CODEWITHSUNDEEP
machine-learningneural-networkclassificationperceptron
bob
bob

Reputation: 629

Can this neural network perform separation?

I have three classes of points:

C1: {(4,1), (2,3), (3,5), (5,4), (1,6)}

C2: {(0,2), (-2,2), (-3,2), (-2,4)}

C3: {(1,-2), (3,-2)}

I also have a single-layer perceptron with 2 inputs, a bias term, and three outputs.

a) Can the net learn to separate the samples? (Assuming that we want yi = 1 if x ∈ Ci and yj = −1 for j != i)

b) Add the sample (-1,6) to C1. Now, can the net learn to separate the samples?

I don't know how to approach this problem. I don't need to specify the actual weights, but how do I determine whether the network will be able to separate the samples or not? Can this be done purely graphically, or is there a written proof?

Upvotes: 0

Views: 77

Answers (1)

shahaf
shahaf

Reputation: 4983

you can see from the graph generated by the following code

import matplotlib.pyplot as plt

C1 = [(4,1), (2,3), (3,5), (5,4), (1,6), (-1,6)]
C2 = [(0,2), (-2,2), (-3,2), (-2,4)]
C3 = [(1,-2), (3,-2)]

plt.scatter([i[0] for i in C1],[i[1] for i in C1], c='b')
plt.scatter([i[0] for i in C2],[i[1] for i in C2], c='r')
plt.scatter([i[0] for i in C3],[i[1] for i in C3], c='g')
plt.show()

enter image description here

the data can be easily separated by linear lines, perceptron aka neural network with just 1 layer can learn to separate linear data

a full neural network with a few layers, can produce non linear separation, so it can do it easily

Upvotes: 2

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