PCA Biplot

Use this page for a cautious PCA-style two-component view, while keeping preprocessing dependence and score-versus-loading boundaries explicit.

Figure purpose

This page should be read as a PCA-style two-component score view. It helps compress several numeric variables into two plotted axes so that broad sample relationships become easier to inspect visually.

The important boundary is that the current implementation is closer to a score plot than to a full classical biplot with explicit loading vectors.

What Licklider shows

The plotted points should be read as sample scores on two derived axes, typically corresponding to a PC1-like and PC2-like view of the current projection. This helps you inspect whether samples appear broadly close together, separated, or unusual in the reduced space.

The current public contract should not be read as exposing a full classical biplot with loading arrows, feature vectors, or a complete feature-contribution display. In practice, this page is safer to read as a two-component score view than as a full score-and-loading figure.

When to use or avoid

Use this figure when a reduced two-axis summary is easier to interpret than a full matrix or many pairwise plots. It can be helpful for exploratory screening of broad structure, approximate separation, or possible outliers in a lower-dimensional view.

Avoid reading separation in this plot as proof of real group difference. Principal components depend on preprocessing, scaling, and the variables included in the decomposition.

Scores and loadings should also be kept separate conceptually. The current page should not imply that the product exposes a full loading-arrow biplot contract.

Required columns

  • Multiple numeric variables that can be summarized into principal-component-like axes
  • A preprocessing context where scaling and inclusion choices are understood as part of the figure

The current implementation supports a PCA-like projection to two derived axes. Docs should keep that wording narrower than the page title alone.

This figure is exploratory. It can suggest that some samples appear close together or farther apart in a reduced space, but it does not prove separation, clustering truth, or one automatic discovery result.

Preprocessing choices matter. Different scaling or feature sets can change what PC1 and PC2 look like, so the plot should be read as one view of structure, not as a final answer.

Licklider cannot automatically determine whether the current scaling, feature inclusion, or preprocessing choices are the scientifically best ones for your question. It also cannot decide from the plot alone whether apparent separation is stable, biologically meaningful, or only a visual artifact of the chosen preprocessing path. If those choices change, the orientation and apparent distances in the plot can change as well.

That is why this figure should be treated as a structure-screening view, not as a standalone inferential result.

Design rationale and references

Licklider keeps the public wording narrower than the page title because classical PCA biplots usually imply both score information and loading information. If the current figure is closer to a score view, the docs should say so explicitly rather than implying a richer loading contract than the user can actually inspect.

The page also emphasizes preprocessing dependence because PCA directions are not fixed properties of the raw dataset alone. Scaling, centering, feature inclusion, and related preprocessing decisions can substantially change the projection. A visually strong separation in PC space is therefore a prompt for follow-up, not a proof of scientific difference.

This figure is positioned as exploratory for the same reason. PCA is useful for reducing dimensionality and screening broad structure, but the reduced axes do not by themselves establish mechanism, cluster truth, or inferential significance.

References

  1. Jolliffe, I. T., & Cadima, J. (2016). Principal component analysis: a review and recent developments. Philosophical Transactions of the Royal Society A, 374(2065), 20150202. https://doi.org/10.1098/rsta.2015.0202
  2. Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal component analysis. Biometrika, 58(3), 453-467. https://doi.org/10.1093/biomet/58.3.453

Alternative figures

  • Use K-means Clustering Plot when the main goal is to inspect one current clustering overlay rather than a purely reduced projection.
  • Use Confidence Ellipse or Convex Hull when grouped scatter overlays are easier to read than a PCA-style reduction.
  • Use Heatmap when you want to preserve the matrix view instead of collapsing variables into two axes.

TODO (Phase02+)

  • Expand only if the public product surface later exposes loading vectors, feature labels, or a clearer biplot-specific contract.