# Tag: LinearAlgebra

The Data Science domain deals with machine learning, data analytics, data science, and statistics. This also includes linear algebra, probability, and distribution. At times, creating and running models and algorithms requires tremendous computational power, either due to the complexity or the size of the dataset being processed. As a result, companies are now creating better and more powerful devices that can run codes more smoothly and speed up your workflow to aid such problems. This article will look at some of the best laptops and workstations released recently that are ideal for…

Full Stack Data Science has become one of the hottest industries in the field of computer science. Starting from traditional mathematics to advance concepts like data engineering, this industry demands a breadth of knowledge and expertise. Its demand has seen an exponential rise in online resources, books, and tutorials. For beginners, it’s overwhelming, to say the least. Most of the time, beginners start with either a python course, a machine learning course, or some basic mathematics course. But many times, a large number of them do not know where to start. And with so many resources to go to, many of them keep scraping through resources. Moving between Udemy, edX, Coursera, and YouTube, many hours are lost.

This is often referred to as the “Kernel Trick”. The above procedure allows us to fit linear decision boundaries in high-dimensional feature spaces without explicitly calculating all of the features in said high-dimensional space into an explicit Feature Matrix X. This is even the case when our high-dimensional feature space of interest is infinitely dimensional! There is a considerable volume of literature on Mercers Theorem and Reproducing Kernel Hilbert Spaces (RKHS) that mathematically supports the above statement, but it’s beyond the scope of this article. Rather I’m going to provide an intuitive explanation supporting this claim based on simple linear algebra and dot products:

Say we have a Feature Matrix X with n observations and p features (i.e.

## What do they tell us about our data?

I have learned about eigenvalues and eigenvectors in University in a linear algebra course. It was very dry and mathematical, so I did not get, what it is all about. But I want to present this topic to you in a more intuitive way and I will use many animations to illustrate it.

First, we will look at how applying a matrix to a vector rotates and scales a vector. This will show us what eigenvalues and eigenvectors are. Then we will learn about principal components and that they are the eigenvectors of the covariance matrix. This knowledge will help us understand our final topic, principal component analysis.

To understand eigenvalues and eigenvectors, we have to first take a look at matrix multiplication.

## One of the most basic yet powerful online learning algorithms in literature.

Online learning is a booming field of research in the AI research space. Many problems in today’s world require machines to learn on the fly and improve or adapt as they collect new information.

In this article, I will explain how to adapt the least-squares regression to compute the optimal weights recursively as new data comes in, and hence make it suitable for online learning applications.

With sufficient data, regression problems can be solved by minimizing the squared errors of the predictions made by a set of weights, and the targets.

This has an analytical solution that can be attained with a bit of linear algebra known as the pseudo inverse:

The optimal set of weights that minimizes the squared error is given by the equation above.

By Vishnu U, Campus Mind Trainee at Mindtree | Exploring Data Science.

(Image source)

Data Science enthusiasts are often self-taught at first instead of a master’s degree taken later on. But, the reality of the vast field of Data Science is realized later on by beginners in the field, and the really valuable time is spent in the wrong way of learning. In this article, I will share few facts I learned through my journey of learning data science over the course of 2 years, which could help you learn in a better way.

### Data Science is an Ocean

Keep Learning — There is no end to this field! (Image source).

Before you get started, get to know the fact that Data Science is a very vast field. Never expect to complete learning in a few months or by doing online courses.

By Harshit Tyagi, Data Science Instructor | Mentor | YouTuber

Machines or your computers only understand numbers and these numbers need to be represented and processed in a way that enables these machines to solve problems by learning from data instead of predefined instruction as in the case of programming.

All types of programming use mathematics at some level and machine learning is programming data to learn the function that best describes the data.

The problem(or process) of finding the best parameters of a function using data is called model training in ML.

Therefore, in a nutshell, machine learning is programming to optimize for the best possible solution and we need math to understand how that problem is solved.

WVU has launched the School of Mathematical and Data Sciences under the leadership of Director Earl Scime and Snehalata Huzurbazar, who will lead the data sciences program.
(WVU Photo)

Recognizing the growing intersection of humanities, social sciences, and STEM, West Virginia University has established a new School of Mathematical and Data Sciences that prepares students for a world where understanding large volumes of data is required in a broad spectrum of professions.

The new School has launched an additional major—data sciences—that will help students develop quantitative and computational skills to create real-world solutions to the world’s most pressing questions, including maintaining dashboards during the COVID-19 pandemic, predicting traffic patterns to improve driver safety and optimizing food delivery apps.

By Aaron Wang, Master of Business Analytics @ MIT | Data Science.

This Data Science cheat sheet covers over a semester of introductory machine learning and is based on MIT’s Machine Learning courses 6.867 and 15.072. You should have at least a basic understanding of statistics and linear algebra, although beginners may still find this resource helpful.

Inspired by Maverick’s Data Science Cheatsheet (hence the 2.0 in the name), located here.

Topics covered:

• Linear and Logistic Regression
• Decision Trees and Random Forest
• SVM
• K-Nearest Neighbors
• Clustering
• Boosting
• Dimension Reduction (PCA, LDA, Factor Analysis)
• Natural Language Processing
• Neural Networks
• Recommender Systems
• Reinforcement Learning
• Anomaly Detection
• Time Series
• A/B Testing

This cheat sheet will be occasionally updated with new and improved info, so consider a follow or star in the GitHub repo to stay up to date.

## Einstein summation, index notation and numpys np.einsum

As a Linear algebra addict and fan of vectors and matrices, it was unclear for me for a long time, why I should use Einstein notation at all. But When I got interested in backpropagation calculus, I got to a point, where tensors got involved and I then realised that thinking in terms of matrices limits my thinking to 2 dimensions. In this article, I will nevertheless use many matrix and vector analogies, so that the topic becomes easier to grasp.

Free indices are indices, which occur on both sides of an equation. For example:

𝑣 could now represent a row or a column vector.

That’t exactly the point of index notation.

Julia is a high-level and general-purpose language that can be used to write code that is fast to execute and easy to implement for scientific calculations. The language is designed to keep all the needs of scientific researchers and data scientists to optimize the experimentation and design implementation. Julia (programming language).

“Julia was built for scientific computing, machine learning, data mining, large-scale linear algebra, distributed and parallel computing”-developers behind the Julia language.

Python is still famous among data science enthusiasts as they get an ecosystem with loaded libraries to makes the work of data science but Python isn’t fast or convenient enough and it comes with securities variabilities as most of the libraries are built from other languages such a JavaScript, Java, C, and C++.

By Taaniya Arora, Data Scientist

Photo by Michael Dziedzic on Unsplash

The field of Natural Language Processing involves building techniques to process text in natural language by people like you and me, and extract insights from it for performing a variety of tasks from interpreting user queries on search engines and returning web pages, to solving customer queries as chatbot assistant. The importance of representing every word into a form that captures the meaning of the word and the overall context becomes crucial especially when major decisions are based upon the insights extracted from text on a large scale — like forecasting stock price change with social media.

In this article, we’ll begin with the basics of linear algebra to get an intuition of sof vectors and their significance for representing specific types of information, the different ways of representing text in vector space, and how the concept has evolved to the state of the art models we have now.

## Systems of Linear Equations

In this article, you’ll be able to use what you learned about vectors and matrices, and linear combinations (respectively Chapter 05, 06 and 07 of Essential Math for Data Science). This will allow you to convert data into systems of linear equations. At the end of this chapter (in Essential Math for Data Science), you’ll see how you can use systems of equations and linear algebra to solve a linear regression problem.

Linear equations are formalizations of the relationship between variables. Take the example of a linear relationship between two variables x and y defined by the following equation:

$boldsymbol{mathbf{y = 2x + 1}}$

You can represent this relationship in a Cartesian plane:

``````# create x and y vectors
x = np.linspace(-2,``````

In my previous post, I explored how to use Pandas to work with data frames and similar structures. In this post, I want to go to the next level and discuss the magical operations available with the NumPy (Numerical Python) library, including fast array manipulation.

### Why should go with NumPy

• Provides Data Structure, Algorithm for the Scientific application which requires numerical data.
• Which supports multi-dimensional array manipulation. NumPy’s array object is called ndarray.
• Easy to reshape, slice, and dice the array. And fast array process capability.
• Makes complex mathematical implementations very simple.
• To perform different numerical and trigonometry functions (i.e.,

Photo by Nick Morrison on Unsplash.

Many of you have started machine learning for some time, maybe a year or two. There are chances that if you would evaluate yourself now, in the theoretical aspects of machine learning, even the things that were very clear when you were learning, you might have forgotten those due to either not using them in practice or relying too much on high-level frameworks.

This 2 months curriculum is for those who are already in the field for some time and will help them in revising all the core concepts.

## Machine Learning Skills Week 1: Mathematical Foundations

This week aims to make sure that you revise all the core mathematical concepts required for beginners to grasp Machine Learning.

General exponentials, love, Schrödinger, and more.
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An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: https://3b1b.co/mat-exp-thanks

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The Romeo-Juliet example is based on this essay by Steven Strogatz:
http://www.stevenstrogatz.com/essays/loves-me-loves-me-not-do-the-math

The book shown at the start is Vladimir Arnold’s (excellent) textbook on ordinary differential equations.
https://amzn.to/3dtXSwj

Need a review of ordinary powers of e?

Or of linear algebra?

Timetable
0:00 – Definition
6:40 – Dynamics of love
13:17 – Linear systems
20:03 – General rotations
22:11 – Visualizing with flow

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Code for this video:

Full implementation is complex: it needs advanced linear algebra.

Types of Recommender Systems:

• Content based. Focus on the attributes of the items: the usual “related items”.
• Collaborative filter (CF). Uses “wisdom of the crowd” to recommend items: eg Amazon. CF is most used on content based systems. It can do feature learning by itself.
The Movie land dataset of movies to study.  These methods can be:
– Memory based CF: singular value decomposition.
– Collaborative CF: computing cosine similarity.

The math of superposition and quantum states.