🗯️MATLAB snippet

Using MATLAB for Latent Variable Models (LVMs) and Dimensionality Reduction can be very effective for detecting and analyzing selective perturbation effects, such as in high-dimensional biological datasets. MATLAB offers robust tools and functions for data analysis, visualization, and model fitting. Below is a guide on how to approach this in MATLAB:

1. Introduction to LVMs and Dimensionality Reduction

Latent Variable Models involve unobserved variables that can help explain the underlying structure in observed data. Dimensionality Reduction simplifies high-dimensional data into lower-dimensional representations while retaining essential information, allowing for the detection of patterns or perturbations.

Common techniques in MATLAB:

• Principal Component Analysis (PCA)
• Factor Analysis
• Independent Component Analysis (ICA)
• t-Distributed Stochastic Neighbor Embedding (t-SNE)
• Uniform Manifold Approximation and Projection (UMAP)

2. PCA for Dimensionality Reduction

PCA is a powerful tool for understanding data by reducing its dimensionality and visualizing it in a lower-dimensional space. It can help identify how perturbation effects influence the main sources of variation.

MATLAB implementation:

 % Load data
 data = readmatrix('data.csv'); % Assuming data is in CSV format
 labels = data(:, end); % Assuming last column contains perturbation labels
 data = data(:, 1:end-1); % Remove labels from data matrix
 ​
 % Perform PCA
 [coeff, score, latent, tsquared, explained] = pca(data);
 ​
 % Plot first two principal components
 figure;
 gscatter(score(:, 1), score(:, 2), labels);
 title('PCA of Data');
 xlabel('Principal Component 1');
 ylabel('Principal Component 2');

3. t-SNE for Non-linear Dimensionality Reduction

t-SNE is useful for visualizing complex structures that PCA may not capture, especially when data does not conform to linear relationships.

MATLAB code:

 % Perform t-SNE
 rng(1); % For reproducibility
 tsne_data = tsne(data);
 ​
 % Plot t-SNE results
 figure;
 gscatter(tsne_data(:, 1), tsne_data(:, 2), labels);
 title('t-SNE of Data');
 xlabel('t-SNE Dimension 1');
 ylabel('t-SNE Dimension 2');

4. Factor Analysis

Factor analysis aims to find latent variables that explain observed relationships among variables.