Why Learning Linear Algebra is Important For Data Science And Machine Learning

Businesses are generating massive amounts of data everyday, and are using the principles of data science and big data analytics to make sense of it. This has led to growing popularity and utilization of data science ,with a lot of companies using it to enhance their product and customer experience, and further develop their business. 

What is Data Science?

Data science is a specialized field of study where we use modern methods and tools to deal with the huge volume of data and search for patterns, evaluate meaningful information, and produce business decisions for the betterment of any company. To construct a predictive model, data science utilizes various machine learning algorithms. Data can be derived from various sources, and can be presented in different formats for analysis.

Linear algebra is a specific branch of mathematics that works with linear equations and what these equations represent in the vector space with the help of matrices. When the information of linear equations is displayed in a systematic format, the result is a matrix. It is a central figure in modern mathematics. Multiple geometrical concepts that we have studied in our school life are mostly based on linear algebra.

To put it in simpler terms, linear algebra as a subject, is based upon vectors and linear functions. It is an integral part of physics and engineering because linear algebra can explain a lot of natural phenomena.

The components of linear algebra can be put into three distinct categories: vectors, linear equations, and matrices.

Vectors

You can perform multiple functions of linear algebra such as addition and multiplication on vectors, and it can also be utilized to express different quantities, such as the momentum of a speeding object. 

Some of the important topics connected to linear equations covered through vectors are:

• Different types of vectors
• Cross product
• Dot product
• Addition of vectors

Matrices

Through a matrix, any type of data can be arranged in the shape of a quadrilateral array. The entire thing can be displayed as Am×n. In this equation, n represents the number of columns, and m represents the total number of rows in the entire matrix. In linear algebra, the significance of matrices is that they can be utilised to manifest the linear equations in a very dense manner. 

The topics covered are as follows:

• Different types of matrices
• Determinant
• Matrix operations
• Transpose of a matrix

Need for Linear Algebra in Machine Learning and Data Science

Linear algebra plays a key role in data science, big data, and machine learning. Every machine learning model is fundamentally based on linear algebra. You may also have to study optimisation theory, probability, vector calculus, etc., if you want to excel in the field of data science and machine learning.

Some advantages of learning linear algebra for data science and machine learning are:

• Creating better machine learning algorithms
• Easy to learn
• Better graphic experience
• Estimating the forecast of machine learning
• Improved statistics

Let us briefly look at some of these benefits

Better Graphic Experience

You can get a better depictive representation in machine learning with the help of linear algebra. You can work your way through different graphical machine learning projects that deal with audio, video, image, and edge detection. Moreover, different parts of data sets used in machine learning are classified through linear algebra. Errors from the trained data can also be removed through these specific classifiers.

Furthermore, linear algebra can be used to find solutions for massivedata sets using a specific technique named matrix decomposition. The two of the most popular matrix decomposition techniques are as follows:

• Q-R
• L-U

Improved Statistics Through Linear Algebra

To process and integrate different data in machine learning, the concept of statistics is very important. With the help of linear algebra, you will be able to understand the concepts of statistics in a simplified manner. Through the utilization of notations, methods, and operation of linear algebra, advanced statistical topics can be amalgamated.

Application of Linear Algebra in Data Science

With the help of linear algebra, you can develop better clairvoyance when it comes to machine learning, and you will also not treat the deep learning algorithm as black boxes. Moreover, linear algebra will help you develop a better model and select appropriate hyperparameters. 

You will also have the ability to make your variations in algorithms, in addition to having the expertise to code algorithms from the beginning. That is how linear algebra can open up a new dimension for you in the field of machine learning and data science.

Let us look at the four different applications of linear algebra in data science and machine learning, and big data analytics:

Loss functions:

In linear algebra, the loss function is an application of the vector norm. Notably, the vector norm can be as simple as its magnitude. Let us understand how the loss function works with an example:

You may have an idea of how a linear regression model fits any provided data:

• First, you need to begin with an arbitrary prediction function (which is a function for a linear regression model).
• To anticipate results, use the individualistic characteristics of data.
• Now, you need to calculate the polarity between the forecasted output and the actual result.
• Use different strategies such as gradient descent to enhance your prediction function.

Regularization:

Regularization is another implementation of the vector norm and it is also an essential topic in data science. With this technique, we can restrict the overfitting of a model. When the training data fits very well in a model, then the model will be considered overfit. This kind of model cannot perform well when provided with advanced data because of the tumult in the practice data. Therefore, the model would not be able to hypothesize data that is new to the model.

Covariance Matrix:

Covariance matrix is used to research the relationship between two uninterpreted variables. It also tells us about the direction of the connection between the interlinked variables. A positive covariance signifies that the decrease or increase in a single variable goes along with the other variables and vice versa.

Support Vector Machine Classification:

Support vector machine classification is regarded as one of the most familiar algorithms with the ability to produce brilliant results. It is related to the vector spaces concept of linear algebra.

Why Should You Learn Linear Algebra Before Studying Machine Learning?

To become an expert in machine learning and data science, you will require the help of linear equations. Mathematical topics such as calculus, linear algebra, and statistics are required to gain in-depth knowledge in machine learning. 

Furthermore, linear algebra assists in building individual intuitions in machine learning and mathematical skills. Linear algebra is considered one of the fundamental blocks in machine learning and data science. Just like you cannot construct a skyscraper without building a strong foundation first, the same applies to linear algebra when it comes to data science.

Suppose, with the help of principal component analysis or PCA, you want to decrease the dimension of your data but how will you be able to decide how many principal components you will need to conserve if you do not have any idea how it can affect your data. That is why you need to know the mechanics of your algorithm.

Instances of Linear Algebra in Machine Learning and Data Science

Below are some best examples of linear algebra in machine learning:

• Images and photographs
• Latent semantic analysis
• Recommender systems
• One-hot encoding
• Deep learning
• Regularization
• Dataset and data files
• Singular-value decomposition
• Linear regression
• Principal component analysis 

By and Large

If you are willing to grow your skills in the field of data science and machine learning and develop your career in the same,  learning linear algebra should be your first step. It will lay the foundations for you to gain in-depth knowledge and experience in field of machine learning, data science, and big data analytics. 

If you already have a bachelor’s degree in mathematics,  you can further boost your career through Hero Vired’s online Data Science, Machine Learning, and Artificial Intelligence program. In this integrated course, instructors will teach you how to analyse data and solve business problems through complex data models. 

Moreover, after finishing this course, you will get access to guaranteed placement and job opportunities to help you step into the world of data science and machine learning.