In this article, I have explained in detail ten awesome applications of Linear Algebra in Data Science. These topics are nothing but clusters of related words. A positive covariance indicates that an increase or decrease in one variable is accompanied by the same in another. Past exam questions on these topics are therefore not suitable when attempting past exam questions. This causes unrequired components of the weight vector to reduce to zero and prevents the prediction function from being overly complex. The topic model outputs the various topics, their distributions in each document, and the frequency of different words it contains. Here, the concept of Kernel Transformations comes into play. Use SVD to decompose the matrix into 3 matrices: Truncate the matrices based on the importance of topics, Start with a small matrix of weights, called a, Slide this kernel on the 2D input data, performing element-wise multiplication, Add the obtained values and put the sum in a single output pixel. This course is part 1 of a 2-part course. There are many ways for engineering features from text data, such as: Word Embeddings is a way of representing words as low dimensional vectors of numbers while preserving their context in the document. In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. This faithful sidekick is often ignored. You must be quite familiar with how a model, say a Linear Regression model, fits a given data: But wait – how can you calculate how different your prediction is from the expected output? We do not need to add additional features on our own. Here are a few kernels you can use: You can download the image I used and try these image processing operations for yourself using the code and the kernels above. Our intuition says that the decision surface has to be a circle or an ellipse, right? Or perhaps you know of some other applications that I could add to the list? Understand fundamental properties of matrices including determinants, inverse matrices, matrix factorisations, eigenvalues and linear transformations. It’s a technique we use to prevent models from overfitting. Vector spaces, subspaces and vector space axioms. Properties and composition of linear transformations. Orthogonal vectors and subspaces. Coding the Matrix: Linear Algebra through Applications to Computer Science @inproceedings{Klein2013CodingTM, title={Coding the Matrix: Linear Algebra through Applications to Computer Science}, author={P. Klein}, year={2013} } You’ll notice that it’s not as well clustered as we obtained after PCA: Natural Language Processing (NLP) is the hottest field in data science right now. It means a baseball player in the first sentence and a jug of juice in the second. It is another application of Singular Value Decomposition. Linear algebra is behind all the powerful machine learning algorithms we are so familiar with. As we will soon see, you should consider linear algebra as a must-know subject in data science. One of the most common classification algorithms that regularly produces impressive results. They are shown as the red-colored vectors in the figure below: You can easily implement PCA in Python using the PCA class in the scikit-learn package: I applied PCA on the Digits dataset from sklearn – a collection of 8×8 images of handwritten digits. Regularization is actually another application of the Norm. In order to guide the students to know the application of matrix in the computer science and technology to stimulate interest in learning. But how do you find it? This paper will cover the various applications of linear algebra in computer science including: internet search, graphics, speech recognition,and artificial intelligence. For now, let us talk about SVD in Dimensionality Reduction. On the other hand, correlation is the standardized value of Covariance. Lectures 1-20 cover the syllabus for the Preliminary Examination in Computer Science. 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