Robust Fuzzy C-Means Clustering Algorithm Based on Normal Shrink and Membership Filtering for Image Segmentation

The robustness and effectiveness of image segmentation using the FCM algorithm can be improved by incorporating local spatial information into the FCM method, which is particularly noise-tolerant. However the introduction of local spatial information gives more computational complexity. Hence to overcome this problem an improved FCM clustering method is proposed which is based on a normal shrink algorithm with membership filtering. The Proposed method gives a faster and more robust result in comparison to FCM. Firstly, a normal shrink denoising algorithm is introduced to preserve the image details and noise immunity. Secondly, membership filtering is introduced, which depends only on the local spatial neighboring properties of the matrix called the membership partition matrix. The Proposed method is faster and simpler as it does not calculate the distance between pixels and cluster centers and between local spatial neighboring. Also, it is very efficient for noise immunity

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

Soft transition from probabilistic to possibilistic fuzzy clustering

In the fuzzy clustering literature, two main types of membership are usually considered: A relative type, termed probabilistic, and an absolute or possibilistic type, indicating the strength of the attribution to any cluster independent from the rest. There are works addressing the unification of the two schemes. Here, we focus on providing a model for the transition from one schema to the other, to exploit the dual information given by the two schemes, and to add flexibility for the interpretation of results. We apply an uncertainty model based on interval values to memberships in the clustering framework, obtaining a framework that we term graded possibility. We outline a basic example of graded possibilistic clustering algorithm and add some practical remarks about its implementation. The experimental demonstrations presented highlight the different properties attainable through appropriate implementation of a suitable graded possibilistic model. An interesting application is found in automated segmentation of diagnostic medical images, where the model provides an interactive visualization tool for this task

Advances in Possibilistic Clustering with Application to Hyperspectral Image Processing

Η ομαδοποίηση δεδομένων είναι μια εδραιωμένη μεθοδολογία ανάλυσης δεδομένων που έχει χρησιμοποιηθεί εκτενώς σε διάφορα πεδία εφαρμογών κατά τη διάρκεια των τελευταίων δεκαετιών. Η παρούσα διατριβή εστιάζει κυρίως στην ευρύτερη οικογένεια των αλγορίθμων βελτιστοποίησης κόστους και πιο συγκεκριμένα στους αλγόριθμους ομαδοποίησης με βάση τα ενδεχόμενα (Possibilistic c-Means, PCM). Συγκεκριμένα, αφού εκτίθενται τα αδύνατα σημεία τους, προτείνονται νέοι (batch και online) PCM αλγόριθμοι που αποτελούν επεκτάσεις των προηγουμένων και αντιμετωπίζουν τα αδύνατα σημεία των πρώτων. Οι προτεινόμενοι αλγόριθμοι ομαδοποίησης βασίζονται κυρίως στην υιοθέτηση των εννοιών (α) της προσαρμοστικότητας παραμέτρων (parameter adaptivity), οι οποίες στους κλασσικούς PCM αλγορίθμους παραμένουν σταθερές κατά την εκτέλεσή τους και (β) της αραιότητας (sparsity). Αυτά τα χαρακτηριστικά προσδίδουν νέα δυναμική στους προτεινόμενους αλγορίθμους οι οποίοι πλέον: (α) είναι (κατ' αρχήν) σε θέση να προσδιορίσουν τον πραγματικό αριθμό των φυσικών ομάδων που σχηματίζονται από τα δεδομένα, (β) είναι ικανοί να αποκαλύψουν την υποκείμενη δομή ομαδοποίησης, ακόμη και σε δύσκολες περιπτώσεις, όπου οι φυσικές ομάδες βρίσκονται κοντά η μία στην άλλη ή/και έχουν σημαντικές διαφορές στις διακυμάνσεις ή/και στις πυκνότητές τους και (γ) είναι εύρωστοι στην παρουσία θορύβου και ακραίων σημείων. Επίσης, δίνονται θεωρητικά αποτελέσματα σχετικά με τη σύγκλιση των προτεινόμενων αλγορίθμων, τα οποία βρίσκουν επίσης εφαρμογή και στους κλασσικούς PCM αλγορίθμους. Η δυναμική των προτεινόμενων αλγορίθμων αναδεικνύεται μέσω εκτεταμένων πειραμάτων, τόσο σε συνθετικά όσο και σε πραγματικά δεδομένα. Επιπλέον, οι αλγόριθμοι αυτοί έχουν εφαρμοστεί με επιτυχία στο ιδιαίτερα απαιτητικό πρόβλημα της ομαδοποίησης σε υπερφασματικές εικόνες. Τέλος, αναπτύχθηκε και μια μέθοδος επιλογής χαρακτηριστικών κατάλληλη για υπερφασματικές εικόνες.Clustering is a well established data analysis methodology that has been extensively used in various fields of applications during the last decades. The main focus of the present thesis is on a well-known cost-function optimization-based family of clustering algorithms, called Possibilistic C-Means (PCM) algorithms. Specifically, the shortcomings of PCM algorithms are exposed and novel batch and online PCM schemes are proposed to cope with them. These schemes rely on (i) the adaptation of certain parameters which remain fixed during the execution of the original PCMs and (ii) the adoption of sparsity. The incorporation of these two characteristics renders the proposed schemes: (a) capable, in principle, to reveal the true number of physical clusters formed by the data, (b) capable to uncover the underlying clustering structure even in demanding cases, where the physical clusters are closely located to each other and/or have significant differences in their variances and/or densities, and (c) immune to the presence of noise and outliers. Moreover, theoretical results concerning the convergence of the proposed algorithms, also applicable to the classical PCMs, are provided. The potential of the proposed methods is demonstrated via extensive experimentation on both synthetic and real data sets. In addition, they have been successfully applied on the challenging problem of clustering in HyperSpectral Images (HSIs). Finally, a feature selection technique suitable for HSIs has also been developed

Soft transition from probabilistic to possibilistic fuzzy clustering, DISI

In the fuzzy clustering literature, two main types of membership are usually considered: a relative type, termed probabilistic, and an absolute or possibilistic type, indicating the strength of the attribution to any cluster independent from the rest. There are works addressing the unification of the two schemes. Here we focus on providing a model for the transition from one schema to the other, to exploit the dual information given by the two schemes, and to add flexibility for the interpretation of results. We apply an uncertainty model based on interval values to memberships in the clustering framework, obtaining a framework that we term graded possibility. We outline a basic example of graded possibilistic clustering algorithm and add some practical remarks about its implementation. The experimental demonstrations presented highlight the different properties attainable through appropriate implementation of a suitable graded possibilistic model. An interesting application is found in automated segmentation of diagnostic medical images, where the model provides an interactive visualization tool for this task