# Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

• Offered byMIT Professional Education

## Matrix Methods in Data Analysis, Signal Processing, and Machine Learning at MIT Professional Education Overview

 Duration 12 hours Total fee Free Mode of learning Online Schedule type Self paced Difficulty level Intermediate Official Website Explore Free Course Credential Certificate

## Matrix Methods in Data Analysis, Signal Processing, and Machine Learning at MIT Professional Education Highlights

• Earn a Certificate of completion from MIT on successful course completion
• Instructor - Prof. Gilbert Strang
• This course explores linear algebra with applications to probability and statistics and optimization, and a complete explanation of deep learning

## Matrix Methods in Data Analysis, Signal Processing, and Machine Learning at MIT Professional Education Course details

Skills you will learn
Who should do this course?
• This course is designed for those who want to learn basics of linear algebra, probability and statistics, optimization, and deep learning, and their relationship.
• Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization?and above all a full explanation of deep learning.

## Matrix Methods in Data Analysis, Signal Processing, and Machine Learning at MIT Professional Education Curriculum

Lecture 1: The Column Space of A Contains All Vectors Ax

Lecture 2: Multiplying and Factoring Matrices

Lecture 3: Orthonormal Columns in Q Give Q?Q = I

Lecture 4: Eigenvalues and Eigenvectors

Lecture 5: Positive Definite and Semidefinite Matrices

Lecture 6: Singular Value Decomposition (SVD)

Lecture 7: Eckart-Young: The Closest Rank k Matrix to A

Lecture 8: Norms of Vectors and Matrices

Lecture 9: Four Ways to Solve Least Squares Problems

Lecture 10: Survey of Difficulties with Ax = b

Lecture 11: Minimizing ?x? Subject to Ax = b

Lecture 12: Computing Eigenvalues and Singular Values

Lecture 13: Randomized Matrix Multiplication

Lecture 14: Low Rank Changes in A and Its Inverse

Lecture 15: Matrices A(t) Depending on t, Derivative = dA/dt

Lecture 16: Derivatives of Inverse and Singular Values

Lecture 17: Rapidly Decreasing Singular Values

Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points

Lecture 19: Saddle Points Continued, Maxmin Principle

Lecture 20: Definitions and Inequalities

Lecture 21: Minimizing a Function Step by Step

Lecture 22: Gradient Descent: Downhill to a Minimum

Lecture 23: Accelerating Gradient Descent (Use Momentum)

Lecture 24: Linear Programming and Two-Person Games

Lecture 26: Structure of Neural Nets for Deep Learning

Lecture 27: Backpropagation: Find Partial Derivatives

Lecture 30: Completing a Rank-One Matrix, Circulants!

Lecture 31: Eigenvectors of Circulant Matrices: Fourier Matrix

Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule

Lecture 33: Neural Nets and the Learning Function

Lecture 34: Distance Matrices, Procrustes Problem

Lecture 35: Finding Clusters in Graphs

Lecture 36: Alan Edelman and Julia Language

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Matrix Methods in Data Analysis, Signal Processing, and Machine Learning
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MIT Professional Education

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