Principal Component Analysis Online: Multivariate Dimensionality Reduction
What Is Principal Component Analysis?
Principal component analysis (PCA) compresses many correlated variables into a few uncorrelated principal components, each a linear combination of the original variables, extracted in order of variance: the first component explains the most variance, the second the next most and is orthogonal to the first. PCA is used for dimensionality reduction, data compression, anomaly detection and exploring the structure among variables, and is common for multi-indicator quality evaluation, process monitoring (with T-squared and SPE) and as a pre-processing step for regression and classification. Before using it, check that the variables are sufficiently correlated.
Correlation or Covariance Matrix?
When the variables have very different units or scales (for example, temperature in hundreds and concentration in percent), use the correlation matrix, which is equivalent to standardizing the variables and prevents scale from dominating the result. When the variables share a unit and you want to preserve the original variance information, use the covariance matrix. The tool defaults to the correlation matrix and allows switching, while also providing the KMO and Bartlett's test of sphericity to judge whether the data are suitable for PCA: PCA is appropriate when KMO is above 0.6 and Bartlett's test is significant.
How to Decide the Number of Components
Common rules: keep components with eigenvalues greater than 1 (Kaiser's criterion); keep the components before the elbow (where the slope flattens) on the scree plot; or keep enough components for the cumulative variance contribution to reach 80-90%. The tool outputs each component's eigenvalue, variance contribution and cumulative contribution, and draws a scree plot to help decide. The retained components should be interpretable: use the loadings to see which original variables each component mainly represents, and rotate if needed to clarify the loading structure. When several criteria agree, the decision is more reliable.
Loadings, Scores and How to Use It
The loading matrix shows the correlation between each original variable and each principal component and is used to interpret the components; scores are the projections of the samples onto the components, which can be plotted to see sample groupings or used as new variables in regression or clustering. Workflow: paste the multi-column data, choose the matrix type, view eigenvalues and contributions, decide the number of components, output loadings and scores, and use the score plot to interpret the sample structure. AI interpretation summarizes the dimensionality-reduction conclusions and suggests component names, and the reduced data can be downloaded for further modeling.