Metric-Aware PCA as a Linear Instance of Geometric Deep Learning

In three linesTheoretical paper positioning Metric-Aware Principal Component Analysis (MAPCA) within geometric deep learning framework. MAPCA parameterises PCA by a positive-definite metric matrix, with solutions equivariant under the orthogonal group preserving the metric. A uniqueness theorem characterises Invariant PCA as the unique linear data-derived metric equivariant under arbitrary diagonal rescaling.

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