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Opérateurs de régularisation pour le subspace clustering flou

Abstract : Subspace clustering is a data mining task which consists in simultaneously identifiying groups of similar data and making this similarity explicit, for example by selecting features characteristic of the groups. In this thesis, we consider a specific family of fuzzy subspace clustering models, which are based on the minimization of a cost function. We propose three desirable qualities of clustering, which are absent from the solutions computed by the previous models. We then propose simple penalty terms which we use to encode these properties in the original cost functions. Some of these terms are non-differentiable and the techniques standard in fuzzy clustering cannot be applied to minimize the new cost functions. We thus propose a new, generic optimization algorithm, which extends the standard approach by combining alternate optimization and proximal gradient descent. We then instanciate this algorithm with operators minimizing the three previous penalty terms and show that the resulting algorithms posess the corresponding qualities.
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Submitted on : Wednesday, September 23, 2020 - 5:42:39 PM
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Arthur Guillon. Opérateurs de régularisation pour le subspace clustering flou. Intelligence artificielle [cs.AI]. Sorbonne Université, 2019. Français. ⟨NNT : 2019SORUS121⟩. ⟨tel-02947213⟩

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