应用背景 - Matlab Forge | Premium MATLAB Algorithms & Functions

MATLAB Probability and Statistical Computing

Application Background: As systems grow increasingly complex, various methods for predicting fault probabilities and statistical calculations have emerged. Using MATLAB software for programming and estimation has become more popular. We introduce 30 probability and statistical prediction methods with source code examples to help beginners practice and learn. Key Technology: When programming probability and statistical predictions in MATLAB, understanding prediction principles and establishing predictive models is essential. Beginners should practice fundamental methods like regression analysis and multiple nonlinear regression, gradually modifying code to master this skill.

MATLAB 201 views Tagged

MATLAB Implementation of Expectation-Maximization (EM) Algorithm

Application Context: In statistical computing, the Expectation-Maximization (EM) algorithm is used to find maximum likelihood or maximum a posteriori estimates of parameters in probabilistic models that depend on unobserved latent variables. The EM algorithm is frequently applied in machine learning and computer vision for data clustering tasks. Key Technology: The EM algorithm iterates through two alternating steps: - E-step (Expectation): Computes the expected value of the log-likelihood function using current estimates of hidden variables - M-step (Maximization): Finds parameters that maximize the expected log-likelihood computed in the E-step Parameters estimated in the M-step are reused in the next E-step, creating an iterative convergence process.

MATLAB 279 views Tagged

Horn-Schunck Optical Flow Algorithm

Application Background The principle of optical flow method for detecting moving objects: assigning a velocity vector (optical flow) to each pixel in an image forms an optical flow field. If there are no moving objects, the optical flow field remains continuous and uniform. When moving objects are present, their optical flow differs from the background, causing discontinuities in the flow field, enabling detection of moving objects and their positions. Key Technologies 1.2 Horn-Schunck Model In 1981, Horn and Schunck introduced a variational approach by incorporating a global smoothness constraint based on the continuous and smooth characteristics of optical flow fields for moving objects. The energy equation consists of: - Data term representing brightness constancy constraint - Smoothness term enforcing flow field continuity

MATLAB 332 views Tagged

0-1 Integer Programming with Recursive Solution Generation

0-1 integer programming has broad applications in assignment problems, knapsack problems, and even TSP problems - all belonging to NP-hard class where exhaustive search becomes infeasible for large-scale instances. This implementation demonstrates a recursive approach to systematically enumerate all possible solutions for verification purposes, with a notable discrepancy found when comparing results against textbook examples.

MATLAB 290 views Tagged

MATLAB Code for Spatial Frequency Response with Implementation Details

Application Background: In mathematics, physics, and engineering, spatial frequency characterizes periodic structures in space. It measures sinusoidal components per unit repetition (determined via Fourier transform), with units in cycles per meter. For image processing applications, spatial frequency is typically expressed in cycles per millimeter or line pairs per millimeter. Key Technology: Spatial frequency theory explains how visual cortex neurons encode spatial frequencies rather than simple edge detection. Experimental evidence shows stronger neuronal responses to sinusoidal gratings at specific orientations compared to edges or bars. This MATLAB implementation demonstrates spatial frequency analysis through Fourier transformation and grating response simulations.

MATLAB 222 views Tagged

3D Polar Coordinate Plotting in MATLAB

Application Context: Extends MATLAB's 2D polar plotting capabilities to 3D polar coordinate visualization, providing enhanced graphical representation options. This plotting program offers various parameter selections to accommodate diverse visualization requirements. Key Technology: MATLAB plotting program implementing 3D polar coordinate graphs with customizable parameters and efficient data rendering.

MATLAB 223 views Tagged

Compressive Sensing Algorithms: Comparative Implementation and Analysis

Application Context Compressive sensing represents a highly valuable source code implementation with significant practical applications in signal processing, image reconstruction, and communication systems. This program provides comparative analysis of multiple algorithms, making it particularly valuable for researchers beginning their exploration of compressive sensing. The implementation demonstrates practical utility while maintaining research-oriented flexibility for algorithm modification and performance evaluation. Key Technologies The codebase implements and compares various compressive sensing algorithms including greedy approaches (OMP, CoSaMP), convex optimization methods (l1-minimization), and iterative thresholding techniques. Each algorithm is implemented with clear parameter configurations and performance metrics to facilitate understanding of trade-offs between reconstruction accuracy and computational complexity.

MATLAB 260 views Tagged

Enhanced Hilbert-Huang Transform Algorithm with Adaptive IMF Screening

Application Background: Empirical Mode Decomposition (EMD) decomposes signals into monocomponent signals called Intrinsic Mode Functions (IMFs), enabling instantaneous frequency calculation through Hilbert transform. The primary challenge in practical Hilbert-Huang transform applications is the endpoint effect. Our solution introduces an adaptive spurious IMF filtering algorithm using residue-to-original-signal correlation coefficient as threshold. Key Technology: Complex signal decomposition into monocomponent signals requires each IMF to satisfy two conditions: (1) Extremum and zero-crossing counts must be equal or differ by one throughout the data length; (2) The mean of upper and lower envelopes must be zero at any point. The implementation involves adaptive sifting with envelope interpolation and statistical boundary handling.

MATLAB 330 views Tagged

ICA Fixed-Point Algorithm (FastICA)

Application Context: This algorithm is derived from fixed-point recursive methodology and is applicable to any data type. Its development enables ICA analysis of high-dimensional data. Also known as the Fixed-Point algorithm, it was proposed by Hyvärinen et al. from University of Helsinki. FastICA employs batch processing where substantial sample data participates in each iteration, making it a rapid optimization iterative algorithm. While distinct from conventional neural networks, it can still be categorized as a neural network algorithm from distributed parallel processing perspective. FastICA exists in multiple forms including fourth-order cumulant-based, maximum likelihood-based, and maximum negentropy-based implementations.

MATLAB 247 views Tagged

Basic Inertial Navigation Simulation Program

Application Context: Inertial navigation uses inertial components (accelerometers) to measure the acceleration of a vehicle, then calculates velocity and position through integration and computation to achieve navigation and positioning. The components of an inertial navigation system are installed within the vehicle, operating without reliance on external information or energy radiation, making it resistant to interference and an autonomous navigation system. Key Technologies: Designed to understand fundamental principles of inertial navigation and perform simulations. Features efficient and practical code implementation with clear structure and comprehensive annotations. The simulation includes numerical integration algorithms (like Euler or Runge-Kutta methods) for motion trajectory calculation and coordinate transformation modules for navigation frame conversions.