Calculator Inputs
Paste numeric features with one categorical class column. Comment lines may start with a hash.
Formula Used
LDA compares within-class variation against between-class variation. It then finds directions maximizing their ratio.
The calculator regularizes SW before Cholesky decomposition. A symmetric transformed problem then provides stable eigenvectors.
How to Use This Calculator
- Paste rows containing numeric features and one class label.
- Select the correct delimiter and header setting.
- Choose whether labels appear first or last.
- Select one or two discriminant components.
- Enable standardization for differently scaled features.
- Adjust regularization when matrices appear unstable.
- Press the calculation button and review every result.
Use the projection alongside eigenvalues and loadings. Training accuracy remains only a diagnostic estimate.
Understanding LDA Projection Analysis
Projection Purpose
LDA transforms labeled observations into directions that maximize useful class separation clearly. It compares differences between class centers against variation existing inside each class today. The resulting projection often reveals structure hidden across several original numerical features.
Scatter Matrix Logic
Within-class scatter measures how tightly observations cluster around their respective class means. Between-class scatter measures how far class means differ from the overall mean directly. LDA selects eigenvectors that produce the strongest ratio between both scatter measures.
Regularization
Regularization stabilizes calculations when features are correlated or sample counts remain small. A positive diagonal value prevents unstable inversions within the within-class scatter matrix. Larger values improve robustness but may soften meaningful discriminant directions slightly overall.
Feature Scaling
Standardization gives differently scaled features comparable influence during matrix construction steps effectively. It becomes important when measurements use unrelated units or dramatically different ranges. Disable standardization only when feature scales already carry deliberate analytical meaning clearly.
Component Selection
One component creates a simple axis for ranking and comparing labeled observations effectively. Two components reveal clusters, overlaps, outliers, and directional class separation more clearly. Available components cannot exceed the smaller class or feature dimensional limit mathematically.
Centroid Interpretation
Projected centroids summarize each class location inside the selected discriminant coordinate system. Wide centroid spacing usually indicates easier separation for nearest-centroid classification decisions overall. However, compact classes may still overlap when individual observations vary substantially nearby.
Eigenvalue Meaning
Eigenvalues quantify discrimination captured by each available linear projection direction numerically. Explained discriminant ratios convert those values into easier proportional comparisons for users. A dominant first ratio suggests one direction contains most useful separation information available.
Accuracy Diagnostic
Nearest-centroid accuracy offers a quick diagnostic rather than complete predictive validation evidence. It classifies each projected observation using the closest projected class centroid location. Use cross-validation before treating this training accuracy as expected production performance seriously.
Input Preparation
Upload clean numeric features and place categorical labels consistently within every row. Choose the delimiter, header setting, label position, and requested component count carefully. Then adjust regularization, scaling, plotting, and numerical solver options as needed safely.
Result Review
Review warnings before interpreting charts because malformed rows can distort every calculation. Inspect eigenvalues, centroid distances, scatter ratios, and classification accuracy together during analysis. No single metric completely describes projection quality across all practical datasets reliably.
Practical Applications
Use LDA for supervised visualization, feature compression, and interpretable class exploration workflows efficiently. It works best when classes share roughly similar covariance patterns and shapes. Combine projection findings with domain knowledge and independent model evaluation results afterward.
Frequently Asked Questions
What does an LDA projection show?
It shows labeled observations along class-separating directions. Greater spacing suggests stronger discrimination. Overlap reveals difficult class boundaries.
How many components can LDA create?
The maximum equals classes minus one. Feature count can reduce that limit. This calculator displays one or two components.
Should I standardize the features?
Standardize features using different units or ranges. Scaling prevents large measurements from dominating. Keep original scales only when deliberately meaningful.
Why does regularization matter?
Regularization improves numerical stability for correlated features. It also helps smaller datasets. Excessive values can weaken meaningful separation.
What does a large eigenvalue mean?
A large eigenvalue indicates strong discrimination. Compare explained ratios across components. Larger ratios represent more captured separation.
Is the reported accuracy a validation score?
No, it uses the submitted training projection. It offers rapid diagnostics only. Use cross-validation for reliable generalization estimates.
Can the calculator handle text categories?
Class labels may contain text. Predictor columns must remain numeric. Encode categorical predictors before submitting them.
Why are my classes overlapping?
Features may not separate classes linearly. Noise can also cause overlap. Consider better features or nonlinear methods.
What causes a singular scatter matrix?
Duplicate or correlated features often cause singularity. Small classes also increase risk. Regularization and feature removal usually help.