Lec-4.4 Linear Algebra for ML Part-II (Arif Butt @ Data Science)
0:01:18 Learning Agenda
0:07:49 Section IV: (Matrix as a Linear Transformation)
0:08:36 What do you mean by applying a Matrix to a Vector?
0:12:55 Algebra Behind Linear Transformations in 2-D Space
0:14:14 Applying an Identity Matrix
0:15:46 Applying a Scaling Matrix
0:20:37 Applying a Reflection Matrix
0:24:40 Applying a Shear Matrix
0:30:49 Applying a Rotation Matrix
0:35:52 Applying a Translation Matrix
0:36:24 Apply Multiple Transformations Simultaneously
0:39:01 Scaling, Translation and Rotation in Three Dimensional Space
0:40:23 Section V: (Eigen Decomposition and SVD)
0:41:54 Eigenvalues and Eigenvectors (An abstract view)
0:45:39 Calculating Eigenvalues and Eigenvectors of a Matrix using Paper-Pencil
0:54:20 Calculating Eigenvalues and Eigenvectors of a Matrix in Python
0:58:20 Relationship between Determinant and Eigenvalues of a Matrix
0:59:19 Relationship between Trace and Eigenvalues of a Matrix
0:59:57 Not all Transformation Matrices have Real Eigenvalues
1:00:55 Eigenvectors and Eigenvalues of a Diagonal Transformation Matrix
1:02:15 Eigendecomposition
1:09:47 Eigendecomposition for Symmetric Matrices
1:11:22 What is Singular Value Decomposition?
1:16:20 Calculating SVD using NumPy
1:21:30 Calculating SVD using SciPy
1:22:05 Calculating SVD using Scikit-learn
1:23:20 Section VI: (Applications of SVD & Eigendecomposition)
1:24:42 Image Compression
1:41:55 What is Principal Component Analysis
1:46:06 Example 1: Dimensionality Reduction of Housing Dataset using NumPy
1:58:46 Example 2: Dimensionality Reduction of Digits Dataset using Scikit-learn
2:12:48 Example 3: Dimensionality Reduction of Iris Dataset using Scikit-learn (Data Visualization)
2:20:44 The Moore-Penrose Pseudoinverse
email: [email protected], [email protected], [email protected]
Lecture Slides and Resources: http://arifbutt.me
Jupyter notebooks: https://github.com/arifpucit/data-sci...