alternative c means clustering algorithms abstract in this paper we propose a new metric to replace the euclidean norm in c means clustering procedures on the basis of the robust statistic and the influence function we claim that the proposed new metric is more robust than the euclidean norm we then create two new clustering methods called the alternative hard c means ahcm and alternative fuzzy c means afcm clustering algorithms these alternative types of c means clustering have more robustness than c means clustering numerical results show that ahcm has better performance than hcm and afcm is better than fcm we recommend afcm for use in cluster analysis recently this afcm algorithm has successfully been used in segmenting the magnetic resonance image of ophthalmology to differentiate the abnormal tissues from the normal tissues

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

shortest path and maximum flow problems in networks with additive losses and gains we introduce networks with additive losses and gains on the arcs if a positive flow of x units enters an arc a then x g a units exit arcs may increase or consume flow i e they are gainy or lossy such networks have various applications e g in financial analysis transportation and data communication problems in such networks are generally intractable in particular the shortest path problem is np hard however there is a pseudo polynomial time algorithm for the problem with nonnegative costs and gains the maximum flow problem is strongly np hard even in networks with integral capacities and with unit gain or with loss two on the arcs and is hard to approximate however it is solvable in polynomial time in unit loss networks using the edmonds karp algorithm our np hardness results contrast efficient polynomial time solutions of path and flow problems in standard and in so called generalized networks with multiplicative losses and gains

a polynomial combinatorial algorithm for generalized minimum cost flow we propose the first combinatorial solution to the generalized minimum cost flow problem flow with losses and gains despite a rich history dating back to kantorovich and dantzig until now the only known way to solve the problem in polynomial time was via general purpose linear programming techniques polynomial combinatorial algorithms were previously known only for the version of our problem without costs we design the first such algorithms for the version with costs our algorithms also find provably good solutions faster than optimal ones providing the first strongly polynomial approximation schemes for the problem our techniques extend to optimize linear programs with two variables per inequality polynomial combinatorial algorithms were previously developed for testing the feasibility of such linear programs we propose the first such methods for the optimization version

a polynomial dual simplex algorithm for the generalized circulation problem this paper presents a polynomial time dual simplex algorithm for the generalized circulation problem an efficient implementation of this algorithm is given that has a worst case running time of o m2 m nlogn logb where n is the number of nodes m is the number of arcs and b is the largest integer used to represent the rational gain factors and integral capacities in the network this running time is as fast as the running time of any combinatorial algorithm that has been proposed thus far for solving the generalized circulation problem

bagging for path based clustering a resampling scheme for clustering with similarity to bootstrap aggregation bagging is presented bagging is used to improve the quality of path based clustering a data clustering method that can extract elongated structures from data in a noise robust way the results of an agglomerative optimization method are influenced by small fluctuations of the input data to increase the reliability of clustering solutions a stochastic resampling method is developed to infer consensus clusters a related reliability measure allows us to estimate the number of clusters based on the stability of an optimized cluster solution under resampling the quality of path based clustering with resampling is evaluated on a large image data set of human segmentations

combinatorial algorithms for the generalized circulation problem we consider a generalization of the maximum flow problem in which the amounts of flow entering and leaving an arc are linearly related more precisely if x e units of flow enter an arc e x e e units arrive at the other end for instance nodes of the graph can correspond to different currencies with the multipliers being the exchange rates we require conservation of flow at every node except a given source node the goal is to maximize the amount of flow excess at the source this problem is a special case of linear programming and therefore can be solved in polynomial time in this paper we present the first polynomial time combinatorial algorithms for this problem the algorithms are simple and intuitive

a selection model for optimal fuzzy clustering algorithm and number of clusters based on competitive comprehensive fuzzy evaluation fuzzy c means fcm and its variants suffer from two problems local minima and cluster validity which have a direct impact on the formation of final clustering there are two strategies optimization and center initialization strategies that address the problem of local minima this paper proposes a center initialization approach based on a minimum spanning tree to keep fcm from local minima with regard to cluster validity various strategies have been proposed on the basis of the fuzzy cluster validity index this paper proposes a selection model that combines multiple pairs of a fuzzy clustering algorithm and cluster validity index to identify the number of clusters and simultaneously selects the optimal fuzzy clustering for a dataset the promising performance of the proposed center initialization method and selection model is demonstrated by experiments on real datasets

negative cycle detection algorithms we study the problem of finding a negative length cycle in a network an algorithm for the negative cycle problem combines a shortest path algorithm and a cycle detection strategy we survey cycle detection strategies study various combinations of shortest path algorithms and cycle detection strategies and find the best combinations one of out discoveries is that a cycle detection strategy of tarjan greatly improves computational performance of a classical shortest path algorithm making it competitive with the fastest known algorithms on a wide range of problems as a part of out study we develop problem families for testing negative cycle algorithms

frbc a fuzzy rule based clustering algorithm fuzzy clustering is superior to crisp clustering when the boundaries among the clusters are vague and ambiguous however the main limitation of both fuzzy and crisp clustering algorithms is their sensitivity to the number of potential clusters and or their initial positions moreover the comprehensibility of obtained clusters is not expertized whereupon in data mining applications the discovered knowledge is not understandable for human users to overcome these restrictions a novel fuzzy rule based clustering algorithm frbc is proposed in this paper like fuzzy rule based classifiers the frbc employs a supervised classification approach to do the unsupervised cluster analysis it tries to automatically explore the potential clusters in the data patterns and identify them with some interpretable fuzzy rules simultaneous classification of data patterns with these fuzzy rules can reveal the actual boundaries of the clusters to illustrate the capability of frbc to explore the clusters in data the experimental results on some benchmark datasets are obtained and compared with other fuzzy clustering algorithms the clusters specified by fuzzy rules are human understandable with acceptable accuracy

reducing the time complexity of the fuzzy c means algorithm in this paper we present an efficient implementation of the fuzzy c means clustering algorithm the original algorithm alternates between estimating centers of the clusters and the fuzzy membership of the data points the size of the membership matrix is on the order of the original data set a prohibitive size if this technique is to be applied to very large data sets with many clusters our implementation eliminates the storage of this data structure by combining the two updates into a single update of the cluster centers this change significantly affects the asymptotic runtime as the new algorithm is linear with respect to the number of clusters while the original is quadratic elimination of the membership matrix also reduces the overhead associated with repeatedly accessing a large data structure empirical evidence is presented to quantify the savings achieved by this new method

a simple statistics based nearest neighbor cluster detection algorithm we propose a new method for autonomously finding clusters in spatial data the proposed method belongs to the so called nearest neighbor approaches for finding clusters it is a repetitive technique which produces changing averages and deviations of nearest neighbor distance parameters and results in a final set of clusters the proposed technique is capable of eliminating background noise outliers and detection of clusters with different densities in a given data set using a wide variety of data sets we demonstrate that the proposed cluster seeking algorithm performs at least as well as various other currently popular algorithms and in several cases surpasses them in performance highlightsa new clustering algorithm based on simple statistics and lattice metrics is given mathematical rationale is explained in detail and theorem proofs are provided performance classification of the ssnn algorithm is illustrated with 2d datasets jain s benchmark dataset is used to show the ssnn cluster finding capability high dimensional image patterns are included as additional clustering examples

robust path based spectral clustering spectral clustering and path based clustering are two recently developed clustering approaches that have delivered impressive results in a number of challenging clustering tasks however they are not robust enough against noise and outliers in the data in this paper based on m estimation from robust statistics we develop a robust path based spectral clustering method by defining a robust path based similarity measure for spectral clustering under both unsupervised and semi supervised settings our proposed method is significantly more robust than spectral clustering and path based clustering we have performed experiments based on both synthetic and real world data comparing our method with some other methods in particular color images from the berkeley segmentation data set and benchmark are used in the image segmentation experiments experimental results show that our method consistently outperforms other methods due to its higher robustness

on unapproximable versions of np complete problems we prove that all of karp s 21 original np complete problems have a version that is hard to approximate these versions are obtained from the original problems by adding essentially the same simple constraint we further show that these problems are absurdly hard to approximate in fact no polynomial time algorithm can even approximate log k of the magnitude of these problems to within any constant factor where logk denotes the logarithm iterated k times unless np is recognized by slightly superpolynomial randomized machines we use the same technique to improve the constant epsilon such that max clique is hard to approximate to within a factor of n epsilon finally we show that it is even harder to approximate two counting problems counting the number of satisfying assignments to a monotone 2sat formula and computing the permanent of 1 0 1 matrices

quantum behaved discrete multi objective particle swarm optimization for complex network clustering abstract complex network research has attracted lots of attention in both academic community and various application fields complex network clustering as one of the key issues in complex network explores the internal organization of the nodes in a complex network the discrete particle swarm optimization strategy has been successfully proposed for network clustering while the existing method works with weak robust in this paper we model the task of complex network clustering as a multi objective optimization problem and solve the problem with the quantum mechanism based particle swarm optimization algorithm which is a parallel algorithm to our knowledge this is the first attempt to apply the quantum mechanism based discrete particle swarm optimization algorithm into network clustering in addition the non dominant sorting selection operation is employed for individual replacement consequently a quantum behaved discrete multi objective particle swarm optimization algorithm is proposed for complex network clustering the experimental results demonstrate that the proposed algorithm performs effectively and achieves competitive performance with the state of the art approaches on the extension of girvan and newman benchmarks and real world networks especially on large scale networks

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

polynomial time highest gain augmenting path algorithms for the generalized circulation problem this paper presents two new combinatorial algorithms for the generalized circulation problem after an initial step in which all flow generating cycles are canceled and excesses are created both algorithms bring these excesses to the sink via highest gain augmenting paths scaling is applied to the fixed amount of flow that the algorithms attempt to send to the sink and both node and arc excesses are used the algorithms have worst case complexities of om2m n log n log b where n is the number of nodes m is the number of arcs and b is the largest integer used to represent the gain factors and capacities in the network this bound is better than the previous best bound for a combinatorial algorithm for the generalized circulation problem and if m on4 3 e it is better than the previous best bound for any algorithm for this problem

a computationally efficient and interference tolerant nonparametric algorithm for lti system identification based on higher order cyclostationarity a new nonparametric algorithm for the identification of linear time invariant systems is proposed the method is based on the cyclic correlations of the input and output signals with a nonlinear transformation of the input signal consequently although it exploits the higher order cyclostationarity properties of the input and output signals its computational complexity is comparable with that of methods based on second order statistics the proposed estimator of the system transfer function is inherently immune to the presence of noise and interference on both input and output signal measurements and turns out to be asymptotically unbiased and consistent moreover bias and variance of the estimate exhibit a rate of convergence to zero equal to that of estimates based on second order statistics finally simulation results show that the proposed algorithm significantly outperforms in terms of both bias and variance of the estimates several nonparametric identification algorithms previously presented in the literature

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

optimality test for generalized fcm and its application to parameter selection in cluster analysis the fuzzy c means fcm clustering algorithm is the best known and most widely used method it was proven to converge to either a local minimum or saddle points by bezdek et al wei and mendel produced efficient optimality tests for fcm fixed points recently a weighting exponent selection for fcm was proposed by yu et al inspired by these results we unify several alternative fcm algorithms into one model called the generalized fuzzy c means gfcm this gfcm model presents a wide variation of fcm algorithms and can easily lead to new and interesting clustering algorithms moreover we construct a general optimality test for gfcm fixed points this is applied to theoretically choose the parameters in the gfcm model the experimental results demonstrate the precision of the theoretical analysis