pattern clustering based on noise modeling in wavelet space we describe an effective approach to object or feature detection in point patterns via noise modeling this is based on use of a redundant or non pyramidal wavelet transform noise modeling is based on a poisson process we illustrate this new method with a range of examples we use the close relationship between image pixelated and point representations to achieve the result of a clustering method with constant time computational cost

adaptive fuzzy rule based classification systems this paper proposes an adaptive method to construct a fuzzy rule based classification system with high performance for pattern classification problems the proposed method consists of two procedures an error correction based learning procedure and an additional learning procedure the error correction based learning procedure adjusts the grade of certainty of each fuzzy rule by its classification performance that is when a pattern is misclassified by a particular fuzzy rule the grade of certainty of that rule is decreased on the contrary when a pattern is correctly classified the grade of certainty is increased because the error correction based learning procedure is not meaningful after all the given patterns are correctly classified we cannot adjust a classification boundary in such a case to acquire a more intuitively acceptable boundary we propose an additional learning procedure we also propose a method for selecting significant fuzzy rules by pruning unnecessary fuzzy rules which consists of the error correction based learning procedure and the concept of forgetting we can construct a compact fuzzy rule based classification system with high performance

model based cluster analysis abstract the problem of dot clustering is studied from a model based viewpoint a set of placement processes is chosen each of which associates a probability with each location in a discrete space in other words a placement is a probability mass function pmf on the space a number of dots is then distributed in accordance with each of these pmfs the pmf and its associated cardinality define a subpopulation of dots this model is extremely general the pmfs are arbitrary given a set of dots generated by such a model maximum a posteriori map methods are applied to recover the most likely set of placements and cardinalities that could have given rise to the dots this identification problem is different from the partitioning problem which asks for the most likely partition of the dot population into subpopulations it is shown how and why map methods are useful in cluster analysis especially when the placement pmfs are non gaussian it is also shown that although the general identification problem is intractable there is a polynomial time solution if the number of subpopulations is bounded it is shown that a similar result holds for the partitioning problem

on triality and automorphisms and derivations of composition algebras abstract the principle of triality for orthogonal transformations on eight dimensional spaces is used to obtain different expressions for the automorphisms derivations and orthogonal transformations of cayley dickson algebras and symmetric composition algebras over fields of arbitrary characteristic

a note on hashing functions and tabu search algorithms abstract woodruff and zemel present four effective functions that can be used for hashing within tabu search algorithms however the authors overlook one property that may affect the performance of algorithms that use the proposed functions this paper clarifies the effects that the birthday paradox may have on algorithms using these functions

model based gaussian and non gaussian clustering abstract the classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms including those based on the sum of squares criterion and on the criterion of friedman and rubin 1967 however as currently implemented it does not allow the specification of which features orientation size and shape are to be common to all clusters and which may differ between clusters also it is restricted to gaussian distributions and it does not allow for noise we propose ways of overcoming these limitations a reparameterization of the covariance matrix allows us to specify that some features but not all be the same for all clusters a practical framework for non gaussian clustering is outlined and a means of incorporating noise in the form of a poisson process is described an approximate bayesian method for choosing the number of clusters is given the performance of the proposed methods is studied by simulation with encouraging results the methods are applied to the analysis of a data set arising in the study of diabetes and the results seem better than those of previous analyses rh

on the cartan jacobson theorem abstract the well known cartan jacobson theorem claims that the lie algebra of derivations of a cayley algebra is central simple if the characteristic is not 2 or 3 in this paper we have studied these two cases with the following results if the characteristic is 2 the theorem is also true but if the characteristic is 3 the derivation algebra is not simple we have also proved that in this last case there is a unique nonzero proper seven dimensional ideal which is a central simple lie algebra of type a2 and the quotient of the derivation algebra modulo this ideal turns out to be isomorphic as a lie algebra to the ideal itself the original motivation of this work was a series of computer aided calculations which proved the simplicity of derivation algebras of cayley algebras in the case of characteristic not 3 these computations also proved the existence of a unique nonzero proper ideal which turns out to be seven dimensional in the algebra of derivations of split cayley algebras in characteristic 3

interquad an interactive quad tree based procedure for solving the discrete alternative multiple criteria problem abstract in this paper an interactive procedure based upon a data structure called a quad tree is developed for solving the discrete alternative multiple criteria problem called interquad the procedure has been designed with large discrete alternative problems in mind interquad takes advantage of the ability of a quad tree to identify store and retrieve nondominated criterion vectors then the user interacts with the nondominated criterion vectors stored in the quad tree in a fashion similar to that of the combined tchebycheff aspiration criterion vector procedure of steuer silverman and whisman

fuzzy sets in pattern recognition methodology and methods abstract an objective of the paper is to discuss a state of the art of methodology and algorithms of fuzzy sets in the field of pattern recognition in real world recognition and classification problems we are faced with fuzziness that is connected with diverse facets of cognitive activity of the human being an origin of sources of fuzziness is related to labels expressed in feature space as well as to labels of classes taken into account in classification procedures an evident difference between a way of information processing by means of probability and fuzzy set theory and a way of interpretation of results is explained in detail in sequel methods of pattern recognition are studied in two main streams namely supervised and unsupervised learning different approaches to designing of classification schemes as e g relation calculus decision making approach etc are put into account a method of feature selection with the aid of fuzzy measure and fuzzy integral is introduced in clustering techniques methods relying on minimization of objective function are analyzed in detail also a problem of cluster validity expressed in terms of clustering indices is addressed numerical examples are also provided

distributed representation of fuzzy rules and its application to pattern classification abstract this paper introduces the concept of distributed representation of fuzzy rules and applies it to classification problems distributed representation is implemented by superimposing many fuzzy rules corresponding to different fuzzy partitions of a pattern space this means that we simulatenously employ many fuzzy rule tables corresponding to different fuzzy partitions in fuzzy inference in order to apply distributed representation of fuzzy rules to pattern classification problems we first propose an algorithm to generate fuzzy rules from numerical data next we propose a fuzzy inference method using the generated fuzzy rules the classification power of distributed representation is compared with that of ordinary fuzzy rules which can be viewed as local representation

clustering of clusters abstract an algorithm for the clustering of existing clusters is introduced in this paper the algorithm was adopted from fuzzy c mean and modifications made to take into account the extra information i e some data samples already form clusters partition coefficients together with some other criteria are used for testing cluster validity the method was applied on chinese character recognition and an encouraging result was obtained

division composition algebras through their derivation algebras abstract composition algebras are algebras with a nondegenerate quadratic multiplicative form in this paper we construct five families of division composition algebras and prove that any division composition algebra with nonabelian derivation algebra belongs to one of these families as a by product we obtain new examples of real division algebras

detection and separation of ring shaped clusters using fuzzy clustering a new fuzzy clustering algorithm designed to detect and characterize ring shaped clusters and combinations of ring shaped and compact spherical clusters has been developed this fkr algorithm includes automatic search for proper initial conditions in the two cases of concentric and excentric intersected combinations of clusters validity criteria based on total fuzzy area and fuzzy density are used to estimate the optimal number of substructures in the data set the fkr algorithm has been tested on a variety of simulated combinations of ring shaped and compact spherical clusters and its performance proved to be very good both in identifying the input shapes and in recovering the input parameters application of the fkr algorithm to an mri image of the heart s left ventricle was used to investigate the possibility of using this algorithm as an aid in image processing

a multiple hyper ellipsoidal subclass model for an evolutionary classifier abstract a pattern classification scheme in which the classifier is able to grow and evolve during the operation process is presented the evolutionary property of the classifier is made possible by modeling the pattern vectors in multiple hyper ellipsoidal subclass distributions learning of the classifier takes place at the subclass levels only this property allows the classifier to retain its previously learned patterns while accepting and learning new pattern classes the classifier is suitable to operate in dynamical environments where continuous updating of the pattern class distributions is needed

maximum likelihood training of probabilistic neural networks a maximum likelihood method is presented for training probabilistic neural networks pnn s using a gaussian kernel or parzen window the proposed training algorithm enables general nonlinear discrimination and is a generalization of fisher s method for linear discrimination important features of maximum likelihood training for pnn s are 1 it economizes the well known parzen window estimator while preserving feedforward nn architecture 2 it utilizes class pooling to generalize classes represented by small training sets 3 it gives smooth discriminant boundaries that often are piece wise flat for statistical robustness 4 it is very fast computationally compared to backpropagation and 5 it is numerically stable the effectiveness of the proposed maximum likelihood training algorithm is assessed using nonparametric statistical methods to define tolerance intervals on pnn classification performance

an evolving construction scheme for fuzzy systems this paper proposes an evolving construction scheme for fuzzy systems ecsfs ecsfs begins with a simple fuzzy system and evolves its structure by adding more fuzzy terms and rules to achieve a better accuracy in a greedy way an interesting feature of ecsfs is that it is able to automatically locate mathematically meaningful points such as the extremum and inflexion points of the approximated function one by one and then adds fuzzy terms based on these points fuzzy systems with such extreme points like their fuzzy terms are more efficient than other fuzzy systems by using the same number of fuzzy rules as a result ecsfs often achieves a better accuracy for fuzzy system identification compared with the previous methods when using the same number of fuzzy rules a number of simulation results are given to illustrate the advantages of the proposed scheme

symmetric composition algebras abstract a construction of all the okubo algebras over fields of characteristic 3 is provided and the complete classification of the composition algebras with associative norm over fields is finished

symmetric triality relations and structurable algebras in this paper some properties of algebras satisfying local symmetric triality relations have been studied including both generalized symmetric composition algebras and the conjugate algebras of any structurable algebras we also discuss a general method of constructing lie algebras from such a system which can permit a construction of the magic square

efficient fuzzy partition of pattern space for classification problems abstract this paper proposes an efficient fuzzy partition method of a pattern space for classification problems the proposed method is based on the sequential subdivision of fuzzy subspaces and the generated fuzzy subspaces have different sizes in the proposed method first an n dimensional pattern space is divided into 2 n fuzzy subspaces with the same size next one of the fuzzy subspaces is selected and subdivided into 2 n fuzzy subspaces this procedure is iterated until a stopping condition is satisfied some criteria for selecting a fuzzy subspace to be subdivided are proposed and compared with each other by computer simulations the proposed method is also compared with other fuzzy classification methods

four fuzzy supervised classification methods for discriminating classes of non convex shape our work deals with modelling and optimising industrial processes such as metal cutting with high speed machining in this field we have chosen to use fuzzy supervised classification methods in order to design a diagnosis system or a process monitoring module the problem we currently meet concerns the shape of the classes we generally obtain these shapes are often non convex and non separable by a hyperplane for these reasons we focus on fuzzy supervised classification methods in order to discriminate these classes the choice of a method is not obvious and we perform a comparative study the two classical methods tested were the fuzzy k nearest neighbours method and a method based on distributed fuzzy rules furthermore we propose two adaptations of the fuzzy pattern matching algorithm called fuzzy pattern matching with exponential function and fuzzy pattern matching multidensity after some refresher on supervised classification the four tested methods are detailed and compared according to the following criteria quality of the discrimination computation time and ability to decide the response of each classifier is illustrated by membership level curves and the quality of diagnosis is studied by the introduction of membership and ambiguity rejects

construction of class regions by a randomized algorithm a randomized subclass method a randomized algorithm is proposed for solving the problem of finding hyper rectangles sufficiently approximating the true region in each class this method yields a suboptimal solution but is more efficient than previous methods the performance is analysed based on a criterion of pac probably approximately correct learning experimental results show that the proposed method can solve large problems which were not able to be solved previously

a new method for extracting and representing object contours in real images this paper introduces a new operator for the calculation of the brightness gradient derived from the compass gradient and a new methodology based on a fuzzy algorithm for extraction of the contour points of objects in a real image a bidimensional geometrical representation of the contours thus extracted is then given in the form of arcs and segments in order to exploit this simplified description as an index for a search in a database of 3 d primitives the procedure described gives good results even in the presence of juxtaposed surfaces of the same nature and color or with contours which do not contrast very well

multiple subclass pattern recognition a maximin correlation approach this paper addresses a correlation based nearest neighbor pattern recognition problem where each class is given as a collection of subclass templates the recognition is performed in two stages in the first stage the class is determined templates for this stage are created using the subclass templates assignment into subclasses occurs in the second stage this two stage approach may be used to accelerate template matching in particular the second stage may be omitted when only the class needs to be determined the authors present a method for optimal aggregation of subclass templates into class templates for each class the new template is optimal in that it maximizes the worst case i e minimum correlation with its subclass templates an algorithm which solves this maximin optimization problem is presented and its correctness is proved in addition test results are provided indicating that the algorithm s execution time is polynomial in the number of subclass templates the authors show tight bounds on the maximin correlation the bounds are functions only of the number of original subclass templates and the minimum element in their correlation matrix the algorithm is demonstrated on a multifont optical character recognition problem

lie algebras with s4 action and structurable algebras abstract the normal symmetric triality algebras sta s and the normal lie related triple algebras lrta s have been recently introduced by the second author in connection with the principle of triality it turns out that the unital normal lrta s are precisely the structurable algebras extensively studied by allison it will be shown that the normal sta s respectively lrta s are the algebras that coordinatize those lie algebras whose automorphism group contains a copy of the alternating respectively symmetric group of degree 4

a primogenitary linked quad tree approach for solution storage and retrieval in heuristic binary optimization abstract a data structure called the primogenitary linked quad tree plqt is used to store and retrieve solutions in heuristic solution procedures for binary optimization problems two ways are proposed to use integer vectors to represent solutions represented by binary vectors one way is to encode binary vectors into integer vectors in a much lower dimension and the other is to use the sorted indices of binary variables with values equal to 0 or equal to 1 the integer vectors are used as composite keys to store and retrieve solutions in the plqt an algorithm processing trial solutions for insertion into or retrieval from the plqt is developed examples are provided to demonstrate the way the algorithm works another algorithm traversing the plqt is also developed computational results show that the plqt approach takes only a very tiny portion of the cpu time taken by a linear list approach for the same purpose for any reasonable application the cpu time taken by the plqt managing trial solutions is negligible as compared to that taken by a heuristic procedure for any reasonably hard to solve binary optimization problem as shown in a tabu search heuristic procedure for the capacitated facility location problem compared to the hashing approach the plqt approach takes the same or less amount of cpu time but much less memory space while completely eliminating collision

local triality and some related algebras abstract eight dimensional symmetric composition algebras give very nice formulae for triality and local triality these latter formulae will be extended to any algebra in a suitable variety the simple algebras in this variety will be shown to be precisely the symmetric composition algebras over fields while the prime algebras are central orders in the simple ones

a fuzzy neural network algorithm for multigroup classification we propose a multigroup classification algorithm based on a hybrid fuzzy neural net framework a key feature of the approach is the adaptation of membership functions to new data in this way learning is reflected in the shape of the membership functions by defining separate membership functions for each fuzzy output class we allow dynamic adjustment of the functions during training the algorithm is successfully tested with real economic data the results suggest economically meaningful interpretations