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:
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:
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');
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');
Factor analysis aims to find latent variables that explain observed relationships among variables.