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Geometric intuition of PCA
Geometric intuition of PCA
Instructor:
Applied AI Course
Duration:
14 mins
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A nice answer on stack exchange that gives simple intuition:
https://stats.stackexchange.com/a/140579/207753
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Why learn PCA?
Mathematical objective function of PCA
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Plotting for exploratory data analysis (EDA)
1.1
Introduction to IRIS dataset and 2D scatter plot
26 min
1.2
3D scatter plot
6 min
1.3
Pair plots
14 min
1.4
Limitations of Pair Plots
2 min
1.5
Histogram and Introduction to PDF(Probability Density Function)
17 min
1.6
Univariate Analysis using PDF
6 min
1.7
CDF(Cumulative Distribution Function)
15 min
1.8
Mean, Variance and Standard Deviation
17 min
1.9
Median
10 min
1.10
Percentiles and Quantiles
9 min
1.11
IQR(Inter Quartile Range) and MAD(Median Absolute Deviation)
6 min
1.12
Box-plot with Whiskers
9 min
1.13
Violin Plots
4 min
1.14
Summarizing Plots, Univariate, Bivariate and Multivariate analysis
6 min
1.15
Multivariate Probability Density, Contour Plot
9 min
1.16
Assignment-1: Data Visualization with Haberman Dataset
4 min
Linear Algebra
2.1
Why learn it ?
4 min
2.2
Introduction to Vectors(2-D, 3-D, n-D) , Row Vector and Column Vector
14 min
2.3
Dot Product and Angle between 2 Vectors
14 min
2.4
Projection and Unit Vector
5 min
2.5
Equation of a line (2-D), Plane(3-D) and Hyperplane (n-D), Plane Passing through origin, Normal to a Plane
23 min
2.6
Distance of a point from a Plane/Hyperplane, Half-Spaces
10 min
2.7
Equation of a Circle (2-D), Sphere (3-D) and Hypersphere (n-D)
7 min
2.8
Equation of an Ellipse (2-D), Ellipsoid (3-D) and Hyperellipsoid (n-D)
6 min
2.9
Square ,Rectangle
6 min
2.10
Hyper Cube,Hyper Cuboid
3 min
2.11
Revision Questions
30 min
Probability and Statistics
3.1
Introduction to Probability and Statistics
17 min
3.2
Population and Sample
7 min
3.3
Gaussian/Normal Distribution and its PDF(Probability Density Function)
27 min
3.4
CDF(Cumulative Distribution function) of Gaussian/Normal distribution
11 min
3.5
Symmetric distribution, Skewness and Kurtosis
24 min
3.6
Standard normal variate (Z) and standardization
5 min
3.7
Kernel density estimation
7 min
3.8
Sampling distribution & Central Limit theorem
19 min
3.9
Q-Q plot:How to test if a random variable is normally distributed or not?
23 min
3.10
How distributions are used?
17 min
3.11
Chebyshev’s inequality
20 min
3.12
Discrete and Continuous Uniform distributions
13 min
3.13
How to randomly sample data points (Uniform Distribution)
10 min
3.14
Bernoulli and Binomial Distribution
11 min
3.15
Log Normal Distribution
12 min
3.16
Power law distribution
12 min
3.17
Box cox transform
12 min
3.18
Applications of non-gaussian distributions?
26 min
3.19
Co-variance
14 min
3.20
Pearson Correlation Coefficient
13 min
3.21
Spearman Rank Correlation Coefficient
7 min
3.22
Correlation vs Causation
3 min
3.23
How to use correlations?
13 min
3.24
Confidence interval (C.I) Introduction
8 min
3.25
Computing confidence interval given the underlying distribution
11 min
3.26
C.I for mean of a random variable
14 min
3.27
Confidence interval using bootstrapping
17 min
3.28
Hypothesis testing methodology, Null-hypothesis, p-value
16 min
3.29
Hypothesis Testing Intution with coin toss example
27 min
3.30
Resampling and permutation test
15 min
3.31
K-S Test for similarity of two distributions
15 min
3.32
Code Snippet K-S Test
6 min
3.33
Hypothesis testing: another example
18 min
3.34
Resampling and Permutation test: another example
19 min
3.35
How to use hypothesis testing?
23 min
3.36
Proportional Sampling
18 min
3.37
Revision Questions
30 min
Interview Questions on Probability and statistics
4.1
Questions & Answers
30 min
Dimensionality reduction and Visualization:
5.1
What is Dimensionality reduction?
3 min
5.2
Row Vector and Column Vector
5 min
5.3
How to represent a data set?
4 min
5.4
How to represent a dataset as a Matrix.
7 min
5.5
Data Preprocessing: Feature Normalisation
20 min
5.6
Mean of a data matrix
6 min
5.7
Data Preprocessing: Column Standardization
16 min
5.8
Co-variance of a Data Matrix
24 min
5.9
MNIST dataset (784 dimensional)
20 min
5.10
Code to Load MNIST Data Set
12 min
PCA(principal component analysis)
6.1
Why learn PCA?
4 min
6.2
Geometric intuition of PCA
14 min
6.3
Mathematical objective function of PCA
13 min
6.4
Alternative formulation of PCA: Distance minimization
10 min
6.5
Eigen values and Eigen vectors (PCA): Dimensionality reduction
23 min
6.6
PCA for Dimensionality Reduction and Visualization
10 min
6.7
Visualize MNIST dataset
5 min
6.8
Limitations of PCA
5 min
6.9
PCA Code example
19 min
6.10
PCA for dimensionality reduction (not-visualization)
15 min
(t-SNE)T-distributed Stochastic Neighbourhood Embedding
7.1
What is t-SNE?
7 min
7.2
Neighborhood of a point, Embedding
7 min
7.3
Geometric intuition of t-SNE
9 min
7.4
Crowding Problem
8 min
7.5
How to apply t-SNE and interpret its output
38 min
7.6
t-SNE on MNIST
7 min
7.7
Code example of t-SNE
9 min
7.8
Revision Questions
30 min
Interview Questions on Dimensionality Reduction
8.1
Questions & Answers
30 min
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