public void Demo_011_Compare_NN_SVM_LR()
{
Console.WriteLine("ニューラルネットワーク、サポートベクトルマシン、線形回帰を比較します。");
Console.WriteLine("WriteLineはPCの処理能力を使うので、裏ですべて計算してから、結果をお見せします。");
//計算時間
DateTime start_NN;
DateTime finish_NN;
TimeSpan span_NN_epoch_100k;
DateTime start_SVM;
DateTime finish_SVM;
TimeSpan span_SVM;
DateTime start_LR;
DateTime finish_LR;
TimeSpan span_LR;
List <double[, ]> list_x = new List <double[, ]>();
List <double[, ]> list_t = new List <double[, ]>();
for (int j = 0; j < 9; j++)
{
double[,] x = new double[1, 1];
x[0, 0] = j;
list_x.Add(x);
double[,] t = new double[1, 1];
if (j < 3 || 5 < j)
{
t[0, 0] = -1;
}
else
{
t[0, 0] = 1;
}
list_t.Add(t);
}
//Console.WriteLine("次は、2層のNeural Networkで試してみます");
//Console.WriteLine("第1層の計数行列はwは2行1列の行列とします");
//Console.WriteLine("活性化関数はSigmoid関数とします");
double[,] w_1 = new double[2, 1];
w_1[0, 0] = 10;
w_1[1, 0] = -10;
//Console.WriteLine("第1層の計数行列 w");
//this.Show_Matrix_Element(w_1);
double[,] b_1 = new double[2, 1];
b_1[0, 0] = -35;
b_1[1, 0] = 55;
//Console.WriteLine("第1層のバイアスベクトル b");
//this.Show_Matrix_Element(b_1);
//第一層は隠れ層なので、別のクラスです
Hidden_Layer hd_1 = new Hidden_Layer();
hd_1.Preset_1_4th_Set_w(w_1);
hd_1.Preset_2_4th_Set_b(b_1);
hd_1.Preset_3_4th_Set_Hyper_Parameter(0.01, 0, 0, 0);
hd_1.Preset_4_4th_Set_activation_Function(new Sigmoid_IFunction());
//Console.WriteLine("\n");
//Console.WriteLine("第2層の計数行列はwは1行2列の行列とします");
//Console.WriteLine("活性化関数は、第2層はHyperbolic_Tangent関数とします");
double[,] w_2 = new double[1, 2];
w_2[0, 0] = 20;
w_2[0, 1] = 20;
//Console.WriteLine("第2層の計数行列 w");
//this.Show_Matrix_Element(w_2);
double[,] b_2 = new double[1, 1];
b_2[0, 0] = -30;
//Console.WriteLine("第2層のバイアスベクトル b");
//this.Show_Matrix_Element(b_2);
//Console.WriteLine("\n\n");
Regression_Final_Layer rfl_2 = new Regression_Final_Layer();
rfl_2.Preset_1_4th_Set_w(w_2);
rfl_2.Preset_2_4th_Set_b(b_2);
rfl_2.Preset_3_4th_Set_Hyper_Parameter(0.001, 0, 0, 0);
rfl_2.Preset_4_4th_Set_activation_Function(new Hyperbolic_Tangent_IFunction());
//Console.WriteLine("\n\n");
int epoch = 1000;
double[] error = new double[list_x.Count];
//double max_error = 0;
//int max_k = 0;
start_NN = DateTime.Now;
for (int j = 0; j < list_x.Count * epoch; j++)
{
/*
* //Console.WriteLine("epoch" + "\t" + j);
* for (int k = 0; k < list_x.Count; k++)
* {
* hd_1.Step_1_3rd_Forward_Propagation(list_x[k]);
* rfl_2.Step_1_3rd_Forward_Propagation(hd_1.Get_f_wx_plus_b());
* error[k] = Math.Abs(rfl_2.Get_f_wx_plus_b()[0, 0] - list_t[k][0, 0]);
* //Console.WriteLine(k + "\t" + error[k].ToString("G3") + "\t" + list_t[k][0, 0] + "\t" + rfl_2.Get_f_wx_plus_b()[0, 0].ToString("G3") + "\t" + hd_1.Get_f_wx_plus_b()[0, 0].ToString("G3") + "\t" + hd_1.Get_f_wx_plus_b()[1, 0].ToString("G3"));
* }
*
* max_k = 0;
* max_error = error[0];
* for (int k = 1; k < list_x.Count; k++)
* {
* if (max_error < error[k])
* {
* max_error = error[k];
* max_k = k;
* }
* }
* //Console.WriteLine("Max error is No." + max_k);
* //Console.WriteLine(" ");
*/
//順伝搬
hd_1.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl_2.Step_1_3rd_Forward_Propagation(hd_1.Get_f_wx_plus_b());
//逆伝搬
rfl_2.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_t.Count]);
//hd_1.Step_2_3rd_Calculate_Delta(rfl_2.Get_w(), rfl_2.Get_delta());
//パラメータの更新
rfl_2.Step_3_3rd_Update();
//hd_1.Step_3_3rd_Update();
}
finish_NN = DateTime.Now;
span_NN_epoch_100k = finish_NN - start_NN;
double[,] y_NN = new double[list_x.Count, 1];
for (int j = 0; j < 9; j++)
{
//順伝搬
hd_1.Step_1_3rd_Forward_Propagation(list_x[j]);
rfl_2.Step_1_3rd_Forward_Propagation(hd_1.Get_f_wx_plus_b());
y_NN[j, 0] = rfl_2.Get_f_wx_plus_b()[0, 0];
}
//SVM、線形回帰の計画行列を定義します。
double[,] X = new double[9, 1];
double[,] t_vec = new double[9, 1];
//Console.WriteLine("\t" + "入力x\t" + "教師t");
for (int j = 0; j < 9; j++)
{
X[j, 0] = j;
if (j < 3 || 5 < j)
{
t_vec[j, 0] = -1;
}
else
{
t_vec[j, 0] = 1;
}
//Console.WriteLine("\t" + X[j, 0] + "\t" + t_vec[j, 0] + "");
}
//SVMの学習です
start_SVM = DateTime.Now;
double[,] variance_covariance = Design_Matrix.Variance_Covariance_Matrix(X);
//係数Aを学習する
double[,] Coefficient_A = Support_Vector_Machine.Learned_Coefficient_A(t_vec, X, new Power_of_10_IKernel(), variance_covariance);
finish_SVM = DateTime.Now;
span_SVM = finish_SVM - start_SVM;
double[,] classified = Support_Vector_Machine.Classification_Design_Matrix(t_vec, X, new Power_of_10_IKernel(), variance_covariance, Coefficient_A, X);
//線形回帰用の計画行列です。
double[,] phi_X = new double[9, 3];
//Console.WriteLine("\t" + "教師t" + "\t" + "exp(-(x-0.5)^2/2 )/√2π" + "\t" + "exp(-(x-2.5)^2/2 )/√2π" + "\t" + "exp(-(x-4.5)^2/2 )/√2π");
for (int j = 0; j < 9; j++)
{
phi_X[j, 0] = Math.Exp(-(X[j, 0] - 1) * (X[j, 0] - 1) / 2.0) / Math.Sqrt(2 * Math.PI);
phi_X[j, 1] = Math.Exp(-(X[j, 0] - 4) * (X[j, 0] - 4) / 2.0) / Math.Sqrt(2 * Math.PI);
phi_X[j, 2] = Math.Exp(-(X[j, 0] - 7) * (X[j, 0] - 7) / 2.0) / Math.Sqrt(2 * Math.PI);
//Console.WriteLine("\t" + t_vec[j, 0] + "\t" + phi_X[j, 0].ToString("G2") + "\t\t\t\t" + phi_X[j, 1].ToString("G2") + "\t\t\t\t" + phi_X[j, 2].ToString("G2"));
}
start_LR = DateTime.Now;
double[,] w = Liner_Regression.Learning_parameter_w_column_vector(phi_X, t_vec);
finish_LR = DateTime.Now;
span_LR = finish_LR - start_LR;
double[,] y_LR = Liner_Regression.Regression_Design_Matrix(phi_X, w);
Console.WriteLine("入力x" + "\t" + "答えt" + "\t" + "NN" + "\t" + "SVM" + "\t" + "LR");
for (int j = 0; j < 9; j++)
{
Console.Write(X[j, 0] + "\t");
Console.Write(t_vec[j, 0] + "\t");
Console.Write(y_NN[j, 0].ToString("G2") + "\t");
Console.Write(classified[j, 0].ToString("G2") + "\t");
Console.Write(y_LR[j, 0].ToString("G2") + "\t");
Console.WriteLine(" ");
}
Console.WriteLine(" ");
Console.WriteLine("NNの計算時間\t\t" + span_NN_epoch_100k.Minutes + "分" + span_NN_epoch_100k.Seconds + "秒");
Console.WriteLine("SVMの計算時間\t\t" + span_SVM.Minutes + "分" + span_SVM.Seconds + "秒");
Console.WriteLine("LRの計算時間\t\t" + span_LR.Minutes + "分" + span_LR.Seconds + "秒");
Console.WriteLine("\n\n" + "NNの精度が良くないですね。");
Console.WriteLine("計数行列wの初期値や、学習回数、ハイパーパラメータなどを調整したのですが、これが限界でした。");
}
public void Demo_006_Neural_Network_2()
{
Console.WriteLine("Neural Networkのデモンストレーションです");
Console.WriteLine("前回は入力が1次元で、教師データが0と1でした。");
Console.WriteLine("今回は教師データを-1と1にした場合、どの程度学習に影響を及ぼすかを調べます。");
//教師データを設定します。
//簡単のためf(x)の一次元とします。
List <double[, ]> list_x = new List <double[, ]>();
List <double[, ]> list_t = new List <double[, ]>();
for (int j = 0; j < 4; j++)
{
double[,] x = new double[1, 1];
x[0, 0] = j * 1.0;
list_x.Add(x);
double[,] t = new double[1, 1];
if (j > 1)
{
t[0, 0] = 1;
}
else
{
t[0, 0] = -1;
}
list_t.Add(t);
}
Console.WriteLine("今回の入力値xと、答えtです");
Console.WriteLine("x > 1 のとき、答えが1になります。それ以外の場合、-1になります。");
Console.Write("x\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine("\t");
Console.Write("t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine("\n");
Console.WriteLine("計数行列Wとバイアスベクトルbを設定します。");
Console.WriteLine("今回のNeural Networkの層は1層とします。");
double[,] W = new double[1, 1];
W[0, 0] = 3;
double[,] b = new double[1, 1];
b[0, 0] = 2;
Console.WriteLine("W[0,0] = " + W[0, 0] + "\t" + "b[0,0] = " + b[0, 0] + "\n\n");
Console.WriteLine("Neural Netoworkを設定しました。負の数を出力するため、活性化関数はHyperbolic_Tangent関数とします");
Console.WriteLine("ハイパーパラメータの値は0.01とします。\n");
Regression_Final_Layer rfl = new Regression_Final_Layer();
rfl.Preset_1_4th_Set_w(W);
rfl.Preset_2_4th_Set_b(b);
rfl.Preset_3_4th_Set_Hyper_Parameter(0.01, 0, 0, 0);
rfl.Preset_4_4th_Set_activation_Function(new Hyperbolic_Tangent_IFunction());
Console.WriteLine("学習前のNeural Networkの出力を確認します。");
Console.WriteLine("f(wx + b)とtの値が近ければ、良い近似であると言えます");
List <double[, ]> list_wx_plus_b = new List <double[, ]>();
List <double[, ]> list_f_wx_plus_b = new List <double[, ]>();
List <double[, ]> list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine("\n\n");
Console.WriteLine("1 epoch 学習しました。予測精度がどの程度変わったのかを確認しましょう");
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("10 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 9; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("100 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 90; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("1,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 900; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("5,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 4000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("10,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 5000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("20,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 10000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("50,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 30000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("100,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 50000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("1,000,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 900000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("教師データを-1と1にしたとたん、学習効率が格段に落ちました");
Console.WriteLine("この現象は、学習すべき計数行列とバイアスベクトルの条件が異なることが原因です。\n\n");
Console.WriteLine("Demo005ではx > 1 のとき1が出力されて、xが1以下のとき0が出力されるようパラメータを学習しました。 ");
Console.WriteLine("すなわち、Sigmoid( w*1 + b )≒0、Sigmoid( w*2 + b )≒1となるw、bを学習しました。");
Console.WriteLine("これを満たすw、bの条件は下記となります。");
Console.WriteLine("01 : w + b << 0");
Console.WriteLine("02 : 2w + b >> 0");
Console.WriteLine("\n" + "Sigmoid関数の変数(wx+b)の符号がx=1、2で切り替わりその絶対値が大きいことが条件になります。");
Console.WriteLine("これを満たすw , bの条件は下記になります。");
Console.WriteLine("01 : w >> 0");
Console.WriteLine("02 : b << 0");
Console.WriteLine("03 : w < |b| < 2w \n\n");
Console.WriteLine("Demo006ではx > 1 のとき1が出力されて、xが1以下のとき-1が出力されるようパラメータを学習しました。 ");
Console.WriteLine("すなわち、tanh( w*1 + b )≒-1、tanh( w*2 + b )≒1となるw、bを学習しました。");
Console.WriteLine("これを満たすw、bの条件は下記となります。");
Console.WriteLine("01 : w + b << 0");
Console.WriteLine("02 : 2w + b >> 0");
Console.WriteLine("03 : -( w + b ) ≒ 2w + b ∵ -tanh( w + b ) ≒ tanh( 2w + b )");
Console.WriteLine("\n" + "tanh(wx+b)は(wx+b)=1.5を堺に符号が反転することが求められます。");
Console.WriteLine("これを満たすw , bの条件は下記になります。");
Console.WriteLine("01 : w >> 0");
Console.WriteLine("02 : b << 0");
Console.WriteLine("03 : b ≒ -3w/2 \n\n");
Console.WriteLine("Demo005とDemo006との差異を下記に示します。");
Console.WriteLine("Demo005 : w < |b| < 2w");
Console.WriteLine("Demo006 : b ≒ -3w/2\n");
Console.WriteLine("Demo006の方がw , bの関係の制約が厳しいです。");
Console.WriteLine("しかし、w , bを学習するための手法(誤差逆伝搬法)は、それぞれのパラメータを独立に更新する手法です。");
Console.WriteLine("パラメータ同士の関係が考慮されないため、demo006は学習効率が低かったと考えられます。\n\n");
Console.WriteLine("学習データの前処理や層の設定などの工夫で、学習効率を上げることができると考えられます");
}
public void Demo_005_Neural_Network_1()
{
Console.WriteLine("Neural Networkのデモンストレーションです");
Console.WriteLine("学習結果がわかりやすいように、1次元のデータで紹介します。\n\n");
//教師データを設定します。
//簡単のためf(x)の一次元とします。
List <double[, ]> list_x = new List <double[, ]>();
List <double[, ]> list_t = new List <double[, ]>();
for (int j = 0; j < 4; j++)
{
double[,] x = new double[1, 1];
x[0, 0] = j * 1.0;
list_x.Add(x);
double[,] t = new double[1, 1];
if (j > 1)
{
t[0, 0] = 1;
}
else
{
t[0, 0] = 0;
}
list_t.Add(t);
}
Console.WriteLine("今回の入力値xと、答えtです");
Console.WriteLine("x > 1 のとき、答えが1になります。それ以外の場合、0になります。");
Console.Write("x\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine("\t");
Console.Write("t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine("\n");
Console.WriteLine("計数行列Wとバイアスベクトルbを設定します。");
Console.WriteLine("今回のNeural Networkの層は1層とします。");
double[,] W = new double[1, 1];
W[0, 0] = 3;
double[,] b = new double[1, 1];
b[0, 0] = 2;
Console.WriteLine("W[0,0] = " + W[0, 0] + "\t" + "b[0,0] = " + b[0, 0] + "\n\n");
Console.WriteLine("Neural Netoworkを設定しました。今回の活性化関数はSigmoid関数とします");
Console.WriteLine("ハイパーパラメータの値は0.01とします。\n");
Regression_Final_Layer rfl = new Regression_Final_Layer();
rfl.Preset_1_4th_Set_w(W);
rfl.Preset_2_4th_Set_b(b);
rfl.Preset_3_4th_Set_Hyper_Parameter(0.01, 0, 0, 0);
rfl.Preset_4_4th_Set_activation_Function(new Sigmoid_IFunction());
Console.WriteLine("学習前のNeural Networkの出力を確認します。");
Console.WriteLine("f(wx + b)とtの値が近ければ、良い近似であると言えます");
List <double[, ]> list_wx_plus_b = new List <double[, ]>();
List <double[, ]> list_f_wx_plus_b = new List <double[, ]>();
List <double[, ]> list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine("\n\n");
Console.WriteLine("1 epoch 学習しました。予測精度がどの程度変わったのかを確認しましょう");
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("10 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 9; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("100 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 90; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("1,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 900; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("5,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 4000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("10,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 5000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("20,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 10000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("50,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 30000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("100,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 50000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
Console.WriteLine("1,000,000 epoch 学習しました。");
for (int j = 0; j < list_x.Count * 900000; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n");
}
public void Demo_007_Neural_Network_3()
{
Console.WriteLine("Neural Networkのデモンストレーションです");
Console.WriteLine("今回は1層では学習できない例を紹介します\n\n");
//教師データを設定します。
//簡単のためf(x)の一次元とします。
List <double[, ]> list_x = new List <double[, ]>();
List <double[, ]> list_t = new List <double[, ]>();
for (int j = 0; j < 6; j++)
{
double[,] x = new double[1, 1];
x[0, 0] = j * 1.0;
list_x.Add(x);
double[,] t = new double[1, 1];
if (j < 2 || 3 < j)
{
t[0, 0] = 1;
}
else
{
t[0, 0] = 0;
}
list_t.Add(t);
}
Console.WriteLine("今回の入力値xと、答えtです");
Console.WriteLine("x < 2 , 3 < x のとき、答えが1になります。それ以外の場合、0です。");
Console.Write("x\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine("\t");
Console.Write("t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine("\n\n");
Console.WriteLine("まずは1層のNeural Networkで試してみます");
Console.WriteLine("計数行列Wとバイアスベクトルbを設定します。");
double[,] W_f = new double[1, 1];
W_f[0, 0] = 3;
double[,] b_f = new double[1, 1];
b_f[0, 0] = 2;
Console.WriteLine("W[0,0] = " + W_f[0, 0] + "\t" + "b[0,0] = " + b_f[0, 0] + "\n\n");
Console.WriteLine("Neural Netoworkを設定しました。今回の活性化関数はSigmoid関数とします");
Console.WriteLine("ハイパーパラメータの値は0.1とします。\n");
Regression_Final_Layer rfl = new Regression_Final_Layer();
rfl.Preset_1_4th_Set_w(W_f);
rfl.Preset_2_4th_Set_b(b_f);
rfl.Preset_3_4th_Set_Hyper_Parameter(0.3, 0, 0.01, 0);
rfl.Preset_4_4th_Set_activation_Function(new Sigmoid_IFunction());
Console.WriteLine("学習前のNeural Networkの出力を確認します。");
List <double[, ]> list_wx_plus_b = new List <double[, ]>();
List <double[, ]> list_f_wx_plus_b = new List <double[, ]>();
List <double[, ]> list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine("\n\n");
Console.WriteLine("100,000 epoch 学習しました。");
int epoch = 100000;
for (int j = 0; j < list_x.Count * epoch; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
rfl.Step_3_3rd_Update();
}
list_wx_plus_b = new List <double[, ]>();
list_f_wx_plus_b = new List <double[, ]>();
list_delta = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
rfl.Step_1_3rd_Forward_Propagation(list_x[j]);
list_wx_plus_b.Add(rfl.Get_wx_plus_b());
list_f_wx_plus_b.Add(rfl.Get_f_wx_plus_b());
rfl.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j]);
list_delta.Add(rfl.Get_delta());
}
Console.WriteLine("W " + rfl.Get_w()[0, 0] + "\t" + "b " + rfl.Get_b()[0, 0]);
Console.Write("x\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("wx + b\t\t");
foreach (double[,] x in list_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("f(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.WriteLine("\n\n\n");
Console.WriteLine("次は、2層のNeural Networkで試してみます");
Console.WriteLine("第1層の計数行列はwは2行1列の行列とします");
Console.WriteLine("活性化関数はSwish関数とします");
double[,] w_1 = new double[2, 1];
w_1[0, 0] = 3;
w_1[1, 0] = -3;
Console.WriteLine("第1層の計数行列 w");
this.Show_Matrix_Element(w_1);
double[,] b_1 = new double[2, 1];
b_1[0, 0] = 2;
b_1[1, 0] = -2;
Console.WriteLine("第1層のバイアスベクトル b");
this.Show_Matrix_Element(b_1);
//第一層は隠れ層なので、別のクラスです
Hidden_Layer hd_1 = new Hidden_Layer();
hd_1.Preset_1_4th_Set_w(w_1);
hd_1.Preset_2_4th_Set_b(b_1);
hd_1.Preset_3_4th_Set_Hyper_Parameter(0.15, 0, 0, 0);
hd_1.Preset_4_4th_Set_activation_Function(new Swish_IFunction());
Console.WriteLine("\n");
Console.WriteLine("第2層の計数行列はwは1行2列の行列とします");
Console.WriteLine("活性化関数は、第2層はSigmoid関数とします");
double[,] w_2 = new double[1, 2];
w_2[0, 0] = 3;
w_2[0, 1] = -3;
Console.WriteLine("第2層の計数行列 w");
this.Show_Matrix_Element(w_2);
double[,] b_2 = new double[1, 1];
b_2[0, 0] = 2;
Console.WriteLine("第2層のバイアスベクトル b");
this.Show_Matrix_Element(b_2);
Console.WriteLine("\n\n");
Regression_Final_Layer rfl_2 = new Regression_Final_Layer();
rfl_2.Preset_1_4th_Set_w(w_2);
rfl_2.Preset_2_4th_Set_b(b_2);
rfl_2.Preset_3_4th_Set_Hyper_Parameter(0.15, 0, 0, 0);
rfl_2.Preset_4_4th_Set_activation_Function(new Sigmoid_IFunction());
Console.WriteLine("\n\n");
Console.WriteLine("学習前のNeural Networkの出力を確認します。");
List <double[, ]> list_wx_plus_b_1 = new List <double[, ]>();
List <double[, ]> list_f_wx_plus_b_1 = new List <double[, ]>();
List <double[, ]> list_wx_plus_b_2 = new List <double[, ]>();
List <double[, ]> list_f_wx_plus_b_2 = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
//順伝搬
hd_1.Step_1_3rd_Forward_Propagation(list_x[j]);
rfl_2.Step_1_3rd_Forward_Propagation(hd_1.Get_f_wx_plus_b());
list_wx_plus_b_1.Add(hd_1.Get_wx_plus_b());
list_f_wx_plus_b_1.Add(hd_1.Get_f_wx_plus_b());
list_wx_plus_b_2.Add(rfl_2.Get_wx_plus_b());
list_f_wx_plus_b_2.Add(rfl_2.Get_f_wx_plus_b());
}
Console.WriteLine("第1層のW ");
this.Show_Matrix_Element(hd_1.Get_w());
Console.WriteLine("第1層のb ");
this.Show_Matrix_Element(hd_1.Get_b());
Console.Write("x\t\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("第1層の(wx + b)\t\t");
foreach (double[,] x in list_wx_plus_b_1)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.Write("\n \t\t\t");
foreach (double[,] x in list_wx_plus_b_1)
{
Console.Write(x[1, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("第1層のf(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b_1)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.Write("\n \t\t\t");
foreach (double[,] x in list_f_wx_plus_b_1)
{
Console.Write(x[1, 0].ToString("G3") + "\t");
}
Console.WriteLine("\n");
Console.WriteLine("第2層のW ");
this.Show_Matrix_Element(rfl_2.Get_w());
Console.WriteLine("第2層のb ");
this.Show_Matrix_Element(rfl_2.Get_b());
Console.Write("第2層の(wx + b)\t\t");
foreach (double[,] x in list_wx_plus_b_2)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("第2層のf(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b_2)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine("\n\n");
Console.WriteLine("100,000 epoch 学習しました。");
epoch = 100000;
for (int j = 0; j < list_x.Count * epoch; j++)
{
//順伝搬
hd_1.Step_1_3rd_Forward_Propagation(list_x[j % list_x.Count]);
rfl_2.Step_1_3rd_Forward_Propagation(hd_1.Get_f_wx_plus_b());
//逆伝搬
rfl_2.Step_2_3rd_Calculate_Target_Function_and_Delta(list_t[j % list_x.Count]);
hd_1.Step_2_3rd_Calculate_Delta(rfl_2.Get_w(), rfl_2.Get_delta());
//パラメータの更新
rfl_2.Step_3_3rd_Update();
hd_1.Step_3_3rd_Update();
}
list_wx_plus_b_1 = new List <double[, ]>();
list_f_wx_plus_b_1 = new List <double[, ]>();
list_wx_plus_b_2 = new List <double[, ]>();
list_f_wx_plus_b_2 = new List <double[, ]>();
for (int j = 0; j < list_x.Count; j++)
{
//順伝搬
hd_1.Step_1_3rd_Forward_Propagation(list_x[j]);
rfl_2.Step_1_3rd_Forward_Propagation(hd_1.Get_f_wx_plus_b());
list_wx_plus_b_1.Add(hd_1.Get_wx_plus_b());
list_f_wx_plus_b_1.Add(hd_1.Get_f_wx_plus_b());
list_wx_plus_b_2.Add(rfl_2.Get_wx_plus_b());
list_f_wx_plus_b_2.Add(rfl_2.Get_f_wx_plus_b());
}
Console.WriteLine("第1層のW ");
this.Show_Matrix_Element(hd_1.Get_w());
Console.WriteLine("第1層のb ");
this.Show_Matrix_Element(hd_1.Get_b());
Console.Write("x\t\t\t");
foreach (double[,] x in list_x)
{
Console.Write(x[0, 0] + "\t");
}
Console.WriteLine(" ");
Console.Write("第1層の(wx + b)\t\t");
foreach (double[,] x in list_wx_plus_b_1)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.Write("\n \t\t\t");
foreach (double[,] x in list_wx_plus_b_1)
{
Console.Write(x[1, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("第1層のf(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b_1)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.Write("\n \t\t\t");
foreach (double[,] x in list_f_wx_plus_b_1)
{
Console.Write(x[1, 0].ToString("G3") + "\t");
}
Console.WriteLine("\n");
Console.WriteLine("第2層のW ");
this.Show_Matrix_Element(rfl_2.Get_w());
Console.WriteLine("第2層のb ");
this.Show_Matrix_Element(rfl_2.Get_b());
Console.Write("第2層の(wx + b)\t\t");
foreach (double[,] x in list_wx_plus_b_2)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("第2層のf(wx + b)\t");
foreach (double[,] x in list_f_wx_plus_b_2)
{
Console.Write(x[0, 0].ToString("G3") + "\t");
}
Console.WriteLine(" ");
Console.Write("t\t\t\t");
foreach (double[,] t in list_t)
{
Console.Write(t[0, 0] + "\t");
}
Console.WriteLine("\n\n");
}