5.2 Multi Layer Perceptron

5.2.1 Multi Layer Perceptron Classifier

In[]:=
session=StartExternalSession["Python"]
Out[]=
ExternalSessionObject
System: Python
EvaluationCount:
None
UUID: 0e6a8775-59d2-47b9-8821-38406f5631c9

Test
〉
In[]:=
5+6
Out[]=
11
〉
In[]:=
​
from numpy import array, matrix
from scipy.io import mmread, mmwrite
import numpy as np
〉
In[]:=
from sklearn.datasets import make_moons
X, y =make_moons(n_samples=100,noise=0.25,random_state=3)
〉
In[]:=
mmwrite('pubi.mtx',X)
In[]:=
trainX=Import["pubi.mtx"];
〉
In[]:=
y
Out[]=
NumericArray
Type: Integer64
Dimensions: {100}

In[]:=
Normal[%]
Out[]=
{1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,1,0,1,0,0,0,0,1,0,1,1,0,0,0,0,0,0,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,1,1,0,0}
In[]:=
cluster=%;total=MapThread[{#1,#2}&,{trainX,cluster}];
In[]:=
clust1=Select[total,#[[2]]0&];
In[]:=
clust2=Select[total,#[[2]]1&];
In[]:=
pclust1=Map[#[[1]]&,clust1];
In[]:=
pclust2=Map[#[[1]]&,clust2];
In[]:=
p0=Show[{ListPlot[pclust1,PlotStyle{Green,PointSize[0.017]}],ListPlot[pclust2,PlotStyle{Red,PointSize[0.017]}]}]
Out[]=
〉
In[]:=
from sklearn.neural_network import MLPClassifier
import mglearn
〉
In[]:=
mlp = MLPClassifier(solver='lbfgs', random_state=0).fit(X,y)
〉
In[]:=
cupi=mlp.predict(X)
cupi
Out[]=
NumericArray
Type: Integer64
Dimensions: {100}

In[]:=
Normal[%]
Out[]=
{1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,1,0,1,0,0,0,0,1,0,1,1,0,0,0,0,0,0,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,1,1,0,0}
In[]:=
zu=%;
In[]:=
zu-cluster
Out[]=
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
〉
In[]:=
import matplotlib.pyplot as plt
〉
In[]:=
mglearn.plots.plot_2d_separator(mlp, X, fill=True, alpha=.3)
〉
In[]:=
mglearn.discrete_scatter(X[:,0],X[:,1],y)
Out[]=
ExternalObject
Name: Line2D
System: Python
​
Type: PythonFunction
IsModule: False
,ExternalObject
Name: Line2D
System: Python
​
Type: PythonFunction
IsModule: False

Running Python under Mathematica here gives an error message! No worries!
〉
In[]:=
plt.show()
This Python command provide the figure in a separate window,
In[]:=
Plot[(Tanh[2x]+1)/2,{x,-2,2}]
Out[]=
In[]:=
myL=ElementwiseLayer[(Tanh[2#]+1)/2&]
Out[]=
ElementwiseLayer

Function:
0.5(tanh(2x)+1)
Output:
array

In[]:=
net=NetInitialize@NetChain[{LinearLayer[15,"Input"2],myL,LinearLayer[15],ElementwiseLayer[Ramp],LinearLayer[1]},"Input"{2}]

5.2.2 Multi Layer Perceptron Regressor

〉
In[]:=
from sklearn.neural_network import MLPRegressor
import numpy as np
import matplotlib.pyplot as plt
import random
〉
In[]:=
x=np.arange(0.,1.,0.01).reshape(-1,1)
〉
In[]:=
y=np.sin(0.3*np.pi*x).ravel()+np.cos(3*np.pi*x*x).ravel()+np.random.normal(0,0.15,x.shape).ravel()
y
〉
In[]:=
nn=MLPRegressor(hidden_layer_sizes=(12),activation='tanh',solver='lbfgs').fit(x,y)
〉
In[]:=
test_x=np.arange(-0.01,1.02,0.01).reshape(-1,1)
test_y=nn.predict(test_x)
〉
In[]:=
fig = plt.figure()
〉
In[]:=
ax1=fig.add_subplot(111)
〉
In[]:=
ax1.scatter(x,y,s=5,c='b',marker="o",label='real')
〉
In[]:=
ax1.plot(test_x,test_y,c='r',label='NN Prediction')
〉
In[]:=
plt.show()