卖钢材做哪个宣传网站,太原市城市建设规划局官方网站,wordpress获取链接,济南模板网站制作有时数据的分类并不像我们想象的那么简单#xff0c;需要高次曲线才能分类。
就像下面的数据#xff1a; 数据集最后给出#xff1a;
我们这样看#xff0c;至少需要达到2次以及以上的曲线才可以进行比较准确的分类。
比如如果已知数据有3列(两列特征)
x1x2y-1-110.50.…有时数据的分类并不像我们想象的那么简单需要高次曲线才能分类。
就像下面的数据 数据集最后给出
我们这样看至少需要达到2次以及以上的曲线才可以进行比较准确的分类。
比如如果已知数据有3列(两列特征)
x1x2y-1-110.50.50011 那么我们的目标是 [ 1, x1, x2, x1*x2, x1^2, x2^2 ] 现在的问题是如何将已经有的两列转化为这么6列
我们可以按照以下推导 def feature_mapping(x1, x2, power):data {}for i in range(0, power 1):for j in range(power - i 1):data[f{}{}.format(i,j)]np.power(x1,i)*np.power(x2,j)return pd.DataFrame(data)x1data[Exam1]
x2data[Exam2]data2feature_mapping(x1,x2,2)
print(data2.head()) f00 f01 f02 f10 f11 f20 0 1.0 0.69956 0.489384 0.051267 0.035864 0.002628 1 1.0 0.68494 0.469143 -0.092742 -0.063523 0.008601 2 1.0 0.69225 0.479210 -0.213710 -0.147941 0.045672 3 1.0 0.50219 0.252195 -0.375000 -0.188321 0.140625 4 1.0 0.46564 0.216821 -0.513250 -0.238990 0.263426 取数据集
x1 data[Exam1]
x2 data[Exam2]data2 feature_mapping(x1, x2, 2)
# print(data2.head())X data2.values
print(X.shape)
y data[Accepted].values.reshape((len(data.iloc[:,-1]), 1))
print(y.shape) (118, 6) (118, 1) 损失函数
因为非线性的很容易进行过拟合所以需要进行正则化。
那么什么是正则化呢
我们先看一下最后得到的损失函数的形式 这里面的最后一项用来调节参数防止出现过拟合和欠拟合。
注意这里的j是从1开始的我们原来的X多加了一列1(索引为0)这里从1开始的没有计算哪个常数。
求导后
for j0: for j1: def sigmoid(z):return 1.0 / (1 np.exp(-z))def cost_function(X, y, theta, lamba):A sigmoid(X theta)first y * np.log(A)second (1 - y) * np.log(1 - A)reg np.sum(np.power(theta[1:], 2)) * lamba / (2 * len(X))return -np.sum(first second) / len(X) regtheta np.zeros((28,1))
lamda 1
cost_init cost_function(X,y,theta,lamda)
print(cost_init) 0.6931471805599454 梯度下降
def gradientDescent(X, y, theta, alpha, iters, lamba):costs []m len(X)reg theta[1:] * lamba / m #后面的惩罚项防止过拟合reg np.insert(reg, 0, values0, axis0) #每次将常数置为0for i in range(iters):A sigmoid(X theta) #预测值theta theta - alpha / m * (X.T (A - y) reg) #梯度下降cost cost_function(X, y, theta, lamba) #损失函数costs.append(cost) return costs, theta 预测
alpha 0.001
iters 200000
lamba 0.001
costs, theta gradientDescent(X, y,theta,alpha,iters,lamba)print(---------------------------)
print(theta)plt.figure()
plt.plot(range(iters), costs, labelCost)
plt.xlabel(Iterations)
plt.ylabel(Cost)
plt.title(Cost Function Convergence)
plt.legend()
plt.show()def predict(X,theta):pre sigmoid(Xtheta)return [1 if i 0.5 else 0 for i in pre ]y_pre predict(X,theta)# 绘制真实值与预测值的比较图
plt.figure()
plt.plot(range(len(y)), y, labelreal_values, linestyle-, markero, colorg)
plt.plot(range(len(y)), y_pre, labelpre_value, linestyle--, markerx, colorr)
plt.xlabel(label)
plt.ylabel(value)
plt.title(differ)
plt.legend()
plt.show() theta[[ 1.87511207] [ 2.023306 ] [-2.13296198] [-0.23971119] [-1.94042125] [-0.757585 ] [-1.56403399] [ 1.18536314] [-1.68977623] [-0.63345976] [-0.53685159] [-0.54677843] [-0.29785185] [-3.10618505] [-0.67450464] [-1.02252107] [-0.48703712] [-0.55736928] [ 0.32233067] [-0.14001433] [-0.07578518] [ 0.00558004] [-2.37395054] [-0.38709684] [-0.49270366] [-0.35696397] [ 0.01562081] [-1.74571902]] 整体代码
import pandas as pd
import numpy as np
import matplotlibmatplotlib.use(tKAgg)
import matplotlib.pyplot as plt# 读取数据
path d:\\JD\\Documents\\大学等等等\\自学部分\\machine_-learning-master\\machine_-learning-master\\ex_2\\ex2data2.txt
data pd.read_csv(path, names[Exam1, Exam2, Accepted])
print(data.head())# fig, ax plt.subplots()
# ax.scatter(data[data[Accepted] 0][Exam1], data[data[Accepted] 0][Exam2], cr, markerx, labely0)
# ax.scatter(data[data[Accepted] 1][Exam1], data[data[Accepted] 1][Exam2], cg, markero, labely1)
# ax.legend()
# ax.set(
# xlabelexam1,
# ylabelexam2
# )
# plt.show()def feature_mapping(x1, x2, power):data {}for i in range(0, power 1):for j in range(power - i 1):data[f{}{}.format(i, j)] np.power(x1, i) * np.power(x2, j)return pd.DataFrame(data)x1 data[Exam1]
x2 data[Exam2]data2 feature_mapping(x1, x2, 6)
# print(data2.head())X data2.values
print(X.shape)
y data[Accepted].values.reshape((len(data.iloc[:, -1]), 1))
print(y.shape)def sigmoid(z):return 1.0 / (1 np.exp(-z))def cost_function(X, y, theta, lamba):A sigmoid(X theta)first y * np.log(A)second (1 - y) * np.log(1 - A)reg np.sum(np.power(theta[1:], 2)) * lamba / (2 * len(X))return -np.sum(first second) / len(X) regtheta np.zeros((28, 1))
lamda 1# cost_init cost_function(X,y,theta,lamda)
# print(cost_init)def gradientDescent(X, y, theta, alpha, iters, lamba):costs []m len(X)reg theta[1:] * lamba / mreg np.insert(reg, 0, values0, axis0)for i in range(iters):A sigmoid(X theta)theta theta - alpha / m * (X.T (A - y) reg)cost cost_function(X, y, theta, lamba)costs.append(cost)return costs, thetaalpha 0.001
iters 200000
lamba 0.001
costs, theta gradientDescent(X, y,theta,alpha,iters,lamba)print(---------------------------)
print(theta)plt.figure()
plt.plot(range(iters), costs, labelCost)
plt.xlabel(Iterations)
plt.ylabel(Cost)
plt.title(Cost Function Convergence)
plt.legend()
plt.show()def predict(X,theta):pre sigmoid(Xtheta)return [1 if i 0.5 else 0 for i in pre ]y_pre predict(X,theta)# 绘制真实值与预测值的比较图
plt.figure()
plt.plot(range(len(y)), y, labelreal_values, linestyle-, markero, colorg)
plt.plot(range(len(y)), y_pre, labelpre_value, linestyle--, markerx, colorr)
plt.xlabel(label)
plt.ylabel(value)
plt.title(differ)
plt.legend()
plt.show() 附件
数据集 0.051267,0.69956,1 -0.092742,0.68494,1 -0.21371,0.69225,1 -0.375,0.50219,1 -0.51325,0.46564,1 -0.52477,0.2098,1 -0.39804,0.034357,1 -0.30588,-0.19225,1 0.016705,-0.40424,1 0.13191,-0.51389,1 0.38537,-0.56506,1 0.52938,-0.5212,1 0.63882,-0.24342,1 0.73675,-0.18494,1 0.54666,0.48757,1 0.322,0.5826,1 0.16647,0.53874,1 -0.046659,0.81652,1 -0.17339,0.69956,1 -0.47869,0.63377,1 -0.60541,0.59722,1 -0.62846,0.33406,1 -0.59389,0.005117,1 -0.42108,-0.27266,1 -0.11578,-0.39693,1 0.20104,-0.60161,1 0.46601,-0.53582,1 0.67339,-0.53582,1 -0.13882,0.54605,1 -0.29435,0.77997,1 -0.26555,0.96272,1 -0.16187,0.8019,1 -0.17339,0.64839,1 -0.28283,0.47295,1 -0.36348,0.31213,1 -0.30012,0.027047,1 -0.23675,-0.21418,1 -0.06394,-0.18494,1 0.062788,-0.16301,1 0.22984,-0.41155,1 0.2932,-0.2288,1 0.48329,-0.18494,1 0.64459,-0.14108,1 0.46025,0.012427,1 0.6273,0.15863,1 0.57546,0.26827,1 0.72523,0.44371,1 0.22408,0.52412,1 0.44297,0.67032,1 0.322,0.69225,1 0.13767,0.57529,1 -0.0063364,0.39985,1 -0.092742,0.55336,1 -0.20795,0.35599,1 -0.20795,0.17325,1 -0.43836,0.21711,1 -0.21947,-0.016813,1 -0.13882,-0.27266,1 0.18376,0.93348,0 0.22408,0.77997,0 0.29896,0.61915,0 0.50634,0.75804,0 0.61578,0.7288,0 0.60426,0.59722,0 0.76555,0.50219,0 0.92684,0.3633,0 0.82316,0.27558,0 0.96141,0.085526,0 0.93836,0.012427,0 0.86348,-0.082602,0 0.89804,-0.20687,0 0.85196,-0.36769,0 0.82892,-0.5212,0 0.79435,-0.55775,0 0.59274,-0.7405,0 0.51786,-0.5943,0 0.46601,-0.41886,0 0.35081,-0.57968,0 0.28744,-0.76974,0 0.085829,-0.75512,0 0.14919,-0.57968,0 -0.13306,-0.4481,0 -0.40956,-0.41155,0 -0.39228,-0.25804,0 -0.74366,-0.25804,0 -0.69758,0.041667,0 -0.75518,0.2902,0 -0.69758,0.68494,0 -0.4038,0.70687,0 -0.38076,0.91886,0 -0.50749,0.90424,0 -0.54781,0.70687,0 0.10311,0.77997,0 0.057028,0.91886,0 -0.10426,0.99196,0 -0.081221,1.1089,0 0.28744,1.087,0 0.39689,0.82383,0 0.63882,0.88962,0 0.82316,0.66301,0 0.67339,0.64108,0 1.0709,0.10015,0 -0.046659,-0.57968,0 -0.23675,-0.63816,0 -0.15035,-0.36769,0 -0.49021,-0.3019,0 -0.46717,-0.13377,0 -0.28859,-0.060673,0 -0.61118,-0.067982,0 -0.66302,-0.21418,0 -0.59965,-0.41886,0 -0.72638,-0.082602,0 -0.83007,0.31213,0 -0.72062,0.53874,0 -0.59389,0.49488,0 -0.48445,0.99927,0 -0.0063364,0.99927,0 0.63265,-0.030612,0
