approximation algorithms for the test cover problem in the test cover problem a set of m items is given together with a collection of subsets called tests a smallest subcollection of tests is to be selected such that for each pair of items there is a test in the selection that contains exactly one of the two items it is known that the problem is np hard and that the greedy algorithm has a performance ratio o log m we observe that unless p np no polynomial time algorithm can do essentially better for the case that each test contains at most k items we give an o log k approximation algorithm we pay special attention to the case that each test contains at most two items a strong relation with a problem of packing paths in a graph is established which implies that even this special case is np hard we prove apx hardness of both problems derive performance guarantees for greedy algorithms and discuss the performance of a series of local improvement heuristics

an efficient algorithm for computing bisimulation equivalence we propose an efficient algorithmic solution to the problem of determining a bisimulation relation on a finite structure working both on the explicit and on the implicit symbolic representation as far as the explicit case is concerned starting from a set theoretic point of view we propose an algorithm that optimizes the solution to the relational coarsest partition problem given by paige and tarjan siam j comput 16 6 1987 973 its use in model checking packages is also discussed and tested for well structured graphs our algorithm reaches a linear worst case behaviour the proposed algorithm is then re elaborated to produce a symbolic version

unsupervised segmentation of markov random field modeled textured images using selectionist relaxation among the existing texture segmentation methods those relying on markov random fields have retained substantial interest and have proved to be very efficient in supervised mode the use of markov random fields in unsupervised mode is however hampered by the parameter estimation problem the recent solutions proposed to overcome this difficulty rely on assumptions about the shapes of the textured regions or about the number of textures in the input image that may not be satisfied in practice in this paper an evolutionary approach selectionist relaxation is proposed as a solution to the problem of segmenting markov random field modeled textures in unsupervised mode in selectionist relaxation the computation is distributed among a population of units that iteratively evolves according to simple and local evolutionary rules a unit is an association between a label and a texture parameter vector the units whose likelihood is high are allowed to spread over the image and to replace the units that receive lower support from the data consequently some labels are growing while others are eliminated starting with an initial random population this evolutionary process eventually results in a stable labelization of the image which is taken as the segmentation in this work the generalized ising model is used to represent textured data because of the awkward nature of the partition function in this model a high temperature approximation is introduced to allow the evaluation of unit likelihoods experimental results on images containing various synthetic and natural textures are reported

pattern identification in dynamical systems via symbolic time series analysis this paper presents symbolic time series analysis stsa of multi dimensional measurement data for pattern identification in dynamical systems the proposed methodology is built upon concepts derived from information theory and automata theory the objective is not merely to classify the time series patterns but also to identify the variations therein to achieve this goal a symbol alphabet is constructed from raw data through partitioning of the data space the maximum entropy method of partitioning is extended to multi dimensional space the resulting symbol sequences generated from time series data are used to model the dynamical information as finite state automata and the patterns are represented by the stationary state probability distributions a novel procedure for determining the structure of the finite state automata based on entropy rate is introduced the diversity among the observed patterns is quantified by a suitable measure the efficacy of the stsa technique for pattern identification is demonstrated via laboratory experimentation on nonlinear systems

warped k means an algorithm to cluster sequentially distributed data many devices generate large amounts of data that follow some sort of sequentiality e g motion sensors e pens eye trackers etc and often these data need to be compressed for classification storage and or retrieval tasks traditional clustering algorithms can be used for this purpose but unfortunately they do not cope with the sequential information implicitly embedded in such data thus we revisit the well known k means algorithm and provide a general method to properly cluster sequentially distributed data we present warped k means wkm a multi purpose partitional clustering procedure that minimizes the sum of squared error criterion while imposing a hard sequentiality constraint in the classification step we illustrate the properties of wkm in three applications one being the segmentation and classification of human activity wkm outperformed five state of the art clustering techniques to simplify data trajectories achieving a recognition accuracy of near 97 which is an improvement of around 66 over their peers moreover such an improvement came with a reduction in the computational cost of more than one order of magnitude

ccs expressions finite state processes and three problems of equivalence abstract we examine the computational complexity of testing finite state processes for equivalence in milner s calculus of communicating systems ccs the equivalence problems in ccs are presented as refinements of the familiar problem of testing whether two nondeterministic finite automata nfa are equivalent i e accept the same language three notions of equivalence proposed for ccs are investigated namely observational equivalence strong observational equivalence and failure equivalence we show that observational equivalence can be tested in polynomial time as defined in ccs observational equivalence is the limit of a sequence of successively finer equivalence relations k where 1 is nondeterministic finite automaton equivalence we prove that for each fixed k deciding k is pspace complete we show that strong observational equivalence can be decided in polynomial time by reducing it to generalized partitioning a new combinatorial problem of independent interest finally we demonstrate that testing for failure equivalence is pspace complete even for a very restricted type of process

a cellular coevolutionary algorithm for image segmentation clustering is inherently a difficult problem both with respect to the definition of adequate models as well as to the optimization of the models we present a model for the cluster problem that does not need knowledge about the number of clusters a priori this property is among others useful in the image segmentation domain which we especially address further we propose a cellular coevolutionary algorithm for the optimization of the model within this scheme multiple agents are placed in a regular two dimensional 2 d grid representing the image which imposes neighboring relations on them the agents cooperatively consider pixel migration from one agent to the other in order to improve the homogeneity of the ensemble of the image regions they represent if the union of the regions of neighboring agents is homogeneous then the agents form alliances on the other hand if an agent discovers a deviant subject it isolates the subject in the experiments we show the effectiveness of the proposed method and compare it to other segmentation algorithms the efficiency can easily be improved by exploiting the intrinsic parallelism of the proposed method

a maximum variance cluster algorithm we present a partitional cluster algorithm that minimizes the sum of squared error criterion while imposing a hard constraint on the cluster variance conceptually hypothesized clusters act in parallel and cooperate with their neighboring clusters in order to minimize the criterion and to satisfy the variance constraint in order to enable the demarcation of the cluster neighborhood without crucial parameters we introduce the notion of foreign cluster samples finally we demonstrate a new method for cluster tendency assessment based on varying the variance constraint parameter

wavelet based feature extraction using probabilistic finite state automata for pattern classification real time data driven pattern classification requires extraction of relevant features from the observed time series as low dimensional and yet information rich representations of the underlying dynamics these low dimensional features facilitate in situ decision making in diverse applications such as computer vision structural health monitoring and robotics wavelet transforms of time series have been widely used for feature extraction owing to their time frequency localization properties in this regard this paper presents a symbolic dynamics based method to model surface images generated by wavelet coefficients in the scale shift space these symbolic dynamics based models e g probabilistic finite state automata pfsa capture the relevant information embedded in the sensor data from the associated perron frobenius operators i e the state transition probability matrices the proposed method of pattern classification has been experimentally validated on laboratory apparatuses for two different applications i early detection of evolving damage in polycrystalline alloy structures and ii classification of mobile robots and their motion profiles

approximately counting hamilton paths and cycles in dense graphs we describe fully polynomial randomized approximation schemes for the problems of determining the number of hamilton paths and cycles in an n vertex graph with minimum degree frac 1 2 a n for any fixed a 0 we show that the exact counting problems are p complete we also describe fully polynomial randomized approximation schemes for counting paths and cycles of all sizes in such graphs

a simulated annealing algorithm for the clustering problem abstract in this paper we discuss the solution of the clustering problem usually solved by the k means algorithm the problem is known to have local minimum solutions which are usually what the k means algorithm obtains the simulated annealing approach for solving optimization problems is described and is proposed for solving the clustering problem the parameters of the algorithm are discussed in detail and it is shown that the algorithm converges to a global solution of the clustering problem we also find optimal parameters values for a specific class of data sets and give recommendations on the choice of parameters for general data sets finally advantages and disadvantages of the approach are presented

experiments in projection and clustering by simulated annealing simulated annealing is a stochastic relaxation algorithm which has been used successfully to optimize functions of many variables this paper analyzes the simulated annealing algorithm when applied to the minimization of functions from two common problems encountered in exploratory pattern analysis projection and clustering the projection is a nonlinear mapping of patterns in high dimension to two dimensions the simulated annealing mapping is compared to gradient descent minimization of the same objective function as well as eigenvector projection the simulated annealing clustering is compared to a k means algorithm empirical results show that simulated annealing can produce results as good as those obtained by conventional methods but are impractical for small data sets because of the high computational cost simulated annealing does in the case of the mapping problem yield a better optimization and better retained structure for large data sets containing tight gaussian clusters

identifying and locating dominating codes np completeness results for directed graphs let g v a be a directed asymmetric graph and c a subset of vertices and let b sub r sup v denote the set of all vertices x such that there exists a directed path from x to v with at most r arcs if the sets b sub r sup v spl cap c v spl isin v respectively v spl isin v spl bsol c are all nonempty and different we call c an r identifying code respectively an r locating dominating code of g in other words if c is an r identifying code then one can uniquely identify a vertex v spl isin v only by knowing which codewords belong to b sub r sup v and if c is r locating dominating the same is true for the vertices v in v spl bsol c we prove that given a directed asymmetric graph g and an integer k the decision problem of the existence of an r identifying code or of an r locating dominating code of size at most k in g is np complete for any r spl ges 1 and remains so even when restricted to strongly connected directed asymmetric bipartite graphs or to directed asymmetric bipartite graphs without directed cycles

set graphs ii complexity of set graph recognition and similar problems a graph g is said to be a set graph if it admits an acyclic orientation that is also extensional in the sense that the out neighborhoods of its vertices are pairwise distinct equivalently a set graph is the underlying graph of the digraph representation of a hereditarily finite set in this paper we continue the study of set graphs and related topics focusing on computational complexity aspects we prove that set graph recognition is np complete even when the input is restricted to bipartite graphs with exactly two leaves the problem remains np complete if in addition we require that the extensional acyclic orientation be also slim that is that the digraph obtained by removing any arc from it is not extensional our approach in fact allows us to also show that the counting variants of the above problems are p complete and prove similar complexity results for problems related to a generalization of extensional acyclic digraphs the so called hyper extensional digraphs which were proposed by aczel to describe hypersets our proofs are based on reductions from variants of the hamiltonian path problem we also consider a variant of the well known notion of a separating code in a digraph the so called open out separating code and show that it is np complete to determine whether an input extensional acyclic digraph contains an open out separating code of given size

faster and more robust point symmetry based k means algorithm based on the recently published point symmetry distance psd measure this paper presents a novel psd measure namely symmetry similarity level ssl operator for k means algorithm our proposed modified point symmetry based k means mpsk algorithm is more robust than the previous psk algorithm by su and chou not only the proposed mpsk algorithm is suitable for the symmetrical intra clusters as the psk algorithm does the proposed mpsk algorithm is also suitable for the symmetrical inter clusters in addition two speedup strategies are presented to reduce the time required in the proposed mpsk algorithm experimental results demonstrate the significant execution time improvement and the extension to the symmetrical inter clusters of the proposed mpsk algorithm when compared to the previous psk algorithm

towards parameter independent data clustering and image segmentation while there are a large amount of clustering algorithms proposed in the literature the clustering results of existing algorithms usually depend on user specified parameters heavily and it is usually difficult to determine the optimal parameters with the pairwise data similarity matrix as the input dominant sets clustering has been shown to be an effective data clustering and image segmentation approach partly due to its ability to find out the underlying data structure and determine the number of clusters automatically however we find that the original dominant sets algorithm is sensitive to the similarity measures used in building the similarity matrix this means that parameter tuning is required to generate satisfactory clustering results and dominant sets clustering results are also parameter dependent in order to remove the dependence on the user specified parameter we study how the similarity measures influence the dominant sets clustering results as a result we propose to transform similarity matrices by histogram equalization before clustering while this transformation is shown to remove the sensitiveness to similarity measures effectively it also results in over segmentation therefore in the next step we present a cluster extension method to overcome the over segmentation effect and generate more reasonable clustering results we test the enhanced clustering algorithm in both data clustering and image segmentation experiments and comparisons with the state of the art algorithms validate the effectiveness of our algorithm highlightswe study how similarity measures influence the dominant sets clustering results we use histogram equalization to remove the dependence on similarity parameters we present a density based cluster extension method to overcome over segmentation experiments validate the effectiveness of our algorithm

three partition refinement algorithms we present improved partition refinement algorithms for three problems lexicographic sorting relational coarsest partition and double lexical ordering our double lexical ordering algorithm uses a new efficient method for unmerging two sorted sets

theory and applications of cellular automata in cryptography this paper deals with the theory and application of cellular automata ca for a class of block ciphers and stream ciphers based on ca state transitions certain fundamental transformations are defined which are block ciphering functions of the proposed enciphering scheme these fundamental transformations are found to generate the simple alternating group of even permutations which in turn is a subgroup of the permutation group these functions are implemented with a class of programmable cellular automata pca built around rules 51 153 and 195 further high quality pseudorandom pattern generators built around rule 90 and 150 programmable cellular automata with a rule selector i e combining function has been proposed as running key generators in stream ciphers both the schemes provide better security against different types of attacks with a simple regular modular and cascadable structure of ca hardware implementation of such schemes idealy suit vlsi implementation

on the combination of self organized systems to generate pseudo random numbers cellular automata ca is a self organizing structure with complex behavior which can be used to generating pseudo random numbers pure ca has a simple structure and has no ability to produce long sequences of random numbers but in order to resolve this problem a programmable controllable ca pcca using actuating factor or combination of different self organizing criticality phenomena can be used the purpose of the aforementioned methods is the use of the ca speed while preventing the automata self organizing factor for specific use in generating random numbers in this paper a pcca by using sandpile model is proposed the sandpile model is a complex system that operates at a critical state between chaos and order this state is known as self organized criticality soc and is characterized by displaying invariant scale behavior in the precise case of the sandpile model by randomly and continuously dropping sand grains on top of a two dimensional grid lattice a power law relationship between the frequency and size of sand avalanches is observed the avalanche behavior and the pure ca behavior are combined in a novel method which can be used as the pseudo random number generator prng experimental results show that this generator is able to reach a random behavior from a pseudo chaotic one by combining two self organized systems in addition to independency of the initial state it has been also indicated that the generated numbers are independent and its probability distribution is likely to be uniform accordingly some tests of prngs such as entropy chi square diehard and several basic statistical tests have been performed and all of them have been successfully passed

on a new class of codes for identifying vertices in graphs we investigate a new class of codes for the optimal covering of vertices in an undirected graph g such that any vertex in g can be uniquely identified by examining the vertices that cover it we define a ball of radius t centered on a vertex spl upsi to be the set of vertices in g that are at distance at most t from spl upsi the vertex spl upsi is then said to cover itself and every other vertex in the ball with center spl upsi our formal problem statement is as follows given an undirected graph g and an integer t spl ges 1 find a minimal set c of vertices such that every vertex in g belongs to a unique set of balls of radius t centered at the vertices in c the set of vertices thus obtained constitutes a code for vertex identification we first develop topology independent bounds on the size of c we then develop methods for constructing c for several specific topologies such as binary cubes nonbinary cubes and trees we also describe the identification of sets of vertices using covering codes that uniquely identify single vertices we develop methods for constructing optimal topologies that yield identifying codes with a minimum number of codewords finally we describe an application of the theory developed in this paper to fault diagnosis of multiprocessor systems

permutation and sampling with maximum length ca or pseudorandom number generation abstract in this paper we study the effect of dynamic permutation and sampling on the randomness quality of sequences generated by cellular automata ca dynamic permutation and sampling have not been explored in previous ca work and a suitable implementation is shown using a two ca model three different schemes that incorporate these two operations are suggested weighted permutation vector sampling with controlled multiplexing weighted permutation vector sampling with irregular decimation and permutation programmed ca sampling the experiment results show that the resulting sequences have varying degrees of improvement in diehard results and linear complexity compared to the ca

a clustering ensemble the aim of clustering ensemble is to combine multiple base partitions into a robust stable and accurate partition one of the key problems of clustering ensemble is how to exploit the cluster structure information in each base partition evidence accumulation is an effective framework which can convert the base partitions into a co association matrix this matrix describes the frequency of a pair of points partitioned into the same cluster but ignores some hidden information in the base partitions in this paper we reveal some of those information by refining the co association matrix from data point and base cluster level from the data point level as pairs of points in the same base cluster may have varied similarities their contributions to the co association matrix can be different from the cluster level since the base clusters may have diversified qualities the contribution of a base cluster as a whole can also be different from those of others after being refined the co association matrix is transformed into a path based similarity matrix so that more global information of the cluster structure is incorporated into the matrix finally spectral clustering is applied to the matrix to generate the final clustering result experimental results on 8 synthetic and 8 real data sets demonstrate that the clustering ensemble based on the refined co association matrix outperforms some state of the art clustering ensemble schemes highlightsa two level refined co association matrix for cluster ensemble is proposed the refined co association matrix is transformed by path based measure a theoretical background of the refinement is given the proposed method outperforms some state of the art ensemble methods

minimizing the size of an identifying or locating dominating code in a graph is np hard let g v e be an undirected graph and c a subset of vertices if the sets br v c v v respectively v v c are all nonempty and different where br v denotes the set of all points within distance r from v we call c an r identifying code respectively an r locating dominating code we prove that given a graph g and an integer k the decision problem of the existence of an r identifying code or of an r locating dominating code of size at most k in g is np complete for any r

invariant trajectory classification of dynamical systems with a case study on ecg an invariant pattern recognition framework for classification of phase space trajectories of nonlinear dynamical systems is presented using statistical shape theory known external influences can be discriminated from true changes of the system the external effects are modeled as a transformation group acting on the phase space and variation of the trajectories not explained by the transformations is accounted for using principal component analysis the approach suggested is highly adaptable to a wide range of situations and individual differences the methodology presented is applied to detect abnormalities in electrocardiograms results based on measured data indicate that the model developed is resistant to the effects of respiration and body position changes which are abundant in ambulatory conditions and cause significant morphological artifacts in the signal the results also show that the detection of an artificially induced acute myocardial infarction is achieved with high performance due to its low computational complexity the method developed can be implemented in real time the method developed also adapts to morphological changes caused by various heart conditions

minimum spanning tree based split and merge a hierarchical clustering method most clustering algorithms become ineffective when provided with unsuitable parameters or applied to datasets which are composed of clusters with diverse shapes sizes and densities to alleviate these deficiencies we propose a novel split and merge hierarchical clustering method in which a minimum spanning tree mst and an mst based graph are employed to guide the splitting and merging process in the splitting process vertices with high degrees in the mst based graph are selected as initial prototypes and k means is used to split the dataset in the merging process subgroup pairs are filtered and only neighboring pairs are considered for merge the proposed method requires no parameter except the number of clusters experimental results demonstrate its effectiveness both on synthetic and real datasets

on the generation of high quality random numbers by two dimensional cellular automata finding good random number generators rngs is a hard problem that is of crucial import in several fields ranging from large scale statistical physics simulations to hardware self test in this paper we employ the cellular programming evolutionary algorithm to automatically generate two dimensional cellular automata ca rngs applying an extensive suite of randomness tests to the evolved cas we demonstrate that they rapidly produce high quality random number sequences moreover based on observations of the evolved cas we are able to handcraft even better rngs which not only outperform previously demonstrated high quality rngs but can be potentially tailored to satisfy given hardware constraints

density peak clustering based on relative density relationship abstract the density peak clustering algorithm treats local density peaks as cluster centers and groups non center data points by assuming that one data point and its nearest higher density neighbor are in the same cluster while this algorithm is shown to be promising in some applications its clustering results are found to be sensitive to density kernels and large density differences across clusters tend to result in wrong cluster centers in this paper we attribute these problems to the inconsistency between the assumption and implementation adopted in this algorithm while the assumption is based totally on relative density relationship this algorithm adopts absolute density as one criterion to identify cluster centers this observation prompts us to present a cluster center identification criterion based only on relative density relationship specifically we define the concept of subordinate to describe the relative density relationship and use the number of subordinates as a criterion to identify cluster centers our approach makes use of only relative density relationship and is less influenced by density kernels and density differences across clusters in addition we discuss the problems of two existing density kernels and present an average distance based kernel in data clustering experiments we validate the new criterion and density kernel respectively and then test the whole algorithm and compare with some other clustering algorithms

fuzzy clustering of fuzzy data based on robust loss functions and ordered weighted averaging abstract in many real cases the data are not expressed in term of single values but are imprecise in all these cases standard clustering methods for single valued data are unable to properly take into account the imprecise nature of the data in this paper by considering the partitioning around medoids pam approach in a fuzzy framework we propose a fuzzy clustering method for imprecise data formalized in a fuzzy manner in particular in order to neutralize the negative effects of possible outlier fuzzy data in the clustering process we proposed a robust fuzzy c medoids clustering method for fuzzy data based on the combination of huber s m estimators and yager s owa ordered weighted averaging operators the proposed method is able to smooth the influence of anomalous data by means of a suitable parameter the so called typicality parameter capable to tune the influence of the outliers the performance of the proposed method has been shown by means of a simulation study composed of experiments on i simple two dimensional dataset ii benchmark datasets and iii the fuzzy art outliers dataset the comparison made with the robust clustering methods known from the literature indicates the competitiveness of the introduced method to others an application of the suggested method to a real dataset is also provided and the results of the method has been compared with other clustering methods suggested in the literature in the application the comparative assessment has shown the informational gain in term of additional information of the proposed method vs the other robust methods