ディープラーニングのパーセプトロンとは？Pythonで実装したサンプルもご紹介

＜目次＞

(１) ディープラーニングのパーセプトロンとは？Pythonで実装したサンプルもご紹介
　(１-１) パーセプトロンとは？
　(１-２) 処理の流れ
　(１-３) サンプルプログラム
　(１-４) 補足：Excelでの検算

(１) ディープラーニングのパーセプトロンとは？Pythonで実装したサンプルもご紹介

(１-１) パーセプトロンとは？

（図１００）

(１-２) 処理の流れ

（図１２１）

＞目次にもどる

(１-３) サンプルプログラム

（サンプルプログラム）

import numpy as np

# グローバル変数
# d:データの次元
d = 2
# N:データ数（パターン別。発火有り/無しそれぞれN個）
N = 10
# 発火するニューロンの平均値
mean = 5
# パラメータwの初期化
# 　⇒「np.zeros(n)」で0を要素とするn要素の配列を作成
w = np.zeros(d)
# dw1,dw2,...dwn,dthetaの定義
# 　⇒ w1,w2,...wn,thetaの初期値は適当な値からスタート可。
dw = np.zeros(d)

# ランダムデータの生成（ただし、１パターンにデータ固定）
def create_random_data(d,N,mean):

    rng = np.random.RandomState(123)
    x1 = rng.randn(N,d) + np.array([0,0])
    x2 = rng.randn(N,d) + np.array([mean,mean])
    x = np.concatenate((x1,x2), axis=0)
    return x

# ステップ関数
def step(x):
    return 1 * (x >= 0)

# 正解値「t」の導出関数
# ⇒i：データの番号。0～N-1番目までは発火しない（0）データ。以降は発火する（1）データ。
def t(i):
    if i < N:
        return 0
    else:
        return 1

def main():

    # ■変数設定  -------------------------------------------------------------
    # x1,x2,tの設定
    # ⇒ゲートの種類に応じて、誤り訂正学習法で使える「データ数回(今回は20)）」のパターンを設定
    x = create_random_data(d,N,mean) 
    # パラメータthetaの初期化
    theta,dtheta = 0,0

    # ■繰り返し学習処理  -------------------------------------------------------------
    # dw1,dw2,...dwn,dthetaが「データ数回(今回は20)」連続で0になるまで繰り返し
    #  ⇒ゲートの「データ数回(今回は20)）」個のパターン全部でデルタ=0なら収束と判断

    # delta_zero_flag: 現在のデータ（x1,x2,...xn）に対してdw1,dw2,...dwn,dthetaが0か？の管理フラグ
    delta_zero_flag = False
    # i1: ループ回数、i2: 現在のデータ数（何番目のデータで計算中か）
    i1,i2,end_counter = 0,0,0
    # end_counter: デルタ（dw1,dw2,...dwn,dtheta）=ゼロがデータの個数（len(x)）回続くまで
    while end_counter < len(x):

        # if: 初回は1番目のデータ（i2=0） 
        if i1 == 0:                         i2 = 0
        # elif: 2回目以降でlen(x)-1の場合は、セットの最後のデータのため、0リセット
        elif i2 != 0 and i2 == len(x)-1:    i2 = 0
        # else: 次のデータを使うためi2加算
        else:                               i2 = i2 + 1       

        # ■w1,w2,...wn,thetaの設定 ------------------------------------------------
        # w1,w2,...wn,thetaの初期値は適当な値からスタート可。
        # 初回以外はデルタ値（dw1,dw2,...dwn,dtheta）を加算して更新
        for j1 in range(d):
            w[j1] = w[j1] + dw[j1]
        theta = theta + dtheta

        # ■yの計算（モデルの出力）--------------------------------------------------
        # 関数「y = f(w*x - theta)」の表現
        y = step(np.dot(w, x[i2]) - theta)

        # ■dw1,dw2,dthetaの計算 --------------------------------------------------
        # モデルの出力(y)と正解の出力(t)の差を用いて計算する。
        for k1 in range(d):
            dw[k1] = (t(i2)-y)*x[i2][k1]
        dtheta = (-1)*(t(i2)-y)

        # ■ループ脱出判定 ---------------------------------------------------------
        # ゲートの「データ数回(今回は20)」パターン(x1,x2,...xn,tの組み合わせ)全てで
        # 修正分(dw1,dw2,...xn,dtheta)が0になった場合に脱出する
        # ------------------------------------------------------------------------
        # (1)最初にFlagをTrueにしておく
        delta_zero_flag = True
        # (2)dw1,dw2,..dwnと確認し、1つでも0でないならフラグをFalseにする（処理を継続する）
        for l1 in range(d):
            if dw[l1] != 0:
                delta_zero_flag = False
        # (3)dthetaを確認し、0ならフラグをFalseにする
        if dtheta != 0:
            delta_zero_flag = False
        # (4)上記で１セット分（dw1,dw2,...,dwn,dtheta）なので、
        #    この時点でdelta_zero_flag == Trueなら１回分のカウントする
        if delta_zero_flag == True:
            end_counter = end_counter + 1
        # (5)ただし、最後のセットで、end_counter < [データ数]なら
        #    全部が0でない（収束していない）として、end_counterをリセット
        if i2 == len(x)-1 and end_counter < len(x):
            end_counter = 0

        print("k= ",i1,"x1 =",'{:.2f}'.format(x[i2][0]),"x2 =",'{:.2f}'.format(x[i2][1]),"t =",t(i2),"w1 =",'{:.2f}'.format(w[0]),"w2 =",'{:.2f}'.format(w[1]),"theta =",theta,"y =",'{:.2f}'.format(y),"dw1 =",'{:.2f}'.format(dw[0]),"dw2 =",'{:.2f}'.format(dw[1]),"dtheta =",dtheta,"end=",i2)

        # ループ変数を更新
        i1 = i1 + 1

if __name__ == "__main__":
    main()

（実行結果例）

k=  0 x1 = -1.09 x2 = 1.00 t = 0 w1 = 0.00 w2 = 0.00 theta = 0 y = 1.00 dw1 = 1.09 dw2 = -1.00 dtheta = 1 end= 0
k=  1 x1 = 0.28 x2 = -1.51 t = 0 w1 = 1.09 w2 = -1.00 theta = 1 y = 1.00 dw1 = -0.28 dw2 = 1.51 dtheta = 1 end= 1  
k=  2 x1 = -0.58 x2 = 1.65 t = 0 w1 = 0.80 w2 = 0.51 theta = 2 y = 0.00 dw1 = -0.00 dw2 = 0.00 dtheta = 0 end= 2   
k=  3 x1 = -2.43 x2 = -0.43 t = 0 w1 = 0.80 w2 = 0.51 theta = 2 y = 0.00 dw1 = -0.00 dw2 = -0.00 dtheta = 0 end= 3 
k=  4 x1 = 1.27 x2 = -0.87 t = 0 w1 = 0.80 w2 = 0.51 theta = 2 y = 0.00 dw1 = 0.00 dw2 = -0.00 dtheta = 0 end= 4   
k=  5 x1 = -0.68 x2 = -0.09 t = 0 w1 = 0.80 w2 = 0.51 theta = 2 y = 0.00 dw1 = -0.00 dw2 = -0.00 dtheta = 0 end= 5 
k=  6 x1 = 1.49 x2 = -0.64 t = 0 w1 = 0.80 w2 = 0.51 theta = 2 y = 0.00 dw1 = 0.00 dw2 = -0.00 dtheta = 0 end= 6   
k=  7 x1 = -0.44 x2 = -0.43 t = 0 w1 = 0.80 w2 = 0.51 theta = 2 y = 0.00 dw1 = -0.00 dw2 = -0.00 dtheta = 0 end= 7 
k=  8 x1 = 2.21 x2 = 2.19 t = 0 w1 = 0.80 w2 = 0.51 theta = 2 y = 1.00 dw1 = -2.21 dw2 = -2.19 dtheta = 1 end= 8   
k=  9 x1 = 1.00 x2 = 0.39 t = 0 w1 = -1.40 w2 = -1.68 theta = 3 y = 0.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 9   
k=  10 x1 = 5.74 x2 = 6.49 t = 1 w1 = -1.40 w2 = -1.68 theta = 3 y = 0.00 dw1 = 5.74 dw2 = 6.49 dtheta = -1 end= 10
k=  11 x1 = 4.06 x2 = 6.18 t = 1 w1 = 4.33 w2 = 4.81 theta = 2 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 11   
k=  12 x1 = 3.75 x2 = 4.36 t = 1 w1 = 4.33 w2 = 4.81 theta = 2 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 12   
k=  13 x1 = 5.91 x2 = 3.57 t = 1 w1 = 4.33 w2 = 4.81 theta = 2 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 13   
k=  14 x1 = 4.86 x2 = 4.14 t = 1 w1 = 4.33 w2 = 4.81 theta = 2 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 14   
k=  15 x1 = 4.74 x2 = 2.20 t = 1 w1 = 4.33 w2 = 4.81 theta = 2 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 15   
k=  16 x1 = 3.23 x2 = 4.30 t = 1 w1 = 4.33 w2 = 4.81 theta = 2 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 16   
k=  17 x1 = 5.93 x2 = 4.83 t = 1 w1 = 4.33 w2 = 4.81 theta = 2 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 17   
k=  18 x1 = 5.00 x2 = 5.69 t = 1 w1 = 4.33 w2 = 4.81 theta = 2 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 18   
k=  19 x1 = 4.12 x2 = 5.28 t = 1 w1 = 4.33 w2 = 4.81 theta = 2 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 19   
～中略～
k=  181 x1 = 0.28 x2 = -1.51 t = 0 w1 = 3.79 w2 = 4.35 theta = 10 y = 0.00 dw1 = 0.00 dw2 = -0.00 dtheta = 0 end= 1
k=  182 x1 = -0.58 x2 = 1.65 t = 0 w1 = 3.79 w2 = 4.35 theta = 10 y = 0.00 dw1 = -0.00 dw2 = 0.00 dtheta = 0 end= 2
k=  183 x1 = -2.43 x2 = -0.43 t = 0 w1 = 3.79 w2 = 4.35 theta = 10 y = 0.00 dw1 = -0.00 dw2 = -0.00 dtheta = 0 end= 3
k=  184 x1 = 1.27 x2 = -0.87 t = 0 w1 = 3.79 w2 = 4.35 theta = 10 y = 0.00 dw1 = 0.00 dw2 = -0.00 dtheta = 0 end= 4
k=  185 x1 = -0.68 x2 = -0.09 t = 0 w1 = 3.79 w2 = 4.35 theta = 10 y = 0.00 dw1 = -0.00 dw2 = -0.00 dtheta = 0 end= 5
k=  186 x1 = 1.49 x2 = -0.64 t = 0 w1 = 3.79 w2 = 4.35 theta = 10 y = 0.00 dw1 = 0.00 dw2 = -0.00 dtheta = 0 end= 6
k=  187 x1 = -0.44 x2 = -0.43 t = 0 w1 = 3.79 w2 = 4.35 theta = 10 y = 0.00 dw1 = -0.00 dw2 = -0.00 dtheta = 0 end= 7
k=  188 x1 = 2.21 x2 = 2.19 t = 0 w1 = 3.79 w2 = 4.35 theta = 10 y = 1.00 dw1 = -2.21 dw2 = -2.19 dtheta = 1 end= 8
k=  189 x1 = 1.00 x2 = 0.39 t = 0 w1 = 1.58 w2 = 2.17 theta = 11 y = 0.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 9
k=  190 x1 = 5.74 x2 = 6.49 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 10
k=  191 x1 = 4.06 x2 = 6.18 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 11
k=  192 x1 = 3.75 x2 = 4.36 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 12
k=  193 x1 = 5.91 x2 = 3.57 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 13
k=  194 x1 = 4.86 x2 = 4.14 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 14
k=  195 x1 = 4.74 x2 = 2.20 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 15
k=  196 x1 = 3.23 x2 = 4.30 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 16
k=  197 x1 = 5.93 x2 = 4.83 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 17
k=  198 x1 = 5.00 x2 = 5.69 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 18
k=  199 x1 = 4.12 x2 = 5.28 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 19
k=  200 x1 = -1.09 x2 = 1.00 t = 0 w1 = 1.58 w2 = 2.17 theta = 11 y = 0.00 dw1 = -0.00 dw2 = 0.00 dtheta = 0 end= 0
k=  201 x1 = 0.28 x2 = -1.51 t = 0 w1 = 1.58 w2 = 2.17 theta = 11 y = 0.00 dw1 = 0.00 dw2 = -0.00 dtheta = 0 end= 1
k=  202 x1 = -0.58 x2 = 1.65 t = 0 w1 = 1.58 w2 = 2.17 theta = 11 y = 0.00 dw1 = -0.00 dw2 = 0.00 dtheta = 0 end= 2
k=  203 x1 = -2.43 x2 = -0.43 t = 0 w1 = 1.58 w2 = 2.17 theta = 11 y = 0.00 dw1 = -0.00 dw2 = -0.00 dtheta = 0 end= 3
k=  204 x1 = 1.27 x2 = -0.87 t = 0 w1 = 1.58 w2 = 2.17 theta = 11 y = 0.00 dw1 = 0.00 dw2 = -0.00 dtheta = 0 end= 4
k=  205 x1 = -0.68 x2 = -0.09 t = 0 w1 = 1.58 w2 = 2.17 theta = 11 y = 0.00 dw1 = -0.00 dw2 = -0.00 dtheta = 0 end= 5
k=  206 x1 = 1.49 x2 = -0.64 t = 0 w1 = 1.58 w2 = 2.17 theta = 11 y = 0.00 dw1 = 0.00 dw2 = -0.00 dtheta = 0 end= 6
k=  207 x1 = -0.44 x2 = -0.43 t = 0 w1 = 1.58 w2 = 2.17 theta = 11 y = 0.00 dw1 = -0.00 dw2 = -0.00 dtheta = 0 end= 7
k=  208 x1 = 2.21 x2 = 2.19 t = 0 w1 = 1.58 w2 = 2.17 theta = 11 y = 0.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 8
k=  209 x1 = 1.00 x2 = 0.39 t = 0 w1 = 1.58 w2 = 2.17 theta = 11 y = 0.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 9
k=  210 x1 = 5.74 x2 = 6.49 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 10
k=  211 x1 = 4.06 x2 = 6.18 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 11
k=  212 x1 = 3.75 x2 = 4.36 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 12
k=  213 x1 = 5.91 x2 = 3.57 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 13
k=  214 x1 = 4.86 x2 = 4.14 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 14
k=  215 x1 = 4.74 x2 = 2.20 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 15
k=  216 x1 = 3.23 x2 = 4.30 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 16
k=  217 x1 = 5.93 x2 = 4.83 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 17
k=  218 x1 = 5.00 x2 = 5.69 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 18
k=  219 x1 = 4.12 x2 = 5.28 t = 1 w1 = 1.58 w2 = 2.17 theta = 11 y = 1.00 dw1 = 0.00 dw2 = 0.00 dtheta = 0 end= 19

（図１３１）

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(１-４) 補足：Excelでの検算

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