BPEC: Belief-Peaks Evidential Clustering

International audienceThis paper introduces a new evidential clustering method based on the notion of "belief peaks" in the framework of belief functions. The basic idea is that all data objects in the neighborhood of each sample provide pieces of evidence that induce belief on the possibility of such sample to become a cluster center. A sample having higher belief than its neighbors and located far away from other local maxima is then characterized as cluster center. Finally, a credal partition is created by minimizing an objective function with the fixed cluster centers. An adaptive distance metric is used to fit for unknown shapes of data structures. We show that the proposed evidential clustering procedure has very good performance with an ability to reveal the data structure in the form of a credal partition, from which hard, fuzzy, possibilistic and rough partitions can be derived. Simulations on synthetic and real-world datasets validate our conclusions

Land cover classification using fuzzy rules and aggregation of contextual information through evidence theory

Land cover classification using multispectral satellite image is a very challenging task with numerous practical applications. We propose a multi-stage classifier that involves fuzzy rule extraction from the training data and then generation of a possibilistic label vector for each pixel using the fuzzy rule base. To exploit the spatial correlation of land cover types we propose four different information aggregation methods which use the possibilistic class label of a pixel and those of its eight spatial neighbors for making the final classification decision. Three of the aggregation methods use Dempster-Shafer theory of evidence while the remaining one is modeled after the fuzzy k-NN rule. The proposed methods are tested with two benchmark seven channel satellite images and the results are found to be quite satisfactory. They are also compared with a Markov random field (MRF) model-based contextual classification method and found to perform consistently better.Comment: 14 pages, 2 figure

On the semantics of fuzzy logic

AbstractThis paper presents a formal characterization of the major concepts and constructs of fuzzy logic in terms of notions of distance, closeness, and similarity between pairs of possible worlds. The formalism is a direct extension (by recognition of multiple degrees of accessibility, conceivability, or reachability) of the najor modal logic concepts of possible and necessary truth.Given a function that maps pairs of possible worlds into a number between 0 and 1, generalizing the conventional concept of an equivalence relation, the major constructs of fuzzy logic (conditional and unconditioned possibility distributions) are defined in terms of this similarity relation using familiar concepts from the mathematical theory of metric spaces. This interpretation is different in nature and character from the typical, chance-oriented, meanings associated with probabilistic concepts, which are grounded on the mathematical notion of set measure. The similarity structure defines a topological notion of continuity in the space of possible worlds (and in that of its subsets, i.e., propositions) that allows a form of logical “extrapolation” between possible worlds.This logical extrapolation operation corresponds to the major deductive rule of fuzzy logic — the compositional rule of inference or generalized modus ponens of Zadeh — an inferential operation that generalizes its classical counterpart by virtue of its ability to be utilized when propositions representing available evidence match only approximately the antecedents of conditional propositions. The relations between the similarity-based interpretation of the role of conditional possibility distributions and the approximate inferential procedures of Baldwin are also discussed.A straightforward extension of the theory to the case where the similarity scale is symbolic rather than numeric is described. The problem of generating similarity functions from a given set of possibility distributions, with the latter interpreted as defining a number of (graded) discernibility relations and the former as the result of combining them into a joint measure of distinguishability between possible worlds, is briefly discussed

Review on Fuzzy Clustering Algorithms

Image segmentation especially fuzzy-based segmentation techniques are widely used due to effective segmentation performance. For this reason, a number of algorithms are proposed in the literature. This paper presents a survey report of different types of classical fuzzy clustering techniques which are available in the literature

Clustering of multiple instance data.

An emergent area of research in machine learning that aims to develop tools to analyze data where objects have multiple representations is Multiple Instance Learning (MIL). In MIL, each object is represented by a bag that includes a collection of feature vectors called instances. A bag is positive if it contains at least one positive instance, and negative if no instances are positive. One of the main objectives in MIL is to identify a region in the instance feature space with high correlation to instances from positive bags and low correlation to instances from negative bags -- this region is referred to as a target concept (TC). Existing methods either only identify a single target concept, do not provide a mechanism for selecting the appropriate number of target concepts, or do not provide a flexible representation for target concept memberships. Thus, they are not suitable to handle data with large intra-class variation. In this dissertation we propose new algorithms that learn multiple target concepts simultaneously. The proposed algorithms combine concepts from data clustering and multiple instance learning. In particular, we propose crisp, fuzzy, and possibilistic variations of the Multi-target concept Diverse Density (MDD) metric, along with three algorithms to optimize them. Each algorithm relies on an alternating optimization strategy that iteratively refines concept assignments, locations, and scales until it converges to an optimal set of target concepts. We also demonstrate how the possibilistic MDD metric can be used to select the appropriate number of target concepts for a dataset. Lastly, we propose the construction of classifiers based on embedded feature space theory to use our target concepts to predict the label of prospective MIL data. The proposed algorithms are implemented, tested, and validated through the analysis of multiple synthetic and real-world data. We first demonstrate that our algorithms can detect multiple target concepts reliably, and are robust to many generative data parameters. We then demonstrate how our approach can be used in the application of Buried Explosive Object (BEO) detection to locate distinct target concepts corresponding to signatures of varying BEO types. We also demonstrate that our classifier strategies can perform competitively with other well-established embedded space approaches in classification of Benchmark MIL data

Early detection of health changes in the elderly using in-home multi-sensor data streams

The rapid aging of the population worldwide requires increased attention from health care providers and the entire society. For the elderly to live independently, many health issues related to old age, such as frailty and risk of falling, need increased attention and monitoring. When monitoring daily routines for older adults, it is desirable to detect the early signs of health changes before serious health events, such as hospitalizations, happen, so that timely and adequate preventive care may be provided. By deploying multi-sensor systems in homes of the elderly, we can track trajectories of daily behaviors in a feature space defined using the sensor data. In this work, we investigate a methodology for learning data distribution from streaming data and tracking the evolution of the behavior trajectories over long periods (years) using high dimensional streaming clustering and provide very early indicators of changes in health. If we assume that habitual behaviors correspond to clusters in feature space and diseases produce a change in behavior, albeit not highly specific, tracking trajectory deviations can provide hints of early illness. Retrospectively, we visualize the streaming clustering results and track how the behavior clusters evolve in feature space with the help of two dimension-reduction algorithms, Principal Component Analysis (PCA) and t-distributed Stochastic Neighbor Embedding (t-SNE). Moreover, our tracking algorithm in the original high dimensional feature space generates early health warning alerts if a negative trend is detected in the behavior trajectory. We validated our algorithm on synthetic data, real-world data and tested it on a pilot dataset of four TigerPlace residents monitored with a collection of motion, bed, and depth sensors over ten years. We used the TigerPlace electronic health records (EHR) to understand the residents' behavior patterns and to evaluate and explain the health warnings generated by our algorithm. The results obtained on the TigerPlace dataset show that most of the warnings produced by our algorithm can be linked to health events documented in the EHR, providing strong support for a prospective deployment of the approach.Includes bibliographical references

Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review

Fifty years have gone by since the publication of the first paper on clustering based on fuzzy sets theory. In 1965, L.A. Zadeh had published “Fuzzy Sets” [335]. After only one year, the first effects of this seminal paper began to emerge, with the pioneering paper on clustering by Bellman, Kalaba, Zadeh [33], in which they proposed a prototypal of clustering algorithm based on the fuzzy sets theory

Robustness and Outliers

Producción CientíficaUnexpected deviations from assumed models as well as the presence of certain amounts of outlying data are common in most practical statistical applications. This fact could lead to undesirable solutions when applying non-robust statistical techniques. This is often the case in cluster analysis, too. The search for homogeneous groups with large heterogeneity between them can be spoiled due to the lack of robustness of standard clustering methods. For instance, the presence of (even few) outlying observations may result in heterogeneous clusters artificially joined together or in the detection of spurious clusters merely made up of outlying observations. In this chapter we will analyze the effects of different kinds of outlying data in cluster analysis and explore several alternative methodologies designed to avoid or minimize their undesirable effects.Ministerio de Economía, Industria y Competitividad (MTM2014-56235-C2-1-P)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA212U13