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Mathematical objective function of PCA

Instructor: Applied AI Course Duration: 13 mins

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Geometric intuition of PCA
Alternative formulation of PCA: Distance minimization
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
Exercise: Perform EDA on Haberman dataset

4 min
2.1
Why learn it ?

4 min
2.2
Introduction to Vectors(2-D, 3-D, n-D)

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)

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
3.1
Introduction to Probability and Statistics
17 min
3.2
Population and Sample
7 min
3.3
Gaussian/Normal Distribution
27 min
3.4
CDF(Cumulative Distribution function) of Gaussian/Normal distribution
11 min
3.5
Symmetric distribution, Skewness and Kurtosis
5 min
3.6
Standard normal variate (z) and standardization
15 min
3.7
Kernal density estimation
7 min
3.8
Sampling distribution and 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
Discrete and Continuous Uniform distributions
13 min
3.11
How to randomly sample data points (Uniform Distribution)
10 min
3.12
Bernoulli and Binomial Distribution
11 min
3.13
Log Normal Distribution
12 min
3.14
Power law distribution
12 min
3.15
Box cox transform
12 min
3.16
Co-variance
14 min
3.17
Pearson Correlation Coefficient
13 min
3.18
Spearman Rank Correlation Coefficient
7 min
3.19
Correlation vs Causation
3 min
3.20
Confidence Interval Introduction
8 min
3.21
Hypothesis testing methodology, Null-hypothesis, p-value
16 min
3.22
Testing methodology, Null-hypothesis, test-statistic, p-value
16 min
3.23
Resampling and permutation test
15 min
3.24
K-S Test
6 min
3.25
K-S Test for similarity of two distributions
15 min
4.1
what is dimensionality reduction?
3 min
4.2
Row vector, Column vector: Iris dataset example
5 min
4.3
Represent a dataset: D= {x_i, y_i}
4 min
4.4
Represent a dataset as a Matrix
7 min
4.5
Data preprocessing: Column Normalization
20 min
4.6
Mean of a data matrix
6 min
4.7
Data preprocessing: Column Standardization
16 min
4.8
Co-variance of a Data Matrix
24 min
4.9
MNIST dataset (784 dimensional)
20 min
4.10
Code to load MNIST Dataset
12 min
6.1
What is t-SNE?
7 min
6.2
Neighborhood of a point, Embedding
7 min
6.3
Geometric intuition of t-SNE
9 min
6.4
Crowding Problem
8 min
6.5
How to apply t-SNE and interpret its output
38 min
6.6
t-SNE on MNIST
7 min
6.7
Code example of t-SNE
9 min