Linear Algebra for Data Science

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Oct 18, 2022

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Many of the people who are aspiring to careers in data science think of hotshot technologies and methods that come under data science like natural language processing, artificial intelligence, machine learning, etc. But they often forget about linear algebra. But today in this article, we are going to discuss linear algebra for data science thoroughly and find out the relation between linear algebra and the world of data science. Not only we are going to discuss what linear algebra is in data science, but we are going to highlight some of the applications and benefits of this field in data science. So, if you are thinking to get into the field of data science, then you should consider getting the upper hand in linear algebra and look for a Data Science Course which will help you get a deep understanding of various concepts needed to become a data scientist. So let us understand what linear algebra is first before we get into why it is needed in data science.

What is linear algebra?

Linear algebra is defined as the branch of mathematics that is used to deal with linear combinations that are used for performing arithmetic functions on columns of numbers that are called vectors or arrays of numbers called matrices. It is very much needed if you are looking to comprehend machine learning. It is very crucial to learn linear algebra if you are looking to work in the field of data science. Some areas where you are going to use this concept in data science will include computer vision and natural language processing. It is indeed a fact that linear algebra is one of the significant areas of mathematics and the primary focus of linear algebra is to study the vectors and linear functions that are needed to understand the fundamental idea.

It is so important because most of the artificial models along with the datasets ate shown in matrixes and to have data processing, data transformation along with model validation, you need to use linear algebra on the given data set. Not only this but all the machine learning algorithms are also constructed using this concept.

Not only data science, but linear algebra is highly utilized in areas of physics and engineering as it helps in driving the understanding of fundamental objects that include planes, lines, and other rotations. To have a knowledge of linear transformations, you need to understand vector spaces, lines, and planes and learn some mappings. The linear functions, matrices, and vectors are part of this, and they are needed to comprehend the linear sets of equations.

Why learn linear algebra for data science?

After understanding linear algebra, we can confirm one thing that is very crucial when it comes to data science. There are various notations that are used to define the algorithms to have their implementation, so with the help of linear algebra, that can be made possible in machine learning. Also, in the article, below we are going to discuss the application of this concept more deeply. In many cases, linear algebra is used to expand, compress, crop, and carry out the various actions on the given dataset. If you want to expand your knowledge of ML topics and their viewpoints, then understanding linear algebra is a must for you.

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Applications of linear algebra in data science

Indeed, linear algebra in data science is very crucial, and below are the applications that will help us understand why!

Machine learning

Machine learning is an important pillar in data science and below are some applications of linear algebra in machine learning. These are the areas where you need to use linear algebra to come up with various algorithms and have a machine-learning model ready for you.

Loss Functions

Let us see how a linear regression model works in the given data:

  • Your start with using an arbitrary prediction function that is used in the regression model.
  • You use it on the independent feature of data that is used to predict the output.
  • Using these calculated values to optimize the prediction function that is used for some strategies for example Gradient Descent.

But when you need to find out how this prediction outcome is different from the expected output, you need a loss function. This is an application of vector norm in linear algebra that is used to calculate the magnitude. There are various vector norms like the L1 norm which is used as the distance you travel when you went from the origin to the vector when the permitted directions are parallel to the axes of the space and the L2 norm which is also known as Euclidean distance. The L2 norm is the shortest distance of the vector from the origin. The distance here is calculated using the Pythagoras theorem.


If you are studying data science and you are interested in Data Science certification, then you must be aware that regularization is important in data science. It is known as the technique that is used to prevent models from overfitting in this field. This is another application of the Norm. Overfit here means when the model fits the given data very well. This is not desired as this will not show accurate results when new data is given. So, with the help of regularization, the complex models are penalized. The L1 and L2 norms we discussed above are used in two types of regularization:

  • L1 regularization used with Lasso Regression
  • L2 regularization used with Ridge Regression

Covariance Matrix

Finding the relationship between two variables is very necessary in data exploration and with the help of covariance or correlation, we can find the relation between two continuous variables. It is used to find the direction of the linear relationship between the variables. If the covariance is coming as positive, then there is a direct relationship between these two variables. But on the same hand, if it is coming as negative, then a change in one will lead to an opposite change in another variable.

Support Vector Machine Classification

If you are looking for the most common classification algorithms then with the use of support vector machines, you can find some amazing results. It works by finding the decision surface and it is related to a supervised machine learning algorithm. This is the algorithm in which we plot the given data item as a point in an n-dimensional space where n is known as the features of the dataset you have, with the value of each feature being the value of a particular coordinate. Then, we need to perform the given classification using a hyperplane that will be used to differentiate the two classes with the help of a maximum margin.

Computer Vision

This is known as the field of artificial intelligence where computers are trained to interpret and understand the visual world by using various kinds of images, videos, and also deep learning models. With the help of this, the algorithms can identify various objects and also classify them. With the help of this concept in artificial learning, the algorithms designed will be able to see visual data. So, what is the use of the linear algorithm in artificial intelligence and in computer vision? Well, we use linear algebra in applications such as image reorganization which includes various image processing techniques. These techniques include image convolution and image representations as tensors that are used algorithms to identify objects and see the data.

Image Convolution

It is one of the building blocks of computer vision. It is an element-wise multiplication of two matrices that is followed by their sum. In the image processing application, there are multidimensional arrays that are present to show an image. An array is multi-dimensional when it has rows and columns representing the pixels of the image as well as other dimensions for the color data.

Natural Language Processing

It is a branch of artificial intelligence that is known to deal with the interaction between computers and human beings’ natural language which is most often the case- English. There are many popular applications of MLP like chatbots, speech recognition, and also text analysis. In the world, we are living right now, we must have used this technology in one way or another. There are various kinds of digital assistants like Siri or Alexa where we are seeing the use of NLP very often. So there is various use of linear algebra when we need to have natural language processing done in data science. Some of them are mentioned below:

Word Embedding

We know that computers do not understand the data- the data which is in text form. So how do you implement NLP with that dataset? So, to use this feature we need to represent that text data numerically. Word embedding is the type of word representation that is understood by the computer. They are representations of words that will allow machine learning algorithms to understand the words and the meaning associated with them. But where does linear algebra come from in this scenario?

Using word embedding, the words are represented as vectors of numbers and their meaning is preserved in the given documents. These representations are obtained from the neutral networks where a large amount of data is called a corpus, a language modeling learning technique. There are many word embedding tools that are now used but let us discuss Word2vec here.

This is the technique that is used for better representation of words in word embedding. There are large amounts of syntactic as well as semantic relationships, and these are captured by Wrod2vec. There are two methods that are used here:

  • Continuous Bag of words: It is used to predict the current work using the context clues in the given window.
  • Skip Gram: This helps in predicting the surrounding context clues within the given window of the current word.

Dimensionality Reduction

We are aware of the fact that there is a massive amount of data that is surrounding us. This is data that we need to process and analyze and store as well. And if come to the image data, then we might have high-resolution data that is needed to be translated to the matrices of numbers. So, dealing with large matrices can become very challenging and this is also tedious work for supercomputers even. So, in this case, we might need to reduce the original data into smaller sets that are relevant to the application that we are going to use. SVD is used most commonly which stands for Singular Value decomposition.  A matrix can be broken down into its component pieces using the SVD matrix decomposition technique, which simplifies matrix calculations.

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There are myriad applications with the use of linear algebra in the data science field and surely that cannot be covered on the page at one time. Data Science is becoming such a vast field that it offers career options to all of us. In the real world, we are expanding our knowledge and finding applications all around us. There are many other computer science areas where we can see the use of linear algebra like cybersecurity algorithms, clustering analysis, and also optimization algorithms. These algorithms are very widely used, and they can be modeled with the help of linear algebra.

In this page, we studied various applications of linear algebra and the three most common fields in data science where we can construct algorithms using this concept. We discovered that by using linear algebra, data science can uncover various hidden trends and find insights in the given data set.

So, if you are looking to have a great career option in the field of data science, then grasping the use of various concepts in data science would be a smart step. Furthermore, with the right learning platform like StarAgile, you can get your hands on the best training materials. Here, you will learn various concepts that will help you with your data science certification. Check out various skills needed so that you can hone them and have a great career as a data scientist.

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