Solving Pattern Recognition Problems via Python and MATLAB.

Problem Statements:

1. Fit a Curve to the given data using Linear Regression Curve Fitting.

2. Fit a Curve to the given data using Gaussian Curve Fitting.

3. Fit a Curve to the given data using Bayesian Curve Fitting

4. Take a normal noise free image and compute the:

   1. KL Divergence of this noise free image with another noisy image obtained after adding noise to this normal image. (You can add dierent types of noise like salt and pepper, Gaussian etc.)

   2. Plot a graph of how the KL Divergence Changes as the image gets more and more noisy.

   3. Also compute the entropy of this normal Image.

   4. Also compute entropy of noisy images and plot how entropy changes as more and more noise is added to the image.

5. Compute the Dirichlet Distribution of the given data and plot the computed Distri- bution.

6. Create some regular and irregular hexagons. A Hexagon can be represented by its 6 points and each point can be represented by 2 (x, y) coordinates. So a single hexagon can be represented as a (6, 2) matrix.

   Create 10 regular and 10 irregular hexagons of dierent shapes and size, with dierent positions on the euclidean plane. Between each pair of hexagons compute the Mahalanobis Distance.

7. Record Your own voice as an audio sample, try to record in a noise free environment so hat there is only one audio source (you). Extract the pitch from this audio sample and use that as an the input data for this laboratory experiment.

   Segment out the dierent words from this audio sample by identifying those places where the pitch drops to a very low value. Also submit along the sample text with this experiment so that the actual words can be identied. Use these segmented words and their pitch values to compute the following distributions:

   1. t-Distribution
   2. F-Distribution
   3. k-Distribution

   Plot 3 dierent graphs for each distribution for the same audio sample.

8. Use MoG (Mixture of Gaussian) Method to represent a Non-Linear Curve.

9. Use the audio sample that you recorded for Experiment-7 and perform bias-variance decom- position on it. The audio sample here represents a stationary random signal which can be decomposed into it’s bias and variance.

10. WAP to compute the best fit distribution for the given 2 patterns like Bernoulli, Beta, Dirichlet, Distribution, Gaussian Distribution. Compute parameters of the distribution using MAP