Related papers: Density-Matrix Spectral Embeddings for Categorical Data: Operator Structure and Stability

Density-Matrix Spectral Embeddings for Categorical Data: Operator Structure and Stability

URL: http://arxiv.org/abs/2603.01975v1
Date: Mon, 02 Mar 2026 15:29:54 GMT
Title: Density-Matrix Spectral Embeddings for Categorical Data: Operator Structure and Stability
Authors: Raquel Bosch-Romeu, Antonio Falcó, osé-Antonio Rodríguez-Gallego,
Abstract summary: We introduce a supervised dimensionality reduction methodology for categorical (and discretized mixed-type) data based on a density-matrix construction induced by class-conditional frequencies.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We introduce a supervised dimensionality reduction methodology for categorical (and discretized mixed-type) data based on a density-matrix construction induced by class-conditional frequencies. Given a labeled dataset encoded in a one-hot survey space, we assemble a frequency matrix whose columns aggregate feature occurrences within each class, and define a normalized Gram-type operator that satisfies the axioms of a density matrix. The resulting representation admits an intrinsic rank bound controlled by the number of classes, enabling low-dimensional spectral embeddings via dominant eigenmodes. Classification is performed in the reduced space through class-conditional kernel density estimation and a maximum-likelihood decision rule. We establish structural invariances, provide complexity estimates, and validate the approach on synthetic benchmarks probing high cardinality, sparsity, noise, and class imbalance.

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