There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Data Mining Practical Machine Learning Tools and Techniques

Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.

/pdf/survey-of-clustering-algorithms-6zezqhbjyo.pdf

Survey of clustering algorithms

Escherichia coli is the predominant nonpathogenic facultative flora of the human intestine. Some E. coli strains, however, have developed the ability to cause disease of the gastrointestinal, urinary, or central nervous system in even the most robust human hosts. Diarrheagenic strains of E. coli can be divided into at least six different categories with corresponding distinct pathogenic schemes. Taken together, these organisms probably represent the most common cause of pediatric diarrhea worldwide. Several distinct clinical syndromes accompany infection with diarrheagenic E. coli categories, including traveler’s diarrhea (enterotoxigenic E. coli), hemorrhagic colitis and hemolytic-uremic syndrome (enterohemorrhagic E. coli), persistent diarrhea (enteroaggregative E. coli), and watery diarrhea of infants (enteropathogenic E. coli). This review discusses the current level of understanding of the pathogenesis of the diarrheagenic E. coli strains and describes how their pathogenic schemes underlie the clinical manifestations, diagnostic approach, and epidemiologic investigation of these important pathogens.

Diarrheagenic Escherichia coli

A review on image segmentation techniques

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. >

http://systemaut.persiangig.com/Fuzzy/IEEE_00227387.pdf

A possibilistic approach to clustering

Classification of objects is an important area of research and application in a variety of fields. In the presence of full knowledge of the underlying probabilities, Bayes decision theory gives optimal error rates. In those cases where this information is not present, many algorithms make use of distance or similarity among samples as a means of classification. The K-nearest neighbor decision rule has often been used in these pattern recognition problems. One of the difficulties that arises when utilizing this technique is that each of the labeled samples is given equal importance in deciding the class memberships of the pattern to be classified, regardless of their `typicalness'. The theory of fuzzy sets is introduced into the K-nearest neighbor technique to develop a fuzzy version of the algorithm. Three methods of assigning fuzzy memberships to the labeled samples are proposed, and experimental results and comparisons to the crisp version are presented.

A fuzzy K-nearest neighbor algorithm

/pdf/fuzzy-models-and-algorithms-for-pattern-recognition-and-30xealsgh3.pdf

Fuzzy Models and Algorithms for Pattern Recognition and Image Processing (The Handbooks of Fuzzy Sets)

Pattern Recognition.- Cluster Analysis for Object Data.- Cluster Analysis for Relational Data.- Classifier Design.- Image Processing and Computer Vision.

Fuzzy Models and Algorithms for Pattern Recognition and Image Processing

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.

http://www.comp.ita.br/~forster/CC-222/material/fuzzyclust/fuzzy01492404.pdf

James M. Keller

Papers

A possibilistic approach to clustering

A fuzzy K-nearest neighbor algorithm

Fuzzy Models and Algorithms for Pattern Recognition and Image Processing (The Handbooks of Fuzzy Sets)

Fuzzy Models and Algorithms for Pattern Recognition and Image Processing

A possibilistic fuzzy c-means clustering algorithm