Clustering compositional data trajectories

Our essay aims at studying suitable statistical methods for the clustering of compositional data in situations where observations are constituted by trajectories of compositional data, that is, by sequences of composition measurements along a domain. Observed trajectories are known as “functional data” and several methods have been proposed for their analysis. In particular, methods for clustering functional data, known as Functional Cluster Analysis (FCA), have been applied by practitioners and scientists in many fields. To our knowledge, FCA techniques have not been extended to cope with the problem of clustering compositional data trajectories. In order to extend FCA techniques to the analysis of compositional data, FCA clustering techniques have to be adapted by using a suitable compositional algebra. The present work centres on the following question: given a sample of compositional data trajectories, how can we formulate a segmentation procedure giving homogeneous classes? To address this problem we follow the steps described below. First of all we adapt the well-known spline smoothing techniques in order to cope with the smoothing of compositional data trajectories. In fact, an observed curve can be thought of as the sum of a smooth part plus some noise due to measurement errors. Spline smoothing techniques are used to isolate the smooth part of the trajectory: clustering algorithms are then applied to these smooth curves. The second step consists in building suitable metrics for measuring the dissimilarity between trajectories: we propose a metric that accounts for difference in both shape and level, and a metric accounting for differences in shape only. A simulation study is performed in order to evaluate the proposed methodologies, using both hierarchical and partitional clustering algorithm. The quality of the obtained results is assessed by means of several indices

Integració a la plataforma webDTI de tècniques de clustering de fibres i visualització de clústers

Estudi, disseny i implementació de diferents tècniques d’agrupament de fibres (clustering) per tal d’integrar a la plataforma DTIWeb diferents algorismes de clustering i tècniques de visualització de clústers de fibres de forma que faciliti la interpretació de dades de DTI als especialistes

A new approach to segmentation based on fusing circumscribed contours, region growing and clustering

One of the major problems in machine vision is the segmentation of images of natural scenes. This paper presents a new proposal for the image segmentation problem which has been based on the integration of edge and region information. The main contours of the scene are detected and used to guide the posterior region growing process. The algorithm places a number of seeds at both sides of a contour allowing stating a set of concurrent growing processes. A previous analysis of the seeds permits to adjust the homogeneity criterion to the regions's characteristics. A new homogeneity criterion based on clustering analysis and convex hull construction is proposed

Improving Clustering Algorithms for Image Segmentation using Contour and Region Information

In image segmentation, clustering algorithms are very popular because they are intuitive and, some of them, easy to implement. For instance, the k-means is one of the most used in the literature, and many authors successfully compare their new proposal with the results achieved by the k-means. However, it is well known that clustering image segmentation has many problems. For instance, the number of regions of the image has to be known a priori, as well as different initial seed placement (initial clusters) could produce different segmentation results. Most of these algorithms could be slightly improved by considering the coordinates of the image as features in the clustering process (to take spatial region information into account). In this paper we propose a significant improvement of clustering algorithms for image segmentation. The method is qualitatively and quantitative evaluated over a set of synthetic and real images, and compared with classical clustering approaches. Results demonstrate the validity of this new approach

A Homogeneous Set-Theoretical Frame for Clustering Fuzzy Relational Data

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process

PhD Students’ Research Group Social Capital in Two Countries: A Clustering Approach with Duocentred Network Measures

The article examines the structure of the collaboration networks of research groups where Slovenian and Spanish PhD students are pursuing their doctorate. The units of analysis are student-supervisor dyads. We use duocentred networks, a novel network structure appropriate for networks which are centred around a dyad. A cluster analysis reveals three typical clusters of research groups. Those which are large and belong to several institutions are labelled under a bridging social capital label. Those which are small, centred in a single institution but have high cohesion are labelled as bonding social capital. Those which are small and with low cohesion are called weak social capital groups. Academic performance of both PhD students and supervisors are highest in bridging groups and lowest in weak groups. Other variables are also found to differ according to the type of research group. At the end, some recommendations regarding academic and research policy are drawn

Manifold clustering for motion segmentation

En aquesta tesi s’estudia el problema de la segmentació del moviment. La tesi presenta una revisió dels principals algoritmes de segmentació del moviment, s’analitzen les característiques principals i es proposa una classificació de les tècniques més recents i importants. La segmentació es pot entendre com un problema d’agrupament d’espais (manifold clustering). Aquest estudi aborda alguns dels reptes més difícils de la segmentació de moviment a través l’agrupament d’espais. S’han proposat nous algoritmes per a l’estimació del rang de la matriu de trajectòries, s’ha presenta una mesura de similitud entre subespais, s’han abordat problemes relacionats amb el comportament dels angles canònics i s’ha desenvolupat una eina genèrica per estimar quants moviments apareixen en una seqüència. L´ultima part de l’estudi es dedica a la correcció de l’estimació inicial d’una segmentació. Aquesta correcció es du a terme ajuntant els problemes de la segmentació del moviment i de l’estructura a partir del moviment.