转载并整理自： https://www.codenong.com/p12366364/ https://www.codenong.com/p12368419/

灰色关联度分析

# -*- coding: utf-8 -*- from sklearn.preprocessing import StandardScaler import pandas as pd import numpy as np import os class GraModel(): '''灰色关联度分析模型''' def __init__(self, inputData, p=0.5, standard=True): ''' 初始化参数 inputData：输入矩阵，纵轴为属性名，第一列为母序列 p：分辨系数，范围0~1，一般取0.5，越小，关联系数间差异越大，区分能力越强 standard：是否需要标准化 ''' self.inputData = np.array(inputData) self.p = p self.standard = standard # 标准化 self.standarOpt() # 建模 self.buildModel() def standarOpt(self): '''标准化输入数据''' if not self.standard: return None self.scaler = StandardScaler().fit(self.inputData) self.inputData = self.scaler.transform(self.inputData) def buildModel(self): # 第一列为母列，与其他列求绝对差 momCol = self.inputData[:, 0] sonCol = self.inputData[:, 0:] for col in range(sonCol.shape[1]): sonCol[:, col] = abs(sonCol[:, col] - momCol) # 求两级最小差和最大差 minMin = sonCol.min() maxMax = sonCol.max() # 计算关联系数矩阵 cors = (minMin + self.p * maxMax) / (sonCol + self.p * maxMax) # 求平均综合关联度 meanCors = cors.mean(axis=0) self.result = {'cors': {'value': cors, 'desc': '关联系数矩阵'}, 'meanCors': {'value': meanCors, 'desc': '平均综合关联系数'}} if __name__ == "__main__": # # 路径目录 # curDir = os.path.dirname(os.path.abspath(__file__)) # 当前目录 # baseDir = os.path.dirname(curDir) # 根目录 # staticDir = os.path.join(baseDir, 'Static') # 静态文件目录 # resultDir = os.path.join(baseDir, 'Result') # 结果文件目录 # 读数 data = [ [1, 1.1, 2, 2.25, 3, 4], [1, 1.166, 1.834, 2, 2.314, 3], [1, 1.125, 1.075, 1.375, 1.625, 1.75], [1, 1, 0.7, 0.8, 0.9, 1.2] ] data = np.array(data).T # 建模 model = GraModel(data, standard=True) print(model.result)

灰色预测

# -*- coding: utf-8 -*- import matplotlib.pyplot as plt import pandas as pd import numpy as np def GM11(x, n): ''' 灰色预测 x：序列，numpy对象 n:需要往后预测的个数 ''' x1 = x.cumsum() # 一次累加 z1 = (x1[:len(x1) - 1] + x1[1:]) / 2.0 # 紧邻均值 z1 = z1.reshape((len(z1), 1)) B = np.append(-z1, np.ones_like(z1), axis=1) Y = x[1:].reshape((len(x) - 1, 1)) # a为发展系数 b为灰色作用量 [[a], [b]] = np.dot(np.dot(np.linalg.inv(np.dot(B.T, B)), B.T), Y) # 计算参数 result = (x[0] - b / a) * np.exp(-a * (n - 1)) - (x[0] - b / a) * np.exp(-a * (n - 2)) S1_2 = x.var() # 原序列方差 e = list() # 残差序列 for index in range(1, x.shape[0] + 1): predict = (x[0] - b / a) * np.exp(-a * (index - 1)) - (x[0] - b / a) * np.exp(-a * (index - 2)) e.append(x[index - 1] - predict) S2_2 = np.array(e).var() # 残差方差 C = S2_2 / S1_2 # 后验差比 if C <= 0.35: assess = '后验差比<=0.35，模型精度等级为好' elif C <= 0.5: assess = '后验差比<=0.5，模型精度等级为合格' elif C <= 0.65: assess = '后验差比<=0.65，模型精度等级为勉强' else: assess = '后验差比>0.65，模型精度等级为不合格' # 预测数据 predict = list() for index in range(x.shape[0] + 1, x.shape[0] + n + 1): predict.append((x[0] - b / a) * np.exp(-a * (index - 1)) - (x[0] - b / a) * np.exp(-a * (index - 2))) predict = np.array(predict) return { 'a': {'value': a, 'desc': '发展系数'}, 'b': {'value': b, 'desc': '灰色作用量'}, 'predict': {'value': result, 'desc': '第%d个预测值' % n}, 'C': {'value': C, 'desc': assess}, 'predict': {'value': predict, 'desc': '往后预测%d个的序列' % (n)}, } if __name__ == "__main__": data = np.array([1.2, 2.2, 3.1, 4.5, 5.6, 6.7, 7.1, 8.2, 9.6, 10.6, 11, 12.4, 13.5, 14.7, 15.2]) x = data[0:10] # 输入数据 y = data[10:] # 需要预测的数据 result = GM11(x, len(y)) predict = result['predict']['value'] predict = np.round(predict, 1) print('真实值:', y) print('预测值:', predict) print(result)