# -*- coding: utf-8 -*-
#
# Perceptronによる二項分類
#
# 2015/04/24 ver1.0
#
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from pandas import Series, DataFrame
from numpy.random import multivariate_normal
#------------#
# Parameters #
#------------#
N1 = 20 # クラス t=+1 のデータ数
Mu1 = [15,10] # クラス t=+1 の中心座標
N2 = 30 # クラス t=-1 のデータ数
Mu2 = [0,0] # クラス t=-1 の中心座標
Variances = [15,30] # 両クラス共通の分散（2種類の分散で計算を実施）
# データセット {x_n,y_n,type_n} を用意
def prepare_dataset(variance):
cov1 = np.array([[variance,0],[0,variance]])
cov2 = np.array([[variance,0],[0,variance]])
df1 = DataFrame(multivariate_normal(Mu1,cov1,N1),columns=['x','y'])
df1['type'] = 1
df2 = DataFrame(multivariate_normal(Mu2,cov2,N2),columns=['x','y'])
df2['type'] = -1
df = pd.concat([df1,df2],ignore_index=True)
df = df.reindex(np.random.permutation(df.index)).reset_index(drop=True)
return df
# Perceptronのアルゴリズム（確率的勾配降下法）を実行
def run_simulation(variance, data_graph, param_graph):
train_set = prepare_dataset(variance)
train_set1 = train_set[train_set['type']==1]
train_set2 = train_set[train_set['type']==-1]
ymin, ymax = train_set.y.min()-5, train_set.y.max()+10
xmin, xmax = train_set.x.min()-5, train_set.x.max()+10
data_graph.set_ylim([ymin-1, ymax+1])
data_graph.set_xlim([xmin-1, xmax+1])
data_graph.scatter(train_set1.x, train_set1.y, marker='o', label=None)
data_graph.scatter(train_set2.x, train_set2.y, marker='x', label=None)
# パラメータの初期値とbias項の設定
w0 = w1 = w2 = 0.0
bias = 0.5 * (train_set.x.mean() + train_set.y.mean())
# Iterationを30回実施
paramhist = DataFrame([[w0,w1,w2]], columns=['w0','w1','w2'])
for i in range(30):
for index, point in train_set.iterrows():
x, y, type = point.x, point.y, point.type
if type * (w0*bias + w1*x + w2*y) <= 0:
w0 += type * bias
w1 += type * x
w2 += type * y
paramhist = paramhist.append(
Series([w0,w1,w2], ['w0','w1','w2']),
ignore_index=True)
# 判定誤差の計算
err = 0
for index, point in train_set.iterrows():
x, y, type = point.x, point.y, point.type
if type * (w0*bias + w1*x + w2*y) <= 0:
err += 1
err_rate = err * 100 / len(train_set)
# 結果の表示
linex = np.arange(xmin-5, xmax+5)
liney = - linex * w1 / w2 - bias * w0 / w2
label = "ERR %.2f%%" % err_rate
data_graph.plot(linex, liney, label=label, color='red')
data_graph.legend(loc=1)
paramhist.plot(ax=param_graph)
param_graph.legend(loc=1)
# Main
if __name__ == '__main__':
fig = plt.figure()
# 2種類の分散で実行
for c, variance in enumerate(Variances):
subplots1 = fig.add_subplot(2,2,c+1)
subplots2 = fig.add_subplot(2,2,c+2+1)
run_simulation(variance, subplots1, subplots2)
fig.show()
という本にレヴィ分布という確率分布が出てきました。
