基于小波分析和机器学习的时间序列分析与识别

研究对象：ECG等时间序列信号

方法：小波变换，简单神经网络

首先导入相关模块，需要安装尺度谱模块：pip install scaleogram

和mat4py模块：pip install mat4py

import numpy as np
import pandas as pd
import pywt
import seaborn as sns
import scaleogram as scg
import matplotlib.pyplot as plt
import matplotlib.gridspec as GridSpec
from mat4py import loadmat
from scipy.fftpack import fft

导入数据，并提取标签

data = loadmat("ECGData.mat")
ecg_total = len(data['ECGData']['Data'])
ecg_data = []
ecg_labels = []
for i in range(0, ecg_total):
    ecg_data.append(data['ECGData']['Data'][i])
    ecg_labels.append(data['ECGData']['Labels'][i])

flat_list_ecg_labels = [item for sublist in ecg_labels for item in sublist]

数据可视化

fig = plt.figure(figsize=(12, 6))
grid = plt.GridSpec(3, 1, hspace=0.6)

arr_signal = fig.add_subplot(grid[0, 0])
chg_signal = fig.add_subplot(grid[1, 0])
nsr_signal = fig.add_subplot(grid[2, 0])

arr_signal.plot(range(0, len(data['ECGData']['Data'][33]), 1), ecg_data[33], color = 'blue')
arr_signal.set_xlim(0, 1000)
arr_signal.set_title('ARR Signal')

chg_signal.plot(range(0, len(data['ECGData']['Data'][100]), 1), ecg_data[100], color = 'red')
chg_signal.set_xlim(0, 1000)
chg_signal.set_title('CHG Signal')

nsr_signal.plot(range(0, len(data['ECGData']['Data'][150]), 1), ecg_data[150], color = 'green')
nsr_signal.set_xlim(0, 1000)
nsr_signal.set_title('NSR Signal')

进行傅里叶变换

nn = 160
signal_length = 1000
full_signal_fft_values = np.abs(fft(ecg_data[nn][:signal_length]))
x_values_fft = range(0, len(data['ECGData']['Data'][nn]), 1)[:signal_length]

fig = plt.figure(figsize=(12, 6))
grid = plt.GridSpec(2, 1,hspace=0.6)

full_signal = fig.add_subplot(grid[0, 0])
fft_comp = fig.add_subplot(grid[1, 0])

full_signal.plot(x_values_fft, ecg_data[nn][:signal_length], color = 'green')
full_signal.set_xlim(0, 512)
full_signal.set_title('Full Signal')
fft_comp.plot(x_values_fft, list(full_signal_fft_values), color = 'purple')
fft_comp.set_xlim(0, 512)
fft_comp.set_ylim(0, 100)
fft_comp.set_title('FFT of full signal')

看下所用的Morlet小波啥个样子

axes = scg.plot_wav('morl', figsize=(12,4))

顺便看下小波族大致包含多少小波类

pywt.families(False)

[‘Haar’,

‘Daubechies’,

‘Symlets’,

‘Coiflets’,

‘Biorthogonal’,

‘Reverse biorthogonal’,

‘Discrete Meyer (FIR Approximation)’,

‘Gaussian’,

‘Mexican hat wavelet’,

‘Morlet wavelet’,

‘Complex Gaussian wavelets’,

‘Shannon wavelets’,

‘Frequency B-Spline wavelets’,

‘Complex Morlet wavelets’]

顺便再给几个小波的波形及相应的频谱

下面进行小波尺度谱变换

选择一个默认的小波
scg.set_default_wavelet('morl')

nn = 33
signal_length = 128
小波变换的尺度范围
scales = scg.periods2scales( np.arange(1, signal_length+1) )
x_values_wvt_arr = range(0,len(ecg_data[nn]),1)

绘制信号
fig1, ax1 = plt.subplots(1, 1, figsize=(9, 3.5));
ax1.plot(x_values_wvt_arr, ecg_data[nn], linewidth=3, color='blue')
ax1.set_xlim(0, signal_length)
ax1.set_title("ECG ARR")

计算小波时间-尺度谱
scg.cws(ecg_data[nn][:signal_length], scales=scales, figsize=(10, 4.0), coi = False, ylabel="Period", xlabel="Time",
        title='ECG_ARR: scaleogram with linear period');

print("Default wavelet function used to compute the transform:", scg.get_default_wavelet(), "(",
      pywt.ContinuousWavelet(scg.get_default_wavelet()).family_name, ")")

下面开始进行机器学习识别，首先准备机器学习所需要的数据

arr_list = ecg_data[0:95]
chf_list = ecg_data[96:125]
nsr_list = ecg_data[126:162]

arr_split_256 = [np.array_split(arr_list[ii], 256) for ii in range(95)]
arr_flatten = [item for sublist in arr_split_256 for item in sublist]

chf_split_256 = [np.array_split(chf_list[ii], 256) for ii in range(29)]
chf_flatten = [item for sublist in chf_split_256 for item in sublist]

nsr_split_256 = [np.array_split(nsr_list[ii], 256) for ii in range(36)]
nsr_flatten = [item for sublist in nsr_split_256 for item in sublist]

reduce_size = 500
full_1500 = (arr_flatten[0:reduce_size] + chf_flatten[0:reduce_size] + nsr_flatten[0:reduce_size])

创建数据集

#机器学习相干模块
from sklearn import preprocessing
from sklearn.model_selection import train_test_split

fs = len(full_1500[0])
sgn_length = 2000   #信号长度
size_dataset = len(full_1500)
scales = range(1, fs)
waveletname = 'morl'   #小波

X_full = np.ndarray(shape=(size_dataset, fs-1, fs-1, 3))
 #开始生成数据
for i in range(0, size_dataset):
    if i % 500 == 0:
        print (i, 'done!')
    for j in range(0, 3):
        signal = full_1500[i]
        coeff, freq = pywt.cwt(signal, scales, waveletname, 1)
        X_full[i, :, :, j] = coeff[:,:fs-1]
#相应的标签
list_ecg_labels_arr = ['ARR']*reduce_size
list_ecg_labels_chf = ['CHF']*reduce_size
list_ecg_labels_nsr = ['NSR']*reduce_size
list_ecg_labels = (list_ecg_labels_arr + list_ecg_labels_chf + list_ecg_labels_nsr)

le = preprocessing.LabelEncoder()
ecg_labels_encoded = le.fit_transform(list_ecg_labels)
X_train, X_test, y_train, y_test = train_test_split(X_full, ecg_labels_encoded, test_size=0.25, random_state=42)

使用尺度谱训练ECG分类器

import sys
from tensorflow import keras

查看一下训练数据

定义基本的神经网络

num_filter, num_classes = 3, 3
model = keras.models.Sequential([
    keras.layers.Flatten(input_shape=[fs-1, fs-1, num_filter]),
    keras.layers.Dense(300, activation="relu"),
    keras.layers.Dense(100, activation="relu"),
    keras.layers.Dense(num_classes, activation="softmax")
])
model.compile(loss="sparse_categorical_crossentropy",
              optimizer="sgd", metrics=["accuracy"])

model.summary()

训练模型

history = model.fit(X_train, y_train, epochs=10, validation_data=(X_test, y_test))

model.evaluate(X_test, y_test)

def plot_learning_curves(history):
    pd.DataFrame(history.history).plot(figsize=(8, 5))
    plt.grid(True)
    plt.gca().set_ylim(0, 1)
    plt.xlabel('epochs', size = 16)
    plt.xticks(fontsize=14)
    plt.yticks(fontsize=14)
    plt.savefig('Figure_epochs.png')
    plt.close()

plot_learning_curves(history)

prediction = model.predict(X_test)
pred_classes = prediction.argmax(axis=1)

绘制混淆矩阵

cm = confusion_matrix(y_test, pred_classes)
cm_norm =  cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]

df_cm = pd.DataFrame(cm_norm, ['ARR', 'CHF', 'NSR'], ['ARR', 'CHF', 'NSR'])
plt.figure(figsize = (10,6))
conf = sns.heatmap(df_cm, annot=True, square=True, annot_kws={"size": 12})
conf.set_xlabel('Prediction')
conf.set_ylabel('True')

基于小波分析和机器学习的时间序列分析与识别 – 哥廷根数学学派的文章 – 知乎 https://zhuanlan.zhihu.com/p/554097033

Original: https://blog.csdn.net/weixin_39402231/article/details/126369488
Author: 哥廷根数学学派
Title: 基于小波分析和机器学习的时间序列分析与识别