Efficient regularized spectral data embedding

Lazhar Labiod () and Mohamed Nadif ()
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Lazhar Labiod: LIPADE, Université de Paris
Mohamed Nadif: LIPADE, Université de Paris

Advances in Data Analysis and Classification, 2021, vol. 15, issue 1, No 6, 99-119

Abstract: Abstract Data embedding (DE) or dimensionality reduction techniques are particularly well suited to embedding high-dimensional data into a space that in most cases will have just two dimensions. Low-dimensional space, in which data samples (data points) can more easily be visualized, is also often used for learning methods such as clustering. Sometimes, however, DE will identify dimensions that contribute little in terms of the clustering structures that they reveal. In this paper we look at regularized data embedding by clustering, and we propose a simultaneous learning approach for DE and clustering that reinforces the relationships between these two tasks. Our approach is based on a matrix decomposition technique for learning a spectral DE, a cluster membership matrix, and a rotation matrix that closely maps out the continuous spectral embedding, in order to obtain a good clustering solution. We compare our approach with some traditional clustering methods and perform numerical experiments on a collection of benchmark datasets to demonstrate its potential.

Keywords: Spectral clustering; Data embedding; Data science; 62H30 Classification and discrimination; cluster analysis (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11634-020-00386-8

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