Supervisors info:
Κωνσταντίνος Δ. Κουτρούμπας, Διευθυντής Ερευνών, Εθνικό Αστεροσκοπείο Αθηνών
Αθανάσιος Α. Ροντογιάννης, Διευθυντής Ερευνών, Εθνικό Αστεροσκοπείο Αθηνών
Summary:
Subspace clustering is the problem of modeling a collection of data points lying in one or more subspaces in the presence of noise, outliers and missing data. To the best of our knowledge, all the algorithms associated to this problem follow a hard clustering philosophy. The study presented in this thesis explores the effectiveness of the possibilistic approach, giving rise to a novel iterative algorithm, called sparse adaptive possibilistic K- subspaces (SAP K-subspaces). SAP K-subspaces algorithm generalizes the sparse possibilistic c-means algorithm (SPCM) [2]. Hence, it inherits the ability to handle reliably data corrupted by noise and containing outliers, as well as data points near the intersections of subspaces. In addition, the new algorithm is suitably initialized with more clusters than those actually exist in the data set and has the ability to gradually eliminate the unnecessary ones in order to conclude with the true clusters, formed by the data. Moreover, it adopts the low-rank approach, introduced in [1], in order to estimate the dimension of the involved subspaces. Experiments on both synthetic and real data illustrate the effectiveness of the proposed method.
[1] Paris V Giampouras, Athanasios A Rontogiannis, and Konstantinos D Koutroumbas. Alternating iteratively reweighted least squares minimization for lowrank matrix factorization. IEEE Transactions on Signal Processing, 67(2):490–503, 2018.
[2] Spyridoula D Xenaki, Konstantinos D Koutroumbas, and Athanasios A Rontogiannis. Sparsityaware possibilistic clustering algorithms. IEEE Transactions on Fuzzy Systems, 24(6):1611–1626, 2016.
Keywords:
clustering-alternating minimization, cluster elimination, low-rank, sparsity, subspace clustering, parameter adaptation, principal component analysis, possibilistic clustering
