This tutorial assumes some familiarity with basic principles of machine learning, the math and code can be developed on the way.

Machine Learning

Learning can be Supervised, Unsupervised, Reinforced and Semi-supervised.

Reinforcement Learning: Learning with a critic, critic may be wrong at times, maybe stochastic, but different from supervisor in case of supervised learning. Supervisor gives feedback, critic only says yes or no.

K-Means algorithm:

1. K as a parameter
2. distance threshold as a parameter

K means crisp decision boundary: grading, fingerprint ROI(Region of Interest)

Reinforcement learning correspinds to lifelong learning, much like our biological learning process.

For crisp decision boundary, some error is always there and is acceptable, but try to minimize the error.

Fuzzy decision boundary: signal noise separation, decision boundary is not well defined

Threshold could be crisp or noisy.

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Algorithms:

1. Polynomial time O(n^k): size of inut is n, number of steps is n^k, eg: sorting, FFT

2. Exponential time O(kⁿ): size of inut is n, number of steps is kⁿ, Travelling salesman problem

3. Ugly: Optimal but takes infinite time

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K Means

• N points can be divided into K clusters, each point has D dimensions

• u_j is mean of the jth cluster

• such that the sum of square distances of each data point to its closest vector u_j is minimum.

• Vector quantizatoin: u_j -> points

• Objective function: distortion measure or cost function \begin{equation} J = \sum_{i = 1}^{N}\sum_{j = 1}^{K} r_{ij} \left |x_i - u_j \right |^2 \end{equation}

• Not taking abs or mod because mod is not differentiable and thus avoided during optimization.

• r _ij is a binary indicator variable: 1 if the ith data point is assigned to the jth cluster, 0 otherwise.

In total there are N data points and K clusters.

• Find {r_ij} and {u_j} such that J is minimised.

To solve use: Expectation Maximization framework or EM method.

Randomly choose K initial clusters with means u_j.

1. Fixed u_j, find assignment r_ij.
2. Take avg of x_ij to find new u_j, repeat from 1.