Case Study: Separate Regularly Scattered Ys

Y clusters can be separated rather easily with fewer times of linear separation. The following code separate 4 classes with just 2 lines (which mean 2 hidden layers).

Y input values are normalised too, doesn't work when being integer numbers; even with this wrapper about output sigmoid:
tf.multiply(tf.sigmoid(...), 3)

Source code:

#libs
import tensorflow        as tf;
import matplotlib.pyplot as pyplot;

#data
X = [[0,0], [0,1], [1,0], [10,10], [20,20]];
Y = [[0],   [1],   [2],   [3],     [3]    ];
Batch_Size = 5;
MAX        = 20;

#normalise
for I in range(len(X)):
  X[I][0] = X[I][0]/MAX;
  X[I][1] = X[I][1]/MAX;
  Y[I][0] = Y[I][0]/3;
#end for

#model
Input     = tf.placeholder(dtype=tf.float32, shape=[Batch_Size,2]);
Expected  = tf.placeholder(dtype=tf.float32, shape=[Batch_Size,1]);

Weight1   = tf.Variable(tf.random_uniform(shape=[2,20], minval=-1, maxval=1));
Bias1     = tf.Variable(tf.random_uniform(shape=[  20], minval=-1, maxval=1));
Hidden1   = tf.nn.relu(tf.matmul(Input,Weight1) + Bias1);

Weight2   = tf.Variable(tf.random_uniform(shape=[20,10], minval=-1, maxval=1));
Bias2     = tf.Variable(tf.random_uniform(shape=[   10], minval=-1, maxval=1));
Hidden2   = tf.nn.relu(tf.matmul(Hidden1,Weight2) + Bias2);

Weight3   = tf.Variable(tf.random_uniform(shape=[10,1], minval=-1, maxval=1));
Bias3     = tf.Variable(tf.random_uniform(shape=[   1], minval=-1, maxval=1));
Output    = tf.sigmoid(tf.matmul(Hidden2,Weight3) + Bias3);

Loss      = tf.reduce_sum(tf.square(Expected-Output));
Optimiser = tf.train.GradientDescentOptimizer(1e-1);
Training  = Optimiser.minimize(Loss);

#train
Sess = tf.Session();
Init = tf.global_variables_initializer();
Sess.run(Init);

Losses = [];
for I in range(10000):
  if (I%1000==0):
    Lossvalue = Sess.run(Loss, feed_dict={Input:X, Expected:Y});
    Losses += [Lossvalue];
    print("Loss:",Lossvalue);
  #end if
  
  Sess.run(Training, feed_dict={Input:X, Expected:Y});
#end for

#result: loss
Lastloss = Sess.run(Loss, feed_dict={Input:X, Expected:Y});
Losses  += [Lastloss];
print("Loss:",Lastloss,"(Last)");

#result: eval
Evalresult = Sess.run(Output, feed_dict={Input:X, Expected:Y});
for I in range(Batch_Size):
  Evalresult[I][0] = round(Evalresult[I][0],9);

print("Eval:\n"+str(Evalresult));

#result: diagram
print("Loss curve:");
pyplot.plot(Losses);
#eof

Colab link:
https://colab.research.google.com/drive/1v0ri7G802XNJy-nzp6lu1ChqaDdprnYY