Home Courses Applied Machine Learning Online Course Mathematical objective function of PCA

Mathematical objective function of PCA

Instructor: Applied AI Course Duration: 13 mins

 

Correction: the scalar projection should be equal to (u1.Xi) / ||u1||

Prev
Next
Geometric intuition of PCA
Alternative formulation of PCA: Distance minimization

820 Comment(s)

Login to comment
1.1
How to Learn from Appliedaicourse

35 min
2.1
Python, Anaconda and relevant packages installations

23 min
2.2
Why learn Python?

4 min
2.3
Keywords and identifiers

6 min
2.4
comments, indentation and statements

9 min
2.5
Variables and data types in Python

32 min
2.6
Standard Input and Output

7 min
2.7
Operators

14 min
2.8
Control flow: if else

10 min
2.9
Control flow: while loop

16 min
2.10
Control flow: for loop

15 min
2.11
Control flow: break and continue

10 min
3.1
Lists

38 min
3.2
Tuples part 1

10 min
3.3
Tuples part-2

4 min
3.4
Sets

16 min
3.5
Dictionary

21 min
3.6
Strings

16 min
4.1
Introduction to IRIS dataset and 2D scatter plot

26 min
4.2
3D scatter plot

6 min
4.3
Pair plots

14 min
4.4
Limitations of Pair Plots

2 min
4.5
Histogram and Introduction to PDF(Probability Density Function)

17 min
4.6
Univariate Analysis using PDF

6 min
4.7
CDF(Cumulative Distribution Function)

15 min
4.8
Mean, Variance and Standard Deviation

17 min
4.9
Median

10 min
4.10
Percentiles and Quantiles

9 min
4.11
IQR(Inter Quartile Range) and MAD(Median Absolute Deviation)

6 min
4.12
Box-plot with Whiskers

9 min
4.13
Violin Plots

4 min
4.14
Summarizing Plots, Univariate, Bivariate and Multivariate analysis

6 min
4.15
Multivariate Probability Density, Contour Plot

9 min
4.16
Assignment-1: Data Visualization with Haberman Dataset

4 min
5.1
Why learn it ?

4 min
5.2
Introduction to Vectors(2-D, 3-D, n-D) , Row Vector and Column Vector

14 min
5.3
Dot Product and Angle between 2 Vectors

14 min
5.4
Projection and Unit Vector

5 min
5.5
Equation of a line (2-D), Plane(3-D) and Hyperplane (n-D), Plane Passing through origin, Normal to a Plane

23 min
5.6
Distance of a point from a Plane/Hyperplane, Half-Spaces

10 min
5.7
Equation of a Circle (2-D), Sphere (3-D) and Hypersphere (n-D)

7 min
5.8
Equation of an Ellipse (2-D), Ellipsoid (3-D) and Hyperellipsoid (n-D)

6 min
5.9
Square ,Rectangle

6 min
5.10
Hyper Cube,Hyper Cuboid

3 min
6.1
Introduction to Probability and Statistics

17 min
6.2
Population and Sample

7 min
6.3
Gaussian/Normal Distribution and its PDF(Probability Density Function)

27 min
6.4
CDF(Cumulative Distribution function) of Gaussian/Normal distribution

11 min
7.1
What is Dimensionality reduction?

3 min
7.2
Row Vector and Column Vector

5 min
7.3
How to represent a data set?

4 min
7.4
How to represent a dataset as a Matrix.

7 min
7.5
Data Preprocessing: Feature Normalisation

20 min
7.6
Mean of a data matrix

6 min
7.7
Data Preprocessing: Column Standardization

16 min
7.8
Co-variance of a Data Matrix

24 min
7.9
MNIST dataset (784 dimensional)

20 min
7.10
Code to Load MNIST Data Set

12 min
9.1
What is t-SNE?

7 min
9.2
Neighborhood of a point, Embedding

7 min
9.3
Geometric intuition of t-SNE

9 min
9.4
Crowding Problem

8 min
9.5
How to apply t-SNE and interpret its output

38 min
9.6
t-SNE on MNIST

7 min
9.7
Code example of t-SNE

9 min
10.1
Business/Real world problem : Problem definition

6 min
11.1
Business/Real world problem : Overview

13 min
12.1
Business/Real world problem Overview

9 min
12.2
Mapping to ML problem :Fields/Features.

6 min
13.1
Business/Real world problem

10 min
14.1
Business/real world problem :Problem definition

6 min
15.1
Business/Real world problem:Problem definition

6 min
16.1
Code Walkthrough (OpenCV using Python)

17.1
Self Driving Car :Problem definition.

14 min
18.1
High Level Design of the Solution

18.2
Sentence Vectors and Docker Containerisation

18.3
Indexing using ElasticSearch

18.4
Deployment using Flask APIs, Docker and ElasticSearch

19.1
Introduction to A/B Tests

19.2
How do we randomly split users ?

19.3
Metrics to compare Control and Treatment

19.4
Permutation-Resampling test

19.5
Q&A: Why permute/shuffle?

19.6
Q&A: How would shuffle programatically?

19.7
Quick Recap [till now]

19.8
Q&A + Polls with participants

19.9
Hypothesis testing: p-values, significance level & errors

19.10
Estimating the power of Permutation Tests

19.11
Code Walkthrough: Permutation Test from scratch.

19.12
Simulations using Code

19.13
Q&A with participants

19.14
Poll + Recap [till now]

19.15
Pros and Cons of Permutation Testing

19.16
Variation: Measuring clicks

19.17
Mann-Whitney-U Test

19.18
Code for Mann-Whitney-U test

19.19
Q&A with participants

19.20
Multiple testing and solutions

19.21
Remdesivir for Covid-19: Research Paper

19.22
Q&A with participants

19.23
Quick Recap (till now)

19.24
Bootstrapping for Confidence Intervals

19.25
Introduction to Multi-Arm-Bandits

19.26
Q&A with participants

20.1
Code Walkthrough: Basic programming & bug-fixing in Python (for AI)

20.2
Code Walkthrough: Numerical algorithms using Python (for AI)

20.3
Code Walkthrough: Numerical methods in Python (for AI) -II

20.4
Code Walkthrough: Problems in Python [ Strings and Regex ]

20.5
Code Walkthrough: Problems in Python [ Strings and Regex -II]

20.6
Code Walkthrough: Dynamic Programming & Python in-built data-structures

20.7
Code Walkthrough: OOP in Python (for AI)- I

20.8
Code Walkthrough: OOP in Python for AI -II

20.9
How to code effectively and build a web-scraper

20.10
Using Web-APIs in Python for Machine Learning

20.11
How to use Github?

20.12
Multi-Processing & Multithreading in Python for AI/ML

20.13
Parallel programming for training and productionization of ML/AI systems [Flask & Gunicorn]

20.14
SQL: Importance and Sample Problems

20.15
Interactive Interview Session on Python programming for ML/AI

20.16
Smart data acquisition for ML and AI

21.1
Code Walkthrough: Live session on Basics of Linear Algebra for AI/ML

21.2
Code Walkthrough: Dimensionality Reduction for ML/AI

22.1
Building a simple Youtube recommendation using basic Math

23.1
Interactive Interview Questions(from top product based companies)

23.2
Scenario based interview questions in AI/ML/DataScience

24.1
High-level design of a self driving system

25.1
Machine Learning design: Search engine for Q&A

25.2
ML System Design: Feature Store

31 min
26.1
Sample Interview and Conceptual Questions [AUDIO]

27.1
An overview of AI Algorithms ( a 10,000 feet view)

27.2
Big-Data & Cloud Storage for ML/AI Applications

27.3
Spark for Data Science and Machine Learning [Architecture and Programming model]- I

27.4
Design and build a Chatbot from Scratch

27.5
Design and build a Chatbot from Scratch-Part 2

27.6
How to build IoT + AI systems

27.7
Sample Interview and Conceptual Questions [AUDIO]