README.md

Sine-Classifier

A simple neural network to classify points generated using a sine function.
The model is trained using gradient descent algorithm with backpropagation for calculating gradients.
Graphics are generated using WinBGI graphics library in C++ language.

Generating Data:

Random points are generated for train and test set and are saved in training_set.txt and test_set.txt.

• Train data:

  • Label 1 (RED) : Points on and above the sine graph.
  • Label 0 (GREEN): Points below the sine graph.

• Test data:

  • Shown in YELLOW.

Neural Network:

Architecture :-

• Input Layer: 2 nodes with two coordinates of a point.
• Hidden Layer1: 20 nodes with sigmoid activation function.
• Hidden Layer2: 20 nodes with sigmoid activation function.
• Output Layer: 1 node with sigmoid activation function.

   

Cost function :-

Mean Squared Error (MSE)

Gradient Descent with Backpropagation :-

Some good resources:-

• Neural networks playlist by 3Blue1Brown
• Backpropagation Example
• The Vanishing Gradient Problem

Results:

• Test data:
  • Points in PINK are classified into Label 1 (RED).
  • Points in BLUE are classified into Label 0 (GREEN).

   

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Regression Approach (Classification using Logistic Regression):

Apart from this neural network classification which is more general, I tried classification using regression also.
I assumed a general sine curve : y = Amplitude * sin(freq * x + Phase) + Offset
And then based on these 4 parameters, tried to fit this graph according to the points given.

Results:

• Graph in WHITE is the fitted graph with the predicted 4 parameters.

• Test data:

  • Points in PINK are classified into Label 1 (RED).
  • Points in BLUE are classified into Label 0 (GREEN).