James M. Keller

A possibilistic approach to clustering

The clustering problem is cast in the framework of possibility theory. The approach differs from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values can be interpreted as degrees of possibility of the points belonging to the classes, i.e., the compatibilities of the points with the class prototypes. An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function. The advantages of the resulting family of possibilistic algorithms are illustrated by several examples. >

A possibilistic fuzzy c-means clustering algorithm

In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint produces unrealistic typicality values for large data sets. In this paper, we propose a new model called possibilistic-fuzzy c-means (PFCM) model. PFCM produces memberships and possibilities simultaneously, along with the usual point prototypes or cluster centers for each cluster. PFCM is a hybridization of possibilistic c-means (PCM) and fuzzy c-means (FCM) that often avoids various problems of PCM, FCM and FPCM. PFCM solves the noise sensitivity defect of FCM, overcomes the coincident clusters problem of PCM and eliminates the row sum constraints of FPCM. We derive the first-order necessary conditions for extrema of the PFCM objective function, and use them as the basis for a standard alternating optimization approach to finding local minima of the PFCM objective functional. Several numerical examples are given that compare FCM and PCM to PFCM. Our examples show that PFCM compares favorably to both of the previous models. Since PFCM prototypes are less sensitive to outliers and can avoid coincident clusters, PFCM is a strong candidate for fuzzy rule-based system identification.

The possibilistic C-means algorithm: insights and recommendations

Recently, the possibilistic C-means algorithm (PCM) was proposed to address the drawbacks associated with the constrained memberships used in algorithms such as the fuzzy C-means (FCM). In this issue, Barni et al. (1996) report a difficulty they faced while applying the PCM, and note that it exhibits an undesirable tendency to converge to coincidental clusters. The purpose of this paper is not just to address the issues raised by Barni et al., but to go further and analytically examines the underlying principles of the PCM and the possibilistic approach, in general. We analyze the data sets used by Barni et al. and interpret the results reported by them in the light of our findings.

Texture description and segmentation through fractal geometry

Abstract Fractal geometry is receiving increased attention as a model for natural phenomena. In this paper we first present a new method for estimating the fractal dimension from image surfaces and show that it performs better at describing and segmenting generated fractal sets. Since the fractal dimension alone is not sufficient to characterize natural textures, we define a new class of texture measures based on the concept of lacunarity and use them, together with the fractal dimension, to describe and segment natural texture images.

Information fusion in computer vision using the fuzzy integral

A method of evidence fusion, based on the fuzzy integral, is developed. This technique nonlinearly combines objective evidence, in the form of a fuzzy membership function, with subjective evaluation of the worth of the sources with respect to the decision. Various new theoretical properties of this technique are developed, and its applicability to information fusion in computer vision is demonstrated through simulation and with object recognition data from forward-looking infrared imagery. >

Neural network implementation of fuzzy logic

Abstract Fuzzy logic has gained increased attention as a methodology for managing uncertainty in a rule-based structure. In a fuzzy logic inference system, more rules can fire at any given time than in a crisp expert system. Since the propositions are modelled as possibility distributions, there is a considerable computation load on the inference engine. In this paper, a neural network structure is proposed as a means of performing fuzzy logic inference. Three variations of the network are described, but in each case, the knowledge of the rule (i.e., the antecedent and consequent clauses) are explicitly encoded in the weights of the net. The theoretical properties of this structure are developed. In fact, the network reduces to crisp modus ponens when the inputs are crisp sets. Also, under suitable conditions the degree of specificity of the consequences of the inference is a monotone function of the degree of specificity of the input. Several simulation studies are included to illustrate the performance of the fuzzy logic inference networks.

Quantitative analysis of properties and spatial relations of fuzzy image regions

Properties of objects and spatial relations between objects play an important role in rule-based approaches for high-level vision. The partial presence or absence of such properties and relationships can supply both positive and negative evidence for region labeling hypotheses. Similarly, fuzzy labeling of a region can generate new hypotheses pertaining to the properties of the region, its relation to the neighboring regions, and, finally, hypotheses pertaining to the labels of the neighboring regions. A unified methodology that can be used to characterize both properties and spatial relationships of object regions in a digital image is presented. The methods proposed for computing the properties and relations of image regions can be used to arrive at more meaningful decisions about the contents of the scene. >

A smart home application to eldercare: Current status and lessons learned

To address an aging population, we have been investigating sensor networks for monitoring older adults in their homes. In this paper, we report ongoing work in which passive sensor networks have been installed in 17 apartments in an aging in place eldercare facility. The network under development includes simple motion sensors, video sensors, and a bed sensor that captures sleep restlessness and pulse and respiration levels. Data collection has been ongoing for over two years in some apartments. This longevity in sensor data collection is allowing us to study the data and develop algorithms for identifying alert conditions such as falls, as well as extracting typical daily activity patterns for an individual. The goal is to capture patterns representing physical and cognitive health conditions and then recognize when activity patterns begin to deviate from the norm. In doing so, we strive to provide early detection of potential problems which may lead to serious health events if left unattended. We describe the components of the network and show examples of logged sensor data with correlated references to health events. A summary is also included on the challenges encountered and the lessons learned as a result of our experiences in monitoring aging adults in their homes.

Linguistic summarization of video for fall detection using voxel person and fuzzy logic

In this paper, we present a method for recognizing human activity from linguistic summarizations of temporal fuzzy inference curves representing the states of a three-dimensional object called voxel person. A hierarchy of fuzzy logic is used, where the output from each level is summarized and fed into the next level. We present a two level model for fall detection. The first level infers the states of the person at each image. The second level operates on linguistic summarizations of voxel persons states and inference regarding activity is performed. The rules used for fall detection were designed under the supervision of nurses to ensure that they reflect the manner in which elders perform these activities. The proposed framework is extremely flexible. Rules can be modified, added, or removed, allowing for per-resident customization based on knowledge about their cognitive and physical ability.

Fusion of handwritten word classifiers

Methods for fusing multiple handwritten word classifiers are compared on standard data. A novel method based on data-dependent densities in a Choquet fuzzy integral is shown to outperform neural networks, Borda and weighted Borda counts, and Sugeno fuzzy integral.