add nonlinearity

result.txt

---epoch 9---
source  label:-1, data:[0 0 0 0 0 0 0 0]
predoct label:-1, weight:[-0.39016744  1.07635597  0.21081006  0.18976978 -0.7392488   0.20338442
 -1.12607911 -1.17872689  0.41622946]
OK
source  label:1, data:[0 1 0 0 0 0 0 1]
predoct label:1, weight:[-0.39016744  1.07635597  0.21081006  0.18976978 -0.7392488   0.20338442
 -1.12607911 -1.17872689  0.41622946]
OK
source  label:1, data:[1 0 1 0 0 0 0 0]
predoct label:1, weight:[-0.39016744  1.07635597  0.21081006  0.18976978 -0.7392488   0.20338442
 -1.12607911 -1.17872689  0.41622946]
OK
source  label:-1, data:[1 1 1 1 1 1 1 1]
predoct label:-1, weight:[-0.39016744  1.07635597  0.21081006  0.18976978 -0.7392488   0.20338442
 -1.12607911 -1.17872689  0.41622946]
OK

simple_perceptron.py

#!/usr/bin/python
# -*- coding: utf-8 -*-
"""
パーセプトロンの実験
参考 荒木雅弘, フリーソフトで作る音声認識システム
"""

import numpy as np
import matplotlib.pyplot as plt

# 重みの初期化
def init_weights(i, j):
    return np.random.uniform(-1.0, 1.0, (i, j))

# バイアス項の追加
def add_bias(d):
    return np.concatenate(([1],d))

def function(w, x):
    return np.dot(w, x)

def comb(x, n=1):
    return x if n == 0 else comb(np.outer(x, x)[np.triu_indices(len(x))], n-1)

def nonlinearity(x):
    return np.concatenate((x, comb(x, 2)))

def train(d, l, w):
    rho = 0.5
    f = np.sign(function(w, d))# -1/1の2値で関数を判定
    j = True
    if f != l:
        # 重み更新
        w += l*rho*d
        j = False
    return f, w


"""
#AND
datas_and_labels = [
    [np.array([0, 0]),np.array([-1])],
    [np.array([0, 1]),np.array([-1])],
    [np.array([1, 0]),np.array([-1])],
    [np.array([1, 1]),np.array([1])],
]
"""
"""
#OR
datas_and_labels = [
    [np.array([0, 0]),np.array([-1])],
    [np.array([0, 1]),np.array([1])],
    [np.array([1, 0]),np.array([1])],
    [np.array([1, 1]),np.array([1])],
]
"""

#XOR
datas_and_labels = [
    [np.array([0, 0]),np.array([-1])],
    [np.array([0, 1]),np.array([1])],
    [np.array([1, 0]),np.array([1])],
    [np.array([1, 1]),np.array([-1])],
]

"""
# Linearly separable
datas_and_labels = [
    [np.array([-1, 0.8]),  np.array([-1])],
    [np.array([-1.2, 0.5]),np.array([-1])],
    [np.array([-0.7, 0.2]),np.array([-1])],
    [np.array([0.2, -1]),  np.array([-1])],
    [np.array([0.3, -0.8]),np.array([-1])],
    [np.array([-0.3, 1]),   np.array([1])],
    [np.array([-0.2, 0.9]), np.array([1])],
    [np.array([0.5, 0.6]),  np.array([1])],
    [np.array([0.7, -0.1]), np.array([1])],
    [np.array([1, -0.4]),   np.array([1])],
]
"""

# weights initialize
nl_len = len(nonlinearity(datas_and_labels[0][0])) + 1
weights = init_weights(1, nl_len)
# training
for epoch in range(10):
    print("---epoch {}---".format(epoch))
    for data, label in datas_and_labels:
        data = nonlinearity(data)
        data = add_bias(data)
        predict, weights = train(data, label, weights)
        print ("source  label:{l}, data:{d}".format(l=label[0], d=data[1:]))
        print ("predoct label:{p}, weight:{w}".format(p=int(predict[0]), w=weights[0]))
        print ("{j}".format(j = "OK" if predict == label else "NG"))

# plot area
xmax = 2.0
ymax = 2.0

# decision surface
h = 0.3
xx, yy = np.meshgrid(np.arange(-xmax, xmax, h),
                     np.arange(-ymax, ymax, h))

area = np.c_[xx.ravel(), yy.ravel()]
area = np.apply_along_axis(nonlinearity, 1, area)
area = np.c_[area, np.ones(len(area))] # bias
predicts = (weights.dot(area.T)).reshape(xx.shape)
plt.contour(xx, yy, predicts)

# datas and labels
for d, l in datas_and_labels:
    plt.scatter(d[0], d[1], c="r" if l > 0 else "b")
plt.xlim(-xmax, xmax)
plt.ylim(-ymax, ymax)
plt.show()