Alpha-Beta Pruning Alpha-Beta pruning is a search algorithm used to reduce the number of nodes in a minimax search tree. When the algorithm evaluates that the subsequent moves of a strategy are worse than those of the p 2022-10-09 Data Science Artificial Intelligence
Breadth-First Search and Depth-First Search Breadth-First Search (BFS) and Depth-First Search (DFS) are two ways of traversing all vertices in a graph. These two basic search algorithms are introduced below. Breadth-First Search • Idea behind B 2022-09-11 Data Science Artificial Intelligence
Linear Regression Linear regression assumes that features and outcomes satisfy a linear relationship. The expressive ability of linear relationship is strong. The influence of each feature on the result can be reflecte 2022-08-13 Data Science Machine Learning
Computation of Eigenvalues and Eigenvectors For a small matrix \(A\), we usually compute its eigenvalues through \(det(A-\lambda I)\). But in reality, this computation is too expensive for most matrices. And in many cases, we only need the larg 2022-07-12 Mathematics Linear Algebra
Principal Component Analysis (PCA) Principal Component Analysis is a technique for simplifying datasets. It is a linear transformation that transforms the data into a new coordinate system such that the first largest variance of any da 2022-07-11 Mathematics Linear Algebra
Singular Value Decomposition (SVD) Part 2 In Singular Value Decomposition (SVD) Part 1, I introduce one way to calculate SVD. And in this post, I would talk about other ideas about solving SVD. Matrix \(A\) is symmetric \[ \begin{aligned} A \ 2022-07-08 Mathematics Linear Algebra
Tensor Operation In machine learning/big data we can think of a tensor as an nD-array. The picture below is an example of a rank 3 tensor with size (3,4,2). Tensor unfolding Unfolding a tensor to a matrix (“matrizati 2022-07-06 Linear Algebra
QR Decomposition The QR (orthogonal triangular) decomposition is the most effective and widely used method to find all the eigenvalues of a general matrix. It decomposes the matrix into a normal orthogonal matrix \(Q\ 2022-06-28 Mathematics Linear Algebra
The Least Squares Problem The Least Squares Problem is one of the most important problem in numerical approximation. The main idea of the least squares problem is to solve the unknown parameters , so that the sum of the square 2022-04-16 Mathematics Linear Algebra
Cholesky Decomposition Cholesky decomposition is to express a symmetric positive definite matrix as a decomposition of the product of a lower triangular matrix and its transpose. It requires that all eigenvalues of the matr 2022-04-15 Mathematics Linear Algebra
