EDUCBA

EDUCBA

MENUMENU
  • Free Tutorials
  • Free Courses
  • Certification Courses
  • 360+ Courses All in One Bundle
  • Login
Home Data Science Data Science Tutorials Machine Learning Tutorial Linear Algebra in Machine Learning
Secondary Sidebar
Machine Learning Tutorial
  • Supervised
    • What is Supervised Learning
    • Supervised Machine Learning
    • Supervised Machine Learning Algorithms
    • Perceptron Learning Algorithm
    • Simple Linear Regression
    • Polynomial Regression
    • Multivariate Regression
    • Regression in Machine Learning
    • Hierarchical Clustering Analysis
    • Linear Regression Analysis
    • Support Vector Regression
    • Multiple Linear Regression
    • Linear Algebra in Machine Learning
    • Statistics for Machine Learning
    • What is Regression Analysis?
    • Clustering Methods
    • Backward Elimination
    • Ensemble Techniques
    • Bagging and Boosting
    • Linear Regression Modeling
    • What is Reinforcement Learning
  • Basic
    • Introduction To Machine Learning
    • What is Machine Learning?
    • Uses of Machine Learning
    • Applications of Machine Learning
    • Naive Bayes in Machine Learning
    • Dataset Labelling
    • DataSet Example
    • Deep Learning Techniques
    • Dataset ZFS
    • Careers in Machine Learning
    • What is Machine Cycle?
    • Machine Learning Feature
    • Machine Learning Programming Languages
    • What is Kernel in Machine Learning
    • Machine Learning Tools
    • Machine Learning Models
    • Machine Learning Platform
    • Machine Learning Libraries
    • Machine Learning Life Cycle
    • Machine Learning System
    • Machine Learning Datasets
    • Machine Learning Certifications
    • Machine Learning Python vs R
    • Optimization for Machine Learning
    • Types of Machine Learning
    • Machine Learning Methods
    • Machine Learning Software
    • Machine Learning Techniques
    • Machine Learning Feature Selection
    • Ensemble Methods in Machine Learning
    • Support Vector Machine in Machine Learning
    • Decision Making Techniques
    • Restricted Boltzmann Machine
    • Regularization Machine Learning
    • What is Regression?
    • What is Linear Regression?
    • Dataset for Linear Regression
    • Decision tree limitations
    • What is Decision Tree?
    • What is Random Forest
  • Algorithms
    • Machine Learning Algorithms
    • Apriori Algorithm in Machine Learning
    • Types of Machine Learning Algorithms
    • Bayes Theorem
    • AdaBoost Algorithm
    • Classification Algorithms
    • Clustering Algorithm
    • Gradient Boosting Algorithm
    • Mean Shift Algorithm
    • Hierarchical Clustering Algorithm
    • Hierarchical Clustering Agglomerative
    • What is a Greedy Algorithm?
    • What is Genetic Algorithm?
    • Random Forest Algorithm
    • Nearest Neighbors Algorithm
    • Weak Law of Large Numbers
    • Ray Tracing Algorithm
    • SVM Algorithm
    • Naive Bayes Algorithm
    • Neural Network Algorithms
    • Boosting Algorithm
    • XGBoost Algorithm
    • Pattern Searching
    • Loss Functions in Machine Learning
    • Decision Tree in Machine Learning
    • Hyperparameter Machine Learning
    • Unsupervised Machine Learning
    • K- Means Clustering Algorithm
    • KNN Algorithm
    • Monty Hall Problem
  • Classification
    • Kernel Methods in Machine Learning
    • Clustering in Machine Learning
    • Machine Learning Architecture
    • Automation Anywhere Architecture
    • Machine Learning C++ Library
    • Machine Learning Frameworks
    • Data Preprocessing in Machine Learning
    • Data Science Machine Learning
    • Classification of Neural Network
    • Neural Network Machine Learning
    • What is Convolutional Neural Network?
    • Single Layer Neural Network
    • Kernel Methods
    • Forward and Backward Chaining
    • Forward Chaining
    • Backward Chaining
  • Deep Learning
    • What Is Deep learning
    • Overviews Deep Learning
    • Application of Deep Learning
    • Careers in Deep Learnings
    • Deep Learning Frameworks
    • Deep Learning Model
    • Deep Learning Algorithms
    • Deep Learning Technique
    • Deep Learning Networks
    • Deep Learning Libraries
    • Deep Learning Toolbox
    • Types of Neural Networks
    • Convolutional Neural Networks
    • Create Decision Tree
    • Deep Learning for NLP
    • Caffe Deep Learning
    • Deep Learning with TensorFlow
  • RPA
    • What is RPA
    • What is Robotics?
    • Benefits of RPA
    • RPA Applications
    • Types of Robots
    • RPA Tools
    • Line Follower Robot
    • What is Blue Prism?
    • RPA vs BPM
  • Interview Questions
    • Deep Learning Interview Questions And Answer
    • Machine Learning Cheat Sheet

Related Courses

Machine Learning Training

Deep Learning Training

Artificial Intelligence Training

Linear Algebra in Machine Learning

By Priya PedamkarPriya Pedamkar

Linear Algebra in Machine Learning

Introduction to Linear Algebra in Machine Learning

Linear Algebra in Machine learning is defined as the part of mathematics that uses vector space and matrices to represent the linear equations, from the implementation of algorithms and techniques in the code(such as Regularization, Deep learning, One hot encoding, Principal Component Analysis, Single Value Decomposition, etc.) to the notations that are used to describe the operations of the machine learning algorithm it acts as the key foundation in the field of machine learning.

Matrix: It is an array of numbers in a rectangular form represented by rows and columns.

Example:

Linear Algebra in Machine Learning Matrix Example 1

Start Your Free Data Science Course

Hadoop, Data Science, Statistics & others

Vector: A vector is a row or a column of a matrix.

Example:

Linear Algebra in Machine Learning Matrix Example 2

Tensor: Tensors are an array of numbers or functions that transmute with certain rules when coordinate changes.

How does Linear Algebra work in Machine Learning?

As Machine Learning is the point of contact for Computer Science and Statistics, Linear Algebra helps in mixing science, technology, finance & accounts, and commerce altogether. Numpy is a library in Python which works on multidimensional arrays for scientific calculations in Data Science and ML.

Linear Algebra functions in various ways as is reflected in some examples listed below:

1. Dataset and Data Files

A data is a matrix or a data structure in Linear Algebra. A dataset contains a set of numbers or data in a tabular manner. Rows represent observations whereas columns represent features of it. Each row is of the same length. So, data is vectorized. Rows are pre-configured and are inserted to the model one at a time for easier and authentic calculations.

2. Images and Photographs

All images are tabular in structure. Each cell in black and white images comprises of height, width, and one-pixel value. Similarly, color images have 3-pixel values in it apart from height and width. It forms a matrix in Linear Algebra. All kinds of editing such as cropping, scaling, etc, and manipulation techniques are performed using algebraic operations.

3. Regularization

Regularization is a method that minimizes the size of coefficients while inserting it into data. L1 and L2 are of some common methods of implementation in regularization which are measures of the magnitude of coefficients in a vector.

All in One Data Science Bundle(360+ Courses, 50+ projects)
Python TutorialMachine LearningAWSArtificial Intelligence
TableauR ProgrammingPowerBIDeep Learning
Price
View Courses
360+ Online Courses | 50+ projects | 1500+ Hours | Verifiable Certificates | Lifetime Access
4.7 (86,241 ratings)

4. Deep Learning

This method is mostly used in neural networks with various real-life solutions, such as machine translation, photo captioning, speech recognition, and many other fields. It works with vectors, matrices, and even tensors as it requires linear data structures added and multiplied together.

5. One Hot Encoding

It is a popular encoding for categorical variables for easier operations in algebra. A table is constructed with one column for each category and a row for each example. Digit 1 is added for categorical value succeeded by 0 in the rest and so on, as cited below:

Linear Algebra in Machine Learning One hot encoding

6. Linear Regression

Linear regression, one of the statistical methods, is used for predicting numerical values for regression problems as well as describing the relationship among variables.

Example: y= A. b where A is dataset or matrix, b is coefficient and y is the output.

7. Principal Component Analysis or PCA

Principal Component Analysis is applicable while working with high-dimensional data for visualization and model operations. When we find irrelevant data, then we tend to remove the redundant column(s). So PCA acts as a solution. Matrix factorization is the main objective of PCA.

8. Single-Value Decomposition or SVD

It is also a matrix factorization method used generally in visualization, noise reduction, etc.

9. Latent Semantic Analysis

In this process, documents are represented as large matrices. Document processed in these matrices is easy to compare, query and use. A matrix is constructed where rows represent words and columns represent documents. SVD is used to reduce the number of columns while preserving the similarity.

10. Recommender Systems

Predictive models rely on the recommendation of products. With the help of Linear Algebra, SVD functions to purify data using Euclidean distance or dot products. For example, when we purchase a book on Amazon, recommendations come based on our purchase history keeping aside other irrelevant items.

Advantages of Linear Algebra in Machine Learning

Given below are the advantages mentioned:

  • Acts as a solid foundation for Machine Learning with the inclusion of both mathematics and statistics.
    Both tabular and images can be used in linear data structures.
  • It is distributive, associative, and communicative as well.
  • It is a simple, constructive, and versatile approach in ML.
  • Linear Algebra is applicable in many fields such as predictions, signal analysis, facial recognition, etc.

Linear Algebra functions in Machine Learning

There are some Linear Algebra functions that are vital in ML and Data Science operations as described below:

1. Linear Function

The linear regression algorithm uses a linear function where output is continuous and has a constant slope. Linear functions have a straight line in the graph.

F(x)=mx+b

Where,

  • F(x) is the value of the function.
  • m is the slope of the line.
  • b is the value of the function when x=0.
  • x is the value of x-coordinate..

Example: y=5x+25

Let x=0, then y=5*1+25=25

Let x=2, then y=5*2+25=40

Linear Algebric Matrix Chart

2. Identity Function

Identity function comes under the unsupervised algorithm and is mostly used in Neural Networks in ML where the output of the multilayer neural network is equal to its input, as cited below.

For every x, f(x) maps to x i.e x maps to itself.

Example: x+0=x

x/1=x

1——–>1

2——–>2

3——–>3

3. Composition

ML uses higher-order composition and pipelining functions in its algorithms for mathematical calculations and visualizations.

Composition function is described as below:

(g o f)(x)=g(f(x))

Example: let g(y)=y

f(x)=x+1

g o f(x+1)=x+1

4. Inverse Function

The inverse is a function that reverses itself. Functions f and g inverse if f o g and g o f are defined and are identity functions.

Example:

Inverse Function

5. Invertible Function

A function that has inverse is invertible.

one-to-one

invertible Function 1

onto

invertible Function 2

Conclusion

Linear Algebra is a subfield of mathematics. However, it has broader use in Machine Learning from notation to the implementation of algorithms in datasets and images. With the help of ML, algebra has got a larger impact in real-life applications such as search-engine analysis, facial recognition, predictions, computer graphics, etc.

Recommended Articles

This is a guide to Linear Algebra in Machine Learning. Here we discuss how did linear algebra work in machine learning with the advantages and some examples. You may also look at the following article to learn more –

  1. Hyperparameter Machine Learning
  2. Clustering in Machine Learning
  3. Data Science Machine Learning
  4. Unsupervised Machine Learning
Popular Course in this category
Machine Learning Training (20 Courses, 29+ Projects)
  19 Online Courses |  29 Hands-on Projects |  178+ Hours |  Verifiable Certificate of Completion
4.7
Price

View Course

Related Courses

Deep Learning Training (18 Courses, 24+ Projects)4.9
Artificial Intelligence AI Training (5 Courses, 2 Project)4.8
0 Shares
Share
Tweet
Share
Primary Sidebar
Footer
About Us
  • Blog
  • Who is EDUCBA?
  • Sign Up
  • Live Classes
  • Corporate Training
  • Certificate from Top Institutions
  • Contact Us
  • Verifiable Certificate
  • Reviews
  • Terms and Conditions
  • Privacy Policy
  •  
Apps
  • iPhone & iPad
  • Android
Resources
  • Free Courses
  • Database Management
  • Machine Learning
  • All Tutorials
Certification Courses
  • All Courses
  • Data Science Course - All in One Bundle
  • Machine Learning Course
  • Hadoop Certification Training
  • Cloud Computing Training Course
  • R Programming Course
  • AWS Training Course
  • SAS Training Course

ISO 10004:2018 & ISO 9001:2015 Certified

© 2022 - EDUCBA. ALL RIGHTS RESERVED. THE CERTIFICATION NAMES ARE THE TRADEMARKS OF THEIR RESPECTIVE OWNERS.

EDUCBA
Free Data Science Course

SPSS, Data visualization with Python, Matplotlib Library, Seaborn Package

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA Login

Forgot Password?

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA
Free Data Science Course

Hadoop, Data Science, Statistics & others

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

Let’s Get Started

By signing up, you agree to our Terms of Use and Privacy Policy.

This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy

Loading . . .
Quiz
Question:

Answer:

Quiz Result
Total QuestionsCorrect AnswersWrong AnswersPercentage

Explore 1000+ varieties of Mock tests View more