In many areas of life, we come across systems where elements are deeply interconnected—whether through physical routes, digital networks, or abstract relationships. Graphs offer a flexible way to represent and make sense of these connections...
In the realm of computer science, 'sorting' refers to the process of arranging a collection of items in a specific, predetermined order. This order is based on certain criteria that are defined beforehand...
Evaluating the performance of parallel computing systems is crucial for understanding their efficiency and identifying potential bottlenecks. Here are some metrics and concepts for evaluating performance...
The Message Passing Interface (MPI) is a standardized and portable message-passing system designed to function on a wide variety of parallel computing architectures. It provides a set of library routines that can be called from programming languages like C, C++, and Fortran to write parallel applica...
Let's start by defining some helpful terms and emphasizing the distinctions between related concepts. In general those concepts are universal and may be applied to any programming language. The differences between the languages will be discussed in greater detail later, when we attempt to explain th...
Multithreading refers to the capability of a CPU, or a single core within a multi-core processor, to execute multiple threads concurrently. A thread is the smallest unit of processing that can be scheduled by an operating system. In a multithreaded environment, a program, or process, can perform mul...
Parallel computing is the process of breaking a task into smaller parts that can be processed simultaneously by multiple processors. These notes explore the different ways of achieving parallelism in hardware and their impact on parallel computing performance...
Designing parallel programs involves breaking down computational tasks into smaller, concurrent units to be executed simultaneously. This approach leverages the power of multiple processors to enhance performance and efficiency. Key steps in this process include partitioning, communication, agglomer...
Multiprocessing involves running multiple processes simultaneously. Each process has its own memory space, making them more isolated from each other compared to threads, which share the same memory. This isolation means that multiprocessing can be more robust and less prone to errors from shared sta...
Asynchronous programming is a technique used to achieve concurrency, where tasks can be executed independently without waiting for other tasks to finish. It allows for nonblocking behavior, in contrast to synchronous execution that waits for one task to complete before starting the next task...
Recommendation systems are a fundamental component in the interface between users and large-scale content providers like Amazon, eBay, and iTunes. These systems personalize user experiences by suggesting products, movies, or content based on past interactions and preferences...
Machine Learning (ML), a subset of artificial intelligence, is the scientific study of algorithms and statistical models that computer systems use to effectively perform a specific task without using explicit instructions. It relies on patterns and inference instead. ML algorithms build a mathematic...
Unsupervised learning, a core component of machine learning, focuses on discerning the inherent structure of data without any labeled examples. Clustering, a pivotal task in unsupervised learning, aims to organize data into meaningful groups or clusters. A quintessential algorithm for clustering is ...
When facing high error rates with a machine learning model, especially when tested on new data, various strategies can be employed to diagnose and address the problem...
Principal Component Analysis (PCA) is a widely used technique in machine learning for dimensionality reduction. It simplifies the complexity in high-dimensional data while retaining trends and patterns...
Linear Regression is a fundamental type of supervised learning algorithm in statistics and machine learning. It's utilized for modeling and analyzing the relationship between a dependent variable and one or more independent variables. The goal is to predict continuous output values based on the inpu...
Neural networks, a core algorithm in machine learning, draw inspiration from the human brain's structure and function. They consist of layers containing interconnected nodes (neurons), each designed to perform specific computational tasks. Neural networks can tackle various classification problems, ...
Multiple linear regression extends the concept of simple linear regression to multiple independent variables. This technique models a dependent variable as a linear combination of several independent variables...
Linear Algebra forms the backbone of many machine learning algorithms, including linear regression. Understanding matrices and vectors is fundamental in this context...
Logistic regression is a statistical method used for classification in machine learning. Unlike linear regression, which predicts continuous values, logistic regression predicts discrete outcomes, like classifying an email as spam or not spam...
Optical Character Recognition (OCR) enables computers to interpret text within images. This process involves a machine learning pipeline comprising several steps, each focused on a specific aspect of OCR, like pedestrian or text detection. The pipeline integrates various techniques, including data s...
These notes outline the key strategies and considerations for developing a spam classification system. This process involves several steps, from feature selection to error analysis, and addresses the challenges of working with skewed datasets...
Anomaly detection involves identifying data points that significantly differ from the majority of the data, often signaling unusual or suspicious activities. This technique is widely used across various domains, such as fraud detection, manufacturing, and system monitoring...
Regularization is a technique used to prevent overfitting in machine learning models, ensuring they perform well not only on the training data but also on new, unseen data...
Support Vector Machines (SVMs) are powerful tools in machine learning, and their formulation can be derived from logistic regression cost functions. This article delves into the mathematical underpinnings of SVMs, starting with logistic regression and transitioning to the SVM framework...
Neural networks represent a cornerstone in the field of machine learning, drawing inspiration from neurological processes within the human brain. These networks excel in processing complex datasets with numerous features, transcending traditional methods like logistic regression in both scalability ...
Training machine learning models on large datasets poses significant challenges due to the computational intensity involved. To effectively handle this, various techniques such as stochastic gradient descent and online learning are employed. Let's delve into these methods and understand how they fac...
Gaussian elimination is a fundamental algorithmic procedure in linear algebra used to solve systems of linear equations, find matrix inverses, and determine the rank of matrices. The procedure systematically applies elementary row operations to transform a given matrix into an upper-triangular form ...
The Gauss-Seidel method is a classical iterative method for solving systems of linear equations of the form $A\mathbf{x} = \mathbf{b}$, where $A$ is an $n \times n$ matrix, $\mathbf{x}$ is the vector of unknowns $(x_1, x_2, \ldots, x_n)$, and $\mathbf{b}$ is a known vector. Unlike direct methods suc...
A linear system of equations is a collection of one or more linear equations involving the same set of variables. Such systems arise in diverse areas such as engineering, economics, physics, and computer science. The overarching goal is to find values of the variables that simultaneously satisfy all...
The inverse of a matrix A is denoted as A^-1. It is a unique matrix such that when it is multiplied by the original matrix A, the result is the identity matrix I. Mathematically, this is expressed as...
LU Decomposition (or LU Factorization) is a powerful and widely used technique in numerical linear algebra for solving systems of linear equations, computing inverses, and determining determinants. The core idea is to factorize a given square matrix $A$ into the product of a lower-triangular matrix ...
The Jacobi method is a classical iterative algorithm used to approximate the solution of a system of linear equations $A\mathbf{x} = \mathbf{b}$. Instead of attempting to solve the system directly using methods such as Gaussian elimination, the Jacobi method iteratively refines an initial guess for ...
Cubic spline interpolation is a refined mathematical tool frequently used within numerical analysis. It's an approximation technique that employs piecewise cubic polynomials, collectively forming a cubic spline. These cubic polynomials are specifically engineered to pass through a defined set of dat...
Linear interpolation is one of the most basic and commonly used interpolation methods. The idea is to approximate the value of a function between two known data points by assuming that the function behaves linearly (like a straight line) between these points. Although this assumption may be simplist...