A Proposition for Fixing the Dimensionality of a Laplacian Low-rank Approximation of any Binary Data-matrix

Alain Lelu (1, 2) , Martine Cadot (3)

1 LASELDI - Laboratoire de Semio-Linguistique, Didactique et Informatique
2 KIWI - Knowledge Information and Web Intelligence
3 ABC - Machine Learning and Computational Biology

Laplacian low-rank approximations are much appreciated in the context of graph spectral methods and Correspondence Analysis. We address here the problem of determining the dimensionality K* of the relevant eigenspace of a general binary datatable by a statistically well-founded method. We propose 1) a general framework for graph adjacency matrices and any rectangular binary matrix, 2) a randomization test for fixing K*. We illustrate with both artificial and real data.

Mots clés: dimensionality reduction; intrinsic dimension; randomization test; low-rank approximation; graph Laplacian; bipartite graph; Correspondence Analysis; Cattell's scree; binary matrix

Domaines: Autre [cs.OH]; Traitement du texte et du document; Apprentissage [cs.LG]; Machine Learning [stat.ML]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Alain Lelu, Martine Cadot. A Proposition for Fixing the Dimensionality of a Laplacian Low-rank Approximation of any Binary Data-matrix. The Fifth International Conference on Information, Process, and Knowledge Management - eKNOW 2013, Feb 2013, Nice, France. pp.70-73. ⟨hal-00773436⟩