The document provides an introduction to unsupervised learning and reinforcement learning. It then discusses eigen values and eigen vectors, showing how to calculate them from a matrix. It provides examples of covariance matrices and using Gaussian elimination to solve for eigen vectors. Finally, it discusses principal component analysis and different clustering algorithms like K-means clustering.

1. INTRODUCTION TO UNSUPERVISED LEARNING
INTRODUCTION TO REINFORCEMENT LEARNING

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Deriving new featuresfrom old ones

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Spread in 1D
Relationship b/w 2D, sign has significance not value
Symmetric about main diagonal

4. Let A be an n x n matrix. A scalar λ is called an eigen value of A if there is a non-zero vector
x such that Ax = λx. Such a vector x is called an eigen vector of A corresponding to λ
1. Form the matrix A – λI
2. Calculate det |A – λI|
3. Find solutions to det |A –λI| = 0, which gives the eigen value.
Find x by Gaussian elimination.
Convert the augmented matrix to row echelon form.
Solve the resulting linear system by back substitution.
https://www.studypug.com/algebra-help/solving-a-linear-system-with-matrices-using-gaussian-elimination

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14. x1 x2
2.5 2.4
0.5 0.7
2.2 2.9
1.9 2.2
3.1 3.0
2.3 2.7
2.0 1.6
1.0 1.1
1.5 1.6
1.1 0.9

15. 3.0
2.5
2.0
1.5
1.0
0.5
3.0
2.5
2.0
1.5
1.0
x1
x2
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9
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3
2
1
Scatterplot of x2 vs x1

16. X1 X2
0.69 0.49
-1.31 -1.21
0.39 0.99
0.09 0.29
1.29 1.09
0.49 0.79
0.19 -0.31
-0.81 -0.81
-0.31 -0.31
-0.71 -1.01

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0.616556 0.615444
0.615444 0.716556
Covariance Matrix
https://www.emathhelp.net/calculators/linear-algebra/eigenvalue-and-eigenvector-
calculator/?i=%5B%5B.616556%2C.615444%5D%2C%5B.615444%2C.716556%5D%5D&steps=on
Eigen Value λ1 = 0.049083 λ2 = 1.28403
Total Sample Variance / Trace = 1.3331134
λ1 = 96.3% variance λ2 = 3.7% variance
0.677873 0.735179
0.735179 -0.67787
TASK Eigen Vector:
use Gaussian elimination Refer pdf pg 11 in continuation
https://www.geeksforgeeks.org/mathematical-approach-to-pca/

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The Mathematics Behind Principal Component Analysis | by Akash Dubey | Towards Data Science

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https://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php

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Retain k dimensions such that 80%-95% of the energy is retained
Eigenvalues & Eigenvectors: Definition, Equation & Examples - Video & Lesson Transcript | Study.com

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25. Distribution
Methods
• Expectation
Maximization
Grid-based
Methods
• CLIQUE
Partitioning
Methods
• K-means
Hierarchical
Based Methods
• BIRCH
• CURE
Density-Based
Methods
• DBSCAN
• OPTICS
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26. Manhattan distance and 3 clusters https://www.gatevidyalay.com/tag/k-means-clustering-numerical-example-pdf/ self study
https://www.datasciencecentral.com/profiles/blogs/steps-to-calculate-centroids-in-cluster-using-k-means-clustering
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