在着微小的时间差异，计算心动间期的差异，即可了解心率变异性(Heart rate variability,HRV)。心率变异性可以评估心脏交感神经与副交感神经对心血管活动的影响，蕴含着心血管方面的大量信息。临床研究表明，心率变异性的降低是心肌梗死、高血压、心绞痛等心血管疾病发病的症状。因此，心率变异性的研究，在评价心血管系统功能、预测心血管疾病的发作，以及为心血管疾病的早期诊断具有重要的意义。Heart rate variability refers to the time variability between cardiac intervals, and its research object is the cardiac interval. Human heart rate is not static, there is a small time difference between two heartbeats, and the heart rate variability (HRV) can be understood by calculating the difference between the cardiac intervals. Heart rate variability can evaluate the effects of cardiac sympathetic and parasympathetic nerves on cardiovascular activity, and contains a lot of cardiovascular information. Clinical studies have shown that reduced heart rate variability is a symptom of cardiovascular disease such as myocardial infarction, hypertension, and angina pectoris. Therefore, the study of heart rate variability is of great significance in evaluating the function of the cardiovascular system, predicting the onset of cardiovascular disease, and early diagnosis of cardiovascular disease.
Poincare散点图是心率变异性一种重要的研究方法。通过使用连续的心搏间期在直角坐标系中绘制图形，反映相邻心搏间期的变化，能显示心搏间期的特征。Poincare散点图有多种形态，包括彗星状、扇形等，不同的形状反映不同的心脏状态。虽然Poincare散点图是一种有效的心率变异性分析方法，但是并不能体现其随时间变化的趋势，对于某些心血管疾病、身体健康状况等不能很好的体现其心率变异性性质。于是，一些学者提出了改进策略，即一阶差分散点图，通过相邻心搏间期的差值来绘制散点图。然而，这种方法又丢失了原有的心搏间期绝对值信息。因此，有学者将二者结合起来，提出了一种RdR散点图，以此来同时反映心搏间期及其变化。The Poincare scatter plot is an important research method for heart rate variability. The characteristics of the heartbeat interval can be displayed by using the continuous heartbeat interval to draw a graph in the rectangular coordinate system to reflect the change of the adjacent heartbeat interval. The Poincare scatter chart has various shapes, including comet shape, fan shape, etc. Different shapes reflect different heart states. Although the Poincare scatter plot is an effective HRV analysis method, it cannot reflect its trend over time, and cannot well reflect its HRV properties for certain cardiovascular diseases and physical health conditions. Therefore, some scholars have proposed an improved strategy, that is, a first-order difference scatter plot, which draws a scatter plot through the difference between adjacent heartbeat intervals. However, this method loses the original absolute value of the heartbeat interval information. Therefore, some scholars have combined the two and proposed a RdR scatter plot to reflect the heart interval and its changes at the same time.
目前，对于不同心血管疾病的心率变异性分析很多。但是，如何根据散点图来识别、区分不同的心血管疾病则相对匮乏。本文即是通过稀疏核主分量分析方法来对RdR散点图进行识别分类。At present, there are many analyses of heart rate variability for different cardiovascular diseases. However, how to identify and distinguish different cardiovascular diseases based on scatter plots is relatively lacking. In this paper, the sparse kernel principal component analysis method is used to identify and classify the RdR scattergram.
发明内容SUMMARY OF THE INVENTION
本发明的目的就在于通过稀疏核主分量分析的方法，来自动识别RdR散点图，对心率变异性作分析，为实现自动化诊断、缓解紧缺的医疗资源、减少医疗资源的浪费、提高就诊效率提供基础。The purpose of the present invention is to automatically identify the RdR scatter diagram and analyze the heart rate variability through the method of sparse kernel principal component analysis, in order to realize automatic diagnosis, alleviate the shortage of medical resources, reduce the waste of medical resources, and improve the efficiency of medical treatment. Provide the basis.
本发明通过以下技术方案来实现上述目的：一种基于稀疏核主分量分析的RdR散点图识别方法，包括以下步骤：The present invention achieves the above object through the following technical solutions: a method for identifying RdR scattergrams based on sparse kernel principal component analysis, comprising the following steps:
步骤1)获取心电信号，对心电信号进行滤波去噪处理，提取R波峰值位置；Step 1) Acquire the ECG signal, perform filtering and denoising processing on the ECG signal, and extract the peak position of the R wave;
步骤2)使用心搏间期绘制RdR散点图，可以通过MATLAB等工具来绘制；Step 2) Use the heartbeat interval to draw the RdR scatter diagram, which can be drawn by tools such as MATLAB;
步骤3)对RdR散点图进行缩放，转成灰度图，并对图像数据进行归一化处理，以减少计算量；Step 3) scaling the RdR scattergram, converting it into a grayscale image, and normalizing the image data to reduce the amount of computation;
步骤4)对获得的散点图样本进行标记；Step 4) marking the obtained scatter plot samples;
步骤5)对样本进行采样，随机抽取75％的数据作为训练样本；Step 5) Sampling the samples, randomly extracting 75% of the data as training samples;
步骤6)设置参数，参数包括近似基的误差参数、高斯核函数参数以及控制限的值；Step 6) setting parameters, the parameters include the error parameter of the approximate basis, the Gaussian kernel function parameter and the value of the control limit;
步骤7)分别对每类样本求解近似基、特征值、特征向量；Step 7) solve approximate basis, eigenvalue, eigenvector for each type of sample respectively;
步骤8)分别计算每个测试样本的SPE，其值与某类样本的SPE差值最小者为测试样本的预测类别，与实际类别比较，计算准确率，若满足要求则步骤9，否则返回步骤6重新设置参数训练；Step 8) Calculate the SPE of each test sample respectively, the smallest difference between its value and the SPE of a certain type of sample is the predicted category of the test sample, compare with the actual category, calculate the accuracy, if it meets the requirements, then step 9, otherwise return to step 9 6 reset the parameter training;
步骤9)获得参数，算法结束。Step 9) The parameters are obtained, and the algorithm ends.
稀疏核主分量分析的基本方法：The basic method of sparse kernel principal component analysis:
主分量分析是一种典型的无监督算法，常用于解决原始空间的线性问题，而为了在特征空间中用线性方法解决原始空间的非线性问题，B.Scholkopf等人提出了核主分量分析(Kernel Principal Component Analysis,KPCA)。Principal component analysis is a typical unsupervised algorithm, which is often used to solve the linear problem of the original space. In order to solve the nonlinear problem of the original space with a linear method in the feature space, B. Scholkopf et al. proposed the kernel principal component analysis ( Kernel Principal Component Analysis, KPCA).
定义从原始空间Rn到特征空间F的非线性映射:假如给定的样本X＝{x1,…,xN},xi∈Rn，则通过映射可以获得一组向量假设该组向量满足则特征空间中的相关阵为Define a nonlinear mapping from the original space R n to the feature space F: If a given sample X={x 1 ,...,x N }, xi ∈R n , then by Mapping can get a set of vectors Suppose the set of vectors satisfies Then the correlation matrix in the feature space is
如果该组向量则可令可知满足条件，代替式中的则KPCA问题可以转换为求特征空间中相关阵的特征值λ即特征向量 If the set of vectors can make know Satisfy the condition, replace the Then the KPCA problem can be transformed into finding the correlation matrix in the feature space The eigenvalue λ of is the eigenvector
其中，是样本的线性组合，令ɑ＝[ɑ1,…,ɑN]T，则当不能显式获得的时候，引入核函数，设首先需要计算：in, is a linear combination of samples, let ɑ＝[ɑ 1 ,…,ɑ N ] T , then when When it cannot be obtained explicitly, introduce a kernel function, set First you need to calculate:
K＝ΦTΦK= ΦTΦ
其中，矩阵K是NxN的矩阵，也称核矩阵。则问题转换为：Among them, the matrix K is an NxN matrix, also called a kernel matrix. Then the problem translates to:
Kɑ＝NλɑKɑ=Nλɑ
其中，ɑ＝[ɑ1,…,ɑN]。当中心化的过程可以直接在K上运算：Among them, ɑ=[ɑ 1 ,…,ɑ N ]. when The centralization process can operate directly on K:
其中，满足是一个NxN的1矩阵。假设得到的特征值λ1≥λ2≥…λn及其对应的特征向量ɑ1,ɑ2,…,ɑN，在特征空间中的第k个特征向量ɑi,k表示的第k个特征向量的第i个值，由归一化得变量x在归一化之后的第k个特征向量方向的投影为第k个主分量，公式为in, Satisfy is an NxN matrix of 1s. suppose to get The eigenvalues λ1≥λ2≥…λn and their corresponding eigenvectors ɑ 1 ,ɑ 2 ,…,ɑ N , the kth eigenvector in the feature space ɑ i,k means The i-th value of the k-th eigenvector of , given by normalized the k-th eigenvector of the variable x after normalization The projection of the direction is the kth principal component, and the formula is
本发明选择一种常用的核函数，径向基核函数来进行计算。当选择径向基核函数时，会有明显的过学习问题，主要是由于径向基核函数对应的特征空间是无线维的，通过该方法得出的主分量的次数与给定样本的维数无关，而与样本数量有关。为解决这个问题，引入了稀疏化方法，即为稀疏核主分量分析(Sparse Kernel Principal ComponentAnalysis,SKPCA)。The present invention selects a commonly used kernel function, the radial basis kernel function, for calculation. When the radial basis kernel function is selected, there will be obvious over-learning problems, mainly because the feature space corresponding to the radial basis kernel function is wireless dimensional, and the number of principal components obtained by this method is related to the dimension of the given sample is not related to the number of samples, but to the number of samples. To solve this problem, a sparse method, namely Sparse Kernel Principal Component Analysis (SKPCA), is introduced.
在核主分量分析中，特征向量能用样本表示为也就是说特征向量是全部样本的线性组合，这为特征向量的稀疏化提供了一种思路。通过近似基求解算法，来求的近似基，从而得到的稀疏化方法。In Kernel Principal Component Analysis, the eigenvectors can be used as samples Expressed as That is, the feature vector is a linear combination of all samples, which provides an idea for the sparseness of feature vectors. Through the approximate basis solving algorithm, to find approximation basis, so that we get sparse method.
近似基求解的具体步骤是：The specific steps of approximate basis solution are:
1.建立集合为近似最大无关组，XA＝φ；1. Build a collection is an approximate maximum independent group, X A = φ;
2.对于k＝2,...,N的求极小值value；2. For k=2,...,N Find the minimum value;
3.如果得到极小值value≤ε，则把对应的元素加到XA当中，否则为Xl。3. If the minimum value value≤ε is obtained, add the corresponding element to X A , otherwise it is X l .
ε是线性相关截尾误差，在有限的样本中求无限维空间的基几乎没有稀疏性，因此选择近似计算。ε is the linear correlation truncation error. There is almost no sparsity in finding the basis of infinite dimensional space in limited samples, so approximate calculation is chosen.
4.返回步骤2，直至完成所有的计算，计算结束。4. Return to step 2 until all calculations are completed and the calculation is over.
其中，步骤2中的求解过程如下：令Among them, the solution process in step 2 is as follows:
由Lagrange条件得-2K0+2Kλ＝0，其中K0＝(k(x1,xk),…,k(xl,xk))T，K是方阵，Kij＝k(xi,xj)。当核函数是高斯径向基核函数时，矩阵K正定，得λmin＝K-1K0即为f(λ)的极小值点。Condition by Lagrange Get -2K 0 +2Kλ=0, where K 0 =(k(x 1 ,x k ),...,k(x l ,x k )) T , K is a square matrix, K ij =k(x i ,x j ). When the kernel function is a Gaussian radial basis kernel function, the matrix K is positive definite, and λ min =K -1 K 0 is the minimum value point of f(λ).
假设求得的一组近似基为用Assuming that a set of approximate bases obtained is use
表示近似基构成的基向量，特征向量可以表示为问题转成 Represents the basis vector formed by the approximate basis, and the eigenvector can be expressed as problem turned into
两边同乘记得Multiply both sides remember have to
可知是特征值与特征向量的问题，即令则It can be seen that it is a problem of eigenvalues and eigenvectors, that is, make but
推导得deduced
其中，K(m,:)表示核矩阵K的第m行，K(:,n)表示第n列，1N＝[1,...,1]表示1行N列的行向量。问题也就转换成了(KI)-1Ksα＝λα，为典型的特征值与特征向量问题。Among them, K(m,:) represents the mth row of the kernel matrix K, K(:,n) represents the nth column, and 1 N =[1,...,1] represents a row vector of 1 row and N columns. The problem is transformed into (K I ) -1 K s α=λα, which is a typical eigenvalue and eigenvector problem.
附图说明Description of drawings
图1为本发明具体方法流程图；Fig. 1 is the specific method flow chart of the present invention;
图2为部分测试样本与各类的SPE差值；Figure 2 shows the SPE difference between some test samples and various types;
图3为某次部分测试结果与实际标记样本对比图。Figure 3 is a comparison diagram of a part of the test results and the actual marked samples.
具体实施方式Detailed ways
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.
如附图1所示，一种基于稀疏核主分量分析的RdR散点图识别方法，包括以下步骤：As shown in accompanying drawing 1, a kind of RdR scatterplot identification method based on sparse kernel principal component analysis, comprises the following steps:
步骤1)获取心电信号，对心电信号进行滤波去噪处理，提取R波峰值位置；Step 1) Acquire the ECG signal, perform filtering and denoising processing on the ECG signal, and extract the peak position of the R wave;
步骤2)使用心搏间期绘制RdR散点图，可以通过MATLAB等工具来绘制；Step 2) Use the heartbeat interval to draw the RdR scatter diagram, which can be drawn by tools such as MATLAB;
步骤3)对RdR散点图进行缩放，转成灰度图，并对图像数据进行归一化处理，以减少计算量；Step 3) scaling the RdR scattergram, converting it into a grayscale image, and normalizing the image data to reduce the amount of computation;
步骤4)对获得的散点图样本进行标记；Step 4) marking the obtained scatter plot samples;
步骤5)对样本进行采样，随机抽取75％的数据作为训练样本；Step 5) Sampling the samples, randomly extracting 75% of the data as training samples;
步骤6)设置参数，参数包括近似基的误差参数、高斯核函数参数以及控制限的值；Step 6) setting parameters, the parameters include the error parameter of the approximate basis, the Gaussian kernel function parameter and the value of the control limit;
步骤7)分别对每类样本求解近似基、特征值、特征向量；Step 7) solve approximate basis, eigenvalue, eigenvector for each type of sample respectively;
步骤8)分别计算每个测试样本的SPE，其值与某类样本的SPE差值最小者为测试样本的预测类别，与实际类别比较，计算准确率，若满足要求则步骤9，否则返回步骤6重新设置参数训练；Step 8) Calculate the SPE of each test sample respectively, the smallest difference between its value and the SPE of a certain type of sample is the predicted category of the test sample, compare with the actual category, calculate the accuracy, if it meets the requirements, then step 9, otherwise return to step 9 6 reset the parameter training;
步骤9)获得参数，算法结束。Step 9) The parameters are obtained, and the algorithm ends.
为便于叙述，使用MIT-BIH数据库中的心电数据，以此数据库的数据作示意性分析介绍。图2是从样本中，选择部分测试样本与各类计算SPE的差值，如选择到类别为“3”的样本，将其分别与各类计算其SPE的最小差值，结果如图(2)，可以看到其与类别为“3”的SPE差值最小。图3是依据本发明方法，某次部分测试结果与实际标记样本对比图，参数true是实际的样本类别，predicted是本发明方法判定的类别，可以看出准确率较高。For the convenience of description, the ECG data in the MIT-BIH database is used, and the data in this database is used as a schematic analysis and introduction. Figure 2 shows the difference between some test samples and various types of calculated SPEs from the samples. For example, if a sample with category "3" is selected, the minimum difference of SPE is calculated with each type, and the result is shown in Figure (2) ), it can be seen that it has the smallest SPE difference with the category "3". Fig. 3 is a comparison diagram of a partial test result and an actual marked sample according to the method of the present invention. The parameter true is the actual sample type, and predicted is the type determined by the method of the present invention. It can be seen that the accuracy rate is high.
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