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Use of Linear Algebra to Solve Data Problems in Machine Learning

Data Problems in Machine Learning

Computers or  Machines only recognize quantities. And certain numbers require to be described and treated in a system that allows machines to determine problems by acquiring from the data instead of learning from predefined instructions in the case of programming.

All kinds of programming use computation at some level. Machine Learning knowledge involves programming data to determine the function that best represents the data.

The obstacle (or method) of finding the best parameters of a function using data is called model training in machine learning.

Accordingly, in a nutshell, machine learning is programming to enhance the best feasible solution – and we have a requirement of math to understand how that complication can be solved.

Learning linear algebra is the first step toward learning Math for Machine Learning.

The mathematical foundation explains the difficulty of rendering data furthermore computing in machine learning models that are known as Linear Algebra.

In the Machine Learning link, all principal phases of explaining a model have linear algebra running on the backend.

Important sections of statement that are approved by linear algebra are:

  • Word Embeddings
  • Dimensionality Reduction
  • Data and learned Model Representation

Data Representation 

The combustible of machine learning models, that is data, needs to be transformed into arrays where you can maintain it in your models. The estimates presented on certain arrays involve procedures like mold multiplication. This addition records the output that is also represented as a transformed matrix/tensor of numbers.

 Word embeddings 

Don’t worry about the technology here – it is just about characterizing large-dimensional data (estimate of a large number of variables in your data) with a smaller dimensional vector. 

Natural Language Processing (NLP) bargains with textual data. Dealing with text means understanding the meaning of a huge corpus of words. Every word describes various meanings which might be related to different words. Vector embeddings in linear algebra permit us to represent these words more accurately.

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Tensors Flowing Through a Neural Network- Deep Learning

We can understand linear algebra in activity across all the major credentials today. Samples include viewpoint analysis on a Twitter or a Linked post (embeddings), identifying a type of lung disease from X-ray images (computer vision), or any speech-to-text bot (NLP).

All of these data types are interpreted by numbers in tensors. We run vectorized procedures to learn models from them working on a neural network. It then outputs a processed tensor which in turn is decoded to generate the final conclusion of the model.

Every state operates mathematical operations on those data arrays. 

Vector Space Transformation-Dimensionality Reduction

 

When it continues to embed, you can principally think of an n-dimensional vector importing displaced with a complex vector that correlates to a lower-dimensional space. This is very important and it’s the one that succeeds in computational complexities. 

For example, here is a three-dimensional vector that is displaced by a two-dimensional space. But you can extrapolate it to a real-world situation wherever you have a very huge number of dimensions. Decreasing dimensions doesn’t mean separating articles from the data. Alternatively, it’s about finding new features that are linear functions of the original features and preserving the variance of the original features.

Getting new variables (features) decodes to finding the principal elements(PCs). This then unites solving eigenvectors and eigenvalues problems. 

Linear Algebra is used in which Industries

 Presently, I hope you are convinced that Linear algebra is encouraging Machine Learning actions in a gathering of areas today.

 Here is a list below to name a few:

  • Chemical Physics
  • Statistics
  • Robotics
  • Quantum Physics
  • Genomics
  • Image Processing
  • Word Embeddings — neural networks/deep learning

What should we know in Linear algebra before starting ML/DL? 

Now, the relevant question is how you can acquire skills to program these concepts of linear algebra. The information is you don’t have to reinvent the hoop, you just need to understand the fundamentals of vector algebra computationally and you then study to program those concepts using NumPy.

NumPy is a specific computation package that gives us entrance to all the underlying concepts of linear algebra. It is secure and fast as it runs compiled C code and it has a vast number of mathematical and scientific functions that we can use.

What does math have to do with machine learning?

 1. All programming involves math at some level.

 2. Machine learning is programming by optimization.

 3. We need math to understand that optimization. 

Mathematics and programming and computers have been tied together since the inception of computer science and programming. ML in particular though is programming by optimization the way that we program computers to do things in ML  is through optimization. And in order to understand optimization and what we are optimizing and why that works we need mathematics and this is what makes machine learning such a more mathematical discipline of programming. Linear algebra will help us understand the objects being optimized in calculus which will help us understand how we optimize those things and then probability and stats will help us understand what that thing is that we are optimizing we are making better.

Why do we care about Linear Algebra?

The core operation in linear algebra is matrix multiplication here are some examples of matrix multiplication in action

-{Dot,scalar, inner }product

 -Discrete Fourier transform

 -Correlation Covariance -pagerank 

 -Linear Regression

 -Hidden layers of neural nets

 -Logistic Regression 

 -Convolutions

-Principal components analysis 

-Newton L-bfgs

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AGGREGATE FUNCTIONS

  • MySQL count()
  • MySQL sum()
  • MySQL avg()
  • MySQL min()
  • MySQL max()

MYSQL JOIN

MySQL JOIN

DATA ANALYTICS

DATA PRE-PROCESSING/WRANGLING

NUMPY

  • Fundamentals of NumPy
  • Types of arrays in NumPy
        Ones
        Empty
        Zeros
        Create Random Array
  • Reshaping of the array
         1-D to 2-D array
         2-D to 3-D array
         3-D to 1-D array
  • Arithmetic operations on  Array
         Addition
         Subtraction
         Multiplication
         Exponential
  • Slicing of the array
        How to slice array
        Change in properties during slicing
  • Transpose of a matrix
        How to take transpose
        Rows and columns  while taking transpose
  • Dot product of the matrix
       How to take Dot product of the Matrix

PANDAS

  • Data Frame
         What is Pandas Dataframe
         Different ways to create a Dataframe
        Read data from different sources and convert them to the Dataframe.
  • Pandas Series
        What is panda Series
        How to create a Panda Series.
  • Data inspection
         Using Count, info, head, tail.
         Using Shape, describe, unique, value etc
  • Data Slicing
        Data Slicing loc and iloc
  • Dataframe operations
         How to create a column or row
        How to delete a column or row
    Operations on Rows and Columns
  • Arithmetic operations on rows and
    columns
  • Handle Duplicate value and Null value
  • Handle outlier data
  • Group by Operations
  • Data Reshaping
  • Merging, Joining ,concatenation and
    append
  • Time series

MATPLOTLIB

  • Matplotlib for 3-D visualization
  • Bar, Pie, line, histogram
  • Countplot, boxplot, heatmap

SCIKIT-LEARN

  • Scikit models
  • Preprocessing using Scikit learn
  • Classification using Scikit-learn
  • Clustering using Scikit-learn
  • Regression using Scikit-learn

STATISTICS

  • Scalar and vector
  • Introduction to linear algebra
  • Measure of central tendency mean
  • Measure of central tendency mode
  • Measure of central tendency mode
  • Variance
  • Standard deviation
    Measure of shape skewness
    Measure of shape kurtosis
    Covariance and correlation

PROBABILITY

  • Importance of probability
  • Discrete and continuous variable
  • Bayes Theorem
  • Central Limit theorem
  • Normal Distribution
  • Bernoulli distribution
  • Uniform Distribution

HYPOTHESIS TESTING

  • Hypothesis testing and mechanism
  • Confidence interval
  • Margin of Errors
  • Confidence levels
  • T test and P values using python
  • Z test and P values using python
  • Chi Squared Distribution using python

LINEAR REGRESSION

  • Types of variables
  • Types of Linear variables
  • Mathematics Behind it
  • Implementation of the model
  • Testing and Check
  • Performance of the model
  • Assumptions of the Linear Regression

POLYNOMIAL REGRESSION

  • Need of polynomial Regression
  • Types of Variables in the Polynomial regression
  • Mathematics behind it
  • Implementation of the model
  • Testing and check performance of the
    model

MULTIPLE REGRESSION

  • Need of multiple Regression
  • Mathematics behind it
  • Implementation of the model
  • Testing and check performance of the model

RANDOM FOREST ALGORITHM

  • Why to use random Forest
  • Assumptions in random Forest
  • Working and Implementation of the Model
  • Data Pre-processing in Random Forest

SUPPORT VECTOR MACHINES

  • Types of SVM
  • Implementation of the SVM
  • Creating confusion matrix

NAIVE BAYES CLASSIFIER ALGORITHM

  • Bayes Theoram
  • Implementation of Naïve Bayes
    Classifier
  • Type of Naïve Bayes Model

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JAVASCRIPT EVENTS

Event listeners and handlers
Mouse events
Keyboard events

DOCUMENT OBJECT MODEL (DOM)

Accessing and manipulating HTML elements
DOM navigation and manipulation
Creating and removing HTML elements

1. INTRODUCTION TO REACT.JS

What is React.js?
History and evolution of React.js
React.js components and their role in
building web applications
Setting up the development environment

JSX

Introduction to JSX
Basic syntax and rules of JSX
Embedding expressions in JSX
Conditional rendering in JSX
Working with lists in JSX

REACT COMPONENTS

Understanding components
Creating class components
Creating functional components
Props and state in React components
Lifecycle methods in React components

REACT EVENTS

Handling events in React
Binding event handlers in React
Passing data to event handlers in React
Conditional rendering based on events in
React

REACT FORMS

Creating forms in React
Handling form submission in React
Controlled and uncontrolled components
in React

REACT ROUTING

Introduction to React Router
Setting up routing in React
Creating routes in React

INTRODUCTION TO MONGODB

What is MongoDB?
Advantages of MongoDB over RDBMS
MongoDB data model and architecture
Setting up the development environment

CRUD OPERATIONS

Creating and inserting documents in
MongoDB
Reading documents from MongoDB
Updating documents in MongoDB
Deleting documents from MongoDB

QUERYING MONGODB

Querying MongoDB using find() method
Querying MongoDB using comparison and
logical operators
Querying MongoDB using regular
expressions
Querying MongoDB using aggregation
framework

INTRODUCTION TO NODE.JS

What is Node.js?
Advantages of Node.js over other serverside technologies
Node.js architecture and event-driven
programming model
Setting up the development environment

NODE.JS MODULES

Introduction to Node.js modules
Creating and using built-in modules
Creating and using custom modules
Working with NPM (Node Package
Manager)

NODE.JS HTTP

Creating HTTP server in Node.js
Understanding HTTP methods and status
codes
Handling HTTP requests and responses
Serving static files in Node.js

EXPRESS.JS FRAMEWORK

Introduction to Express.js framework
Creating and configuring Express.js
application
Handling HTTP requests and responses in
Express.js
Implementing middleware in Express.js

NODE.JS DATABASE CONNECTIVITY

Introduction to database connectivity in
Node.js
Connecting to MongoDB database in
Node.js
Performing CRUD operations in Node.js
using MongoDB
Using Mongoose ORM with MongoDB in
Node.js

NODE.JS SECURITY

Introduction to security in Node.js
Understanding and implementing
authentication and authorization in
Node.js
Implementing HTTPS in Node.js
Preventing common security vulnerabilities
in Node.js

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