增加前向逐步回归

Regression/regression.py

@@ -112,7 +112,7 @@ def regularize(xMat, yMat):
 	Website:
 		http://www.cuijiahua.com/
 	Modify:
-		2017-11-23
+		2017-12-03
 	"""	
 	inxMat = xMat.copy()														#数据拷贝
 	inyMat = yMat.copy()
@@ -123,44 +123,81 @@ def regularize(xMat, yMat):
 	inxMat = (inxMat - inMeans) / inVar											#数据减去均值除以方差实现标准化
 	return inxMat, inyMat
 
+def rssError(yArr,yHatArr):
+	"""
+	函数说明:计算平方误差
+	Parameters:
+		yArr - 预测值
+		yHatArr - 真实值
+	Returns:
+		
+	Website:
+		http://www.cuijiahua.com/
+	Modify:
+		2017-12-03
+	"""
+	return ((yArr-yHatArr)**2).sum()
+
 def stageWise(xArr, yArr, eps = 0.01, numIt = 100):
 	"""
 	函数说明:前向逐步线性回归
 	Parameters:
-		xArr - x数据集
-		yArr - y数据集
+		xArr - x输入数据
+		yArr - y预测数据
+		eps - 每次迭代需要调整的步长
+		numIt - 迭代次数
 	Returns:
-		
+		returnMat - numIt次迭代的回归系数矩阵
 	Website:
 		http://www.cuijiahua.com/
 	Modify:
-		2017-11-23
+		2017-12-03
 	"""
 	xMat = np.mat(xArr); yMat = np.mat(yArr).T 										#数据集
-	yMean = np.mean(yMat, 0)														#计算y的均值
-	yMat = yMat - yMean																#
-	xMat = regularize(xMat)
+	xMat, yMat = regularize(xMat, yMat)												#数据标准化
 	m, n = np.shape(xMat)
-	returnMat = np.zeros((numIt, n))
-	ws = np.zeros((n, 1))
+	returnMat = np.zeros((numIt, n))												#初始化numIt次迭代的回归系数矩阵
+	ws = np.zeros((n, 1))															#初始化回归系数矩阵
 	wsTest = ws.copy()
 	wsMax = ws.copy()
-	for i in range(numIt):
-		print ws.T
-		lowestError = inf; 
-		for j in range(n):
-			for sign in [-1,1]:
+	for i in range(numIt):															#迭代numIt次
+		# print(ws.T)																	#打印当前回归系数矩阵
+		lowestError = float('inf'); 												#正无穷
+		for j in range(n):															#遍历每个特征的回归系数
+			for sign in [-1, 1]:
 				wsTest = ws.copy()
-				wsTest[j] += eps*sign
-				yTest = xMat*wsTest
-				rssE = rssError(yMat.A,yTest.A)
-				if rssE < lowestError:
+				wsTest[j] += eps * sign												#微调回归系数
+				yTest = xMat * wsTest												#计算预测值
+				rssE = rssError(yMat.A, yTest.A)									#计算平方误差
+				if rssE < lowestError:												#如果误差更小，则更新当前的最佳回归系数
 					lowestError = rssE
 					wsMax = wsTest
 		ws = wsMax.copy()
-		returnMat[i,:] = ws.T
+		returnMat[i,:] = ws.T 														#记录numIt次迭代的回归系数矩阵
 	return returnMat
 
-if __name__ == '__main__':
+def plotstageWiseMat():
+	"""
+	函数说明:绘制岭回归系数矩阵
+	Website:
+		http://www.cuijiahua.com/
+	Modify:
+		2017-12-03
+	"""
+	font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)
 	xArr, yArr = loadDataSet('abalone.txt')
-	stageWise(xArr, yArr)
+	returnMat = stageWise(xArr, yArr, 0.005, 1000)
+	fig = plt.figure()
+	ax = fig.add_subplot(111)
+	ax.plot(returnMat)	
+	ax_title_text = ax.set_title(u'前向逐步回归:迭代次数与回归系数的关系', FontProperties = font)
+	ax_xlabel_text = ax.set_xlabel(u'迭代次数', FontProperties = font)
+	ax_ylabel_text = ax.set_ylabel(u'回归系数', FontProperties = font)
+	plt.setp(ax_title_text, size = 15, weight = 'bold', color = 'red')
+	plt.setp(ax_xlabel_text, size = 10, weight = 'bold', color = 'black')
+	plt.setp(ax_ylabel_text, size = 10, weight = 'bold', color = 'black')
+	plt.show()
+
+
+if __name__ == '__main__':
+	plotstageWiseMat()