A fuzzy clustering algorithm to detect planar and quadric shapes

In this paper, we introduce a new fuzzy clustering algorithm to detect an unknown number of planar and quadric shapes in noisy data. The proposed algorithm is computationally and implementationally simple, and it overcomes many of the drawbacks of the existing algorithms that have been proposed for similar tasks. Since the clustering is performed in the original image space, and since no features need to be computed, this approach is particularly suited for sparse data. The algorithm may also be used in pattern recognition applications

Clustering of nonstationary data streams: a survey of fuzzy partitional methods

YesData streams have arisen as a relevant research topic during the past decade. They are real‐time, incremental in nature, temporally ordered, massive, contain outliers, and the objects in a data stream may evolve over time (concept drift). Clustering is often one of the earliest and most important steps in the streaming data analysis workflow. A comprehensive literature is available about stream data clustering; however, less attention is devoted to the fuzzy clustering approach, even though the nonstationary nature of many data streams makes it especially appealing. This survey discusses relevant data stream clustering algorithms focusing mainly on fuzzy methods, including their treatment of outliers and concept drift and shift.Ministero dell‘Istruzione, dell‘Universitá e della Ricerca

Subspace Clustering: A Possibilistic Approach

Ως συσταδοποίηση υποχώρων ορίζεται το πρόβλημα της μοντελοποίησης δεδομένων που βρίσκονται σε έναν ή και περισσότερους υποχώρους υπό την παρουσία θορύβου και περιέχουν ακραίες παρατηρήσεις και ελλιπή δεδομένα. Εξ όσων γνωρίζουμε, όλοι οι αλγόριθμοι που επιλύουν αυτό το πρόβλημα υποθέτουν ότι μια παρατήρηση ανήκει αυστηρά σε έναν υποχώρο. Η παρούσα διατριβή εξετάζει την περίπτωση όπου ένα σημείο μπορεί ταυτόχρονα και ανεξάρτητα να ανήκει σε παραπάνω από έναν υποχώρο. Ως αποτέλεσμα έχουμε την δημιουργία ενός καινούργιου αλγορίθμου, του sparse adaptive possibilistic K-subspaces (SAP K-subspaces). Ο αλγόριθμος αυτός αποτελεί γενίκευση του αλγορίθμου sparse possibilistic c-means algorithm (SPCM) [2], πράγμα που σημαίνει ότι μπορεί να διαχειριστεί με αξιοπιστία δεδομένα τόσο με θόρυβο και ακραίες τιμές όσο και δεδομένα τα οποία βρίσκονται σε τομές υποχώρων. Επίσης, ο καινούργιος αλγόριθμος αρχικοποιείται με περισσότερες συστάδες από τις πραγματικές, έχοντας την δυνατότητα απαλοιφής των περιττών συστάδων και τελικά την εύρεση αυτών που σχηματίζονται απο τα δεδομένα. Επιπλέον, υιοθετεί μια προσέγγιση εύρεσης γινομένου πινάκων χαμηλής τάξης για την εκτίμηση της διάστασης των υποχώρων [1]. Πειράματα σε συνθετικά και αληθινά δεδομένα επιβεβαιώνουν την αποτελεσματικότητα του αλγορίθμου. [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.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

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin