CISC271, Linear Data Analysis: Lectures

Description:

These lectures are approximately aligned with classes in the course notes. There may be differences between the notes and the videos because these evolve over time.

Prerequisite material is overviewed in a series of videos that are available under the "Prerequisites" topic in the navigation bar, which is to the left of this text.

The lectures were produced using technology that is described in this video:
https://youtu.be/ltOxgb28ZKY

 No. PDF Video Week   1 1 Class #01 Introduction To Linear Data Analysis 1a Course Overview 1b Course Organization 1c Matrix Columns 1d Eigenfacts 2 Class #02 The Graph Adjacency Matrix 2a Introduction To Graphs 2b Relevant Definitions For Graphs 2c The Adjacency Matrix 2d Non-Bipartite Graphs 3 Class #03 A Graph Laplacian Matrix 3a The Degree Matrix 3b A Laplacian Matrix 3c Properties Of A Laplacian Matrix 3d The Fiedler Vector Week   2 4 Class #04 Vector Spaces 4a Introduction To Vector Spaces 4b Block Partitioning A Matrix 4c Vector-Space Properties 4d The Column Space 4e The Null Space 5 Class #05 Spanning Sets And Basis Vectors 5a Introduction To Vector Spaces 5b Relevant Definitions For Basis Vectors 5c Basis Vectors For A Column Space 5d Orthogonal Subspaces 6 Class #06 Diagonalizable Matrices 6a Similar Matrices 6b Diagonalizability 6c Examples of Diagonalizability 6d The Matrix Square Root Week   3 7 Class #07 Normal Matrices And Spectral Decomposition 7a Real Normal Matrices 7b Real Orthogonal Matrices 7c Real Symmetric Matrices 7d The Spectral Theorem 8 Class #08 Positive [Semi-]Definite Matrices 8a Positive Definite Matrices 8b The Quadratic Form 8c Mean And Variance Of Data 8d The Covariance Matrix 9 Class #09 Design Matrix And Standardized Data 9a Variables And Observations 9b Variables As Vectors 9c Zero-Mean Data 9d Unit-Variance Data 9e Standardized Data For Regression 9f Measuring Standard Deviations Week   4 10 Test #1 Basic Linear Analysis 11 Class #11 Orthogonal Projection 11a Concepts In Orthogonal Projection 11b Projecting A Vector To A Vector 11c Projecting A Vector To A Vector Space 11d The Normal Equation 11e Overdetermined Linear Equations 12 Class #12 Patterns - Linear Regression 12a Concepts In Statistical Regression 12b Concepts In Linear Regression 12c Examples Of Linear Regression 12d Data Standardization For Linear Regression 12e Residual Error In Linear Regression Week   5 13 Class #13 Cross-Validating Linear Regression 13a Validation Of Linear Regression 13b Training Sets And Testing Sets 13c K-Fold Cross-Validation Of Linear Regression 13d Examples Of 5-Fold Cross-Validation 14 Class #14 Singular Value Decomposition, Or SVD 14a Introduction To The SVD 14b The Left-Transpose Product 14c The Right-Transpose Product 14d Structure Of The SVD 15 Class #15 Orthonormal Basis Vectors And The SVD 15a I Did Not Shoot The SVD 15b Examples Of The SVD 15c Matrix Spaces And The SVD 15d The Null Space And The SVD 15e Orthonormal Basis Vectors And The SVD Week   6 16 Test #2 Matrices and Linear Regression 17 Class #17 Matrix Approximation 17a Matrix Norms 17b L2 Matrix Norm And Frobenius Matrix Norm 17c Matrix Series From The SVD 17d Low-Rank Approximations 17e Scree Plot Of Singular Values 18 Class #18 Principal Components Analysis, Or PCA 18a Introduction To PCA 18b PCA From Covariance Matrix 18c PCA As Spectral Decomposition 18d Computing Data Scores Using PCA Reading Week Holiday Special Week   7 19 Class #19 Unsupervised Learning - K-Means Clustering 19a A Conceptual Hierarchy Of Machine Learning 19b Hyperplane of Separation 19c Basics Of Vector Clustering 19d A K-Means Clustering Algorithm 19e Clustering The Iris Data 20 Class #20 Classification - Linear Separability 20a Separating Two Clusters 20b A Hyperplane From Cluster Centroids 20c Hyperplanes For Multiple Clusters 20d The Davies-Bouldin Index For Clusters 21 Class #21 PCA - Matrix Algebra and Dimensionality Reduction 21a Revisiting PCA 21b The Scatter Matrix Of Variables For PCA 21c PCA As Matrix Approximation 21d PCA As Dimensionality Reduction Week   8 22 Test #3 The SVD, PCA, And Dimensionality Reduction 23 Class #23 PCA And The Rayleigh Quotient 23a PCA, Scores, And The SVD 23b PCA Maximizes A Linear Transformation 23c The Rayleigh Quotient And PCA 24 Class #24 Patterns - Linear Discriminant Analysis, or LDA 24a Finding Patterns In Labeled Data 24b Example Of PCA For Labeled Data 24c Fisher's Linear Discriminant, Or LDA 24d Example Of LDA For Labeled Data 24e Example Of LDA For Iris Data Week   9 25 Class #25 Classification - Assessment With Confusion Matrix 25a Data Labels As Dependent Variables 25b Confusion Matrix For Binary Labels 25c Example Of Confusion Matrix 26 Class #26 Classification - Assessment With ROC Curve 26a Receiver Operator Characteristic, Or ROC 26b ROC And The Confusion Matrix 26c Example ROC Curve For Fictitious Virus 27 Class #27 Classification - Single Artificial Neuron 27a Artificial Neurons 27b Data Flow And Computations For Neurons 27c Hyperplane Separation For Neurons Week   10 28 Test #4 LDA, Assessment, Odds Of Occurrence 29 Class #29 Odds Of Occurrence And Probability 29a Odds Of Hyperplane Classification 29b Odds And Probability 29c The Logistic Function For Odds 29d Properties Of The Logistic Function 30 Class #30 Supervised Learning - Perceptron Rule 30a Perceptron Model Of Neurons 30b Deriving The Perceptron Rule 30c Pseudocode For The Perceptron Rule 30d Perceptron Rule For Iris Data Week   11 31 Class #31 Classification - Logistic Regression 31a Shortcomings Of Perceptrons 31b Scores From Logistic Activation 31c Residual Error Of Scores 31d Logistic Regression For Iris Data 32 Class #32 Nonlinear Separation - Embeddings And Gram Matrix 32a Some Data Are Nonlinearly Separable 32b Embedding A Vector Space 32c Gram Matrix For An Embedding 33 Class #33 Nonlinear Separation - Kernel PCA 33a High-Dimensional PCA 33b Scatter Matrix Of Observations 33c Kernel PCA Using The Gram Matrix 33d Kernel PCA For Iris Data Week   12 34 Test #5 Machine Learning 35 Class #35 Spectral Clustering Of Data 35a Fielder Vector And Spectral Decomposition 35b Spectral Clustering Using Eigenvectors 35c Distance Matrix And Spectral Clustering 36 Class #36 The Curse Of Dimensionality 36a The Curse of Dimensionality 36b Dimensionality And Hypercube Vertices 36c Dimensionality And Uniform Distributions 36d Dimensionality And Gaussian Distributions 37 Class #37 Course Summary 37a Course Summary 37b Unplanned Recording Events Extra Material Table of Contents References

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