principal component analysis of raw data in matlab

To perform Principal Component Analysis (PCA) on raw data in MATLAB, you can follow these steps:

1. Load your raw data into MATLAB as a matrix. Each row should represent an observation, and each column should represent a variable.

2. Standardize the data by subtracting the mean of each variable and dividing by its standard deviation. This step ensures that all variables are on the same scale.

main.m
% Load raw data into a matrix
data = [ ... ]; % your raw data goes here

% Standardize the data
data_standardized = zscore(data);
130 chars
6 lines

3. Use the pca function to perform PCA on the standardized data. Specify the desired number of principal components to retain.

main.m
% Perform PCA
[coeff, score, latent, ~, explained] = pca(data_standardized);
77 chars
3 lines

• coeff contains the principal component loading vectors (eigenvectors) for each variable.
• score contains the principal component scores (projected data) for each observation.
• latent contains the variance explained by each principal component.
• explained contains the percentage of total variance explained by each principal component.

4. You can visualize the results by plotting the cumulative explained variance.

main.m
% Plot cumulative explained variance
figure;
plot(cumsum(explained), 'ko-', 'LineWidth', 2);
xlabel('Number of Principal Components');
ylabel('Cumulative Explained Variance (%)');
title('Cumulative Explained Variance');
grid on;
229 chars
8 lines

5. You can also choose the number of principal components based on the cumulative explained variance and project the data onto the selected number of components.

main.m
% Select the number of principal components to retain (e.g., 2)
num_components = 2;

% Project the data onto the selected components
data_projected = score(:, 1:num_components) * coeff(:, 1:num_components)';
208 chars
6 lines

Now you have performed PCA on your raw data and can use the projected data for further analysis or visualization.

Please note that PCA assumes linearity and normality in the data. If your data violates these assumptions, alternative dimensionality reduction techniques may be more appropriate.