On classification with incomplete data

We address the incomplete-data problem in which feature vectors to be classified are missing data (features). A (supervised) logistic regression algorithm for the classification of incomplete data is developed. Single or multiple imputation for the missing data is avoided by performing analytic integration with an estimated conditional density function (conditioned on the observed data). Conditional density functions are estimated using a Gaussian mixture model (GMM), with parameter estimation performed using both expectation-maximization (EM) and variational Bayesian EM (VB-EM). The proposed supervised algorithm is then extended to the semisupervised case by incorporating graph-based regularization. The semisupervised algorithm utilizes all available data-both incomplete and complete, as well as labeled and unlabeled. Experimental results of the proposed classification algorithms are shown     

Content-based image retrieval based on a fuzzy approach

A typical content-based image retrieval (CBIR) system would need to handle the vagueness in the user queries as well as the inherent uncertainty in image representation, similarity measure, and relevance feedback. We discuss how fuzzy set theory can be effectively used for this purpose and describe an image retrieval system called FIRST (fuzzy image retrieval system) which incorporates many of these ideas. FIRST can handle exemplar-based, graphical-sketch-based, as well as linguistic queries involving region labels, attributes, and spatial relations. FIRST uses fuzzy attributed relational graphs (FARGs) to represent images, where each node in the graph represents an image region and each edge represents a relation between two regions. The given query is converted to a FARG, and a low-complexity fuzzy graph matching algorithm is used to compare the query graph with the FARGs in the database. The use of an indexing scheme based on a leader clustering algorithm avoids an exhaustive search of the FARG database. We quantify the retrieval performance of the system in terms of several standard measures.     

A comparison of fuzzy shell-clustering methods for the detection ofellipses

In this paper, we introduce a shell-clustering algorithm for ellipsoidal clusters based on the so-called “radial distance” which can be easily extended to superquadric clusters. We compare our algorithm with other algorithms in the literature that are based on the algebraic distance, the approximate distance, the normalized radial distance, and the exact distance. We evaluate the performance of each algorithm on two-dimensional data sets containing “scattered” ellipses, partial ellipses, outliers, and ellipses of disparate sizes, and summarize the relative strengths and weaknesses of each algorithm     

A belief maintenance scheme for hierarchical knowledge-based image analysis systems

A variety of belief maintenance schemes for image analysis have been suggested and used to date. In the recent past, several researchers have suggested the use of the Dempster-Shafer theory of evidence for representation of belief. This approach appears to be particularly suited for knowledge-based image analysis systems because of its intuitively convincing ways of representing beliefs, support, plausibility, ignorance, dubiety, and a host of other measures that can be used for the purpose of decision making. It also provides a very attractive technique to combine these measures obtained from disparate knowledge sources. In this article, we show how the Dempster-Shafer theoretic concepts of refinement and coarsening can be used to aggregate and propagate evidence in a multi-resolution image analysis system based on a hierarchical knowledge base.     

Evidence aggregation networks for fuzzy logic inference

Fuzzy logic has been applied in many engineering disciplines. The problem of fuzzy logic inference is investigated as a question of aggregation of evidence. A fixed network architecture employing general fuzzy unions and intersections is proposed as a mechanism to implement fuzzy logic inference. It is shown that these networks possess desirable theoretical properties. Networks based on parameterized families of operators (such as Yager's union and intersection) have extra predictable properties and admit a training algorithm which produces sharper inference results than were earlier obtained. Simulation studies corroborate the theoretical properties.     

Are fuzzy definitions of basic attributes of image objects reallyuseful?

Computer vision applications often involve measuring properties of objects in images. Typically, thresholding or segmentation techniques are used to obtain crisp object boundaries before object properties are computed. In this correspondence, we explore the possibility of using fuzzy definitions for measuring object properties without having to make crisp decisions about object boundaries prematurely. We present theorems which indicate that the use of fuzzy definitions to measure properties in intensity-based image analysis almost always gives accurate results. We also present experimental evidence and reasoning which show that fuzzy definitions are not always useful in feature-based methods     

Fuzzy and possibilistic shell clustering algorithms and theirapplication to boundary detection and surface approximation. I

Traditionally, prototype-based fuzzy clustering algorithms such as the Fuzzy C Means (FCM) algorithm have been used to find “compact” or “filled” clusters. Recently, there have been attempts to generalize such algorithms to the case of hollow or “shell-like” clusters, i.e., clusters that lie in subspaces of feature space. The shell clustering approach provides a powerful means to solve the hitherto unsolved problem of simultaneously fitting multiple curves/surfaces to unsegmented, scattered and sparse data. In this paper, we present several fuzzy and possibilistic algorithms to detect linear and quadric shell clusters. We also introduce generalizations of these algorithms in which the prototypes represent sets of higher-order polynomial functions. The suggested algorithms provide a good trade-off between computational complexity and performance, since the objective function used in these algorithms is the sum of squared distances, and the clustering is sensitive to noise and outliers. We show that by using a possibilistic approach to clustering, one can make the proposed algorithms robust     

Clustering algorithms based on volume criteria

Clustering algorithms such as the K-means algorithm and the fuzzy C-means algorithm are based on the minimization of the trace of the (fuzzy) within-fluster scatter matrix. In this paper, we explore the use of determinant (volume) criteria for clustering. We derive an algorithm called the minimum scatter volume (MSV) algorithm, that minimizes the scatter volume, and another algorithm called the minimum cluster volume (MCV) that minimizes the sum of the volumes of the individual clusters. The behavior of MSV is shown to be similar to that of K-means, whereas MCV is more versatile     

Low-complexity fuzzy relational clustering algorithms for Webmining

This paper presents new algorithms-fuzzy c-medoids (FCMdd) and robust fuzzy c-medoids (RFCMdd)-for fuzzy clustering of relational data. The objective functions are based on selecting c representative objects (medoids) from the data set in such a way that the total fuzzy dissimilarity within each cluster is minimized. A comparison of FCMdd with the well-known relational fuzzy c-means algorithm (RFCM) shows that FCMdd is more efficient. We present several applications of these algorithms to Web mining, including Web document clustering, snippet clustering, and Web access log analysis