discrete time lq optimal control problems for infinite markov jump parameter systems optimal control problems for discrete time linear systems subject to markovian jumps in the parameters are considered for the case in which the markov chain takes values in a countably infinite set two situations are considered the noiseless case and the case in which an additive noise is appended to the model the solution for these problems relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution to the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd which turn out to be equivalent to the spectral radius of certain infinite dimensional linear operators in a banach space being less than one for the long run average cost ss and sd guarantee existence and uniqueness of a stationary measure and consequently existence of an optimal stationary control policy furthermore an extension of a lyapunov equation result is derived for the countably infinite markov state space case

partial information state based optimization of partially observable markov decision processes and the separation principle we propose a partial information state based approach to the optimization of the long run average performance in a partially observable markov decision process pomdp in this approach the information history is summarized at least partially by a or a few statistic s not necessary sufficient called a partial information state and actions depend on the partial information state rather than system states we first propose the single policy based comparison principle under which we derive an hjb type of optimality equation and policy iteration for the optimal policy in the partial information state based policy space we then introduce the q sufficient statistics and show that if the partial information state is q sufficient then the optimal policy in the partial information state based policy space is optimal in the space of all feasible information state based policies we show that with some further conditions the well known separation principle holds the results are obtained by applying the direct comparison based approach initially developed for discrete event dynamic systems

two integrals and some modified versions critical remarks the aim of this paper is to discuss different constructions of integrals sections 3 and 4 based on decomposable measures section 1 according to the classification of the continuous t conorms in essentially two types namely v and archimedean t conorms there exist mainly two types of integrals namely the constructions of sugeno section 3 and of weber section 4 further constructions corresponding to the archimedean case result to be special cases or not well defined section 4 in all cases a crucial property is some restricted distribution law for the pair with an appropriate operation section 2 some applications shall illustrate the use of the two integrals section 5

technical communique a unified approach to markov decision problems and performance sensitivity analysis we propose a simple approach that provides a unified formulation for the performance sensitivity analysis of markov chains and markov decision problems with both infinite horizon average cost and discounted performance criteria

spectral embedded clustering a framework for in sample and out of sample spectral clustering spectral clustering sc methods have been successfully applied to many real world applications the success of these sc methods is largely based on the manifold assumption namely that two nearby data points in the high density region of a low dimensional data manifold have the same cluster label however such an assumption might not always hold on high dimensional data when the data do not exhibit a clear low dimensional manifold structure e g high dimensional and sparse data the clustering performance of sc will be degraded and become even worse than k means clustering in this paper motivated by the observation that the true cluster assignment matrix for high dimensional data can be always embedded in a linear space spanned by the data we propose the spectral embedded clustering sec framework in which a linearity regularization is explicitly added into the objective function of sc methods more importantly the proposed sec framework can naturally deal with out of sample data we also present a new laplacian matrix constructed from a local regression of each pattern and incorporate it into our sec framework to capture both local and global discriminative information for clustering comprehensive experiments on eight real world high dimensional datasets demonstrate the effectiveness and advantages of our sec framework over existing sc methods and k means based clustering methods our sec framework significantly outperforms sc using the nystrom algorithm on unseen data

learning representative exemplars using one class gaussian process regression abstract an exemplar is an observation that represents a group of similar observations exemplars from data are examined to divide entire heterogeneous data into several homogeneous subgroups wherein each subgroup is represented by an exemplar with its inherent sparsity an exemplar based learning model provides a parsimonious model to represent or cluster large scale data a novel exemplar learning method using one class gaussian process gp regression is proposed in this study the proposed method constructs data distribution support from one class gp regression using automatic relevance determination prior and heterogeneous gp noise exemplars that correspond to the basis vectors of the constructed support function are then automatically located during the training process the proposed method is applied to various data sets to examine its operability characteristics of data representation and cluster analysis the exemplars of some real data generated by the proposed method are also reported

data clustering using a model granular magnet we present a new approach to clustering based on the physical properties of an inhomogeneous ferromagnet no assumption is made regarding the underlying distribution of the data we assign a potts spin to each data point and introduce an interaction between neighboring points whose strength is a decreasing function of the distance between the neighbors this magnetic system exhibits three phases at very low temperatures it is completely ordered all spins are aligned at very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered whereas different clusters remain uncorrelated this intermediate phase is identified by a jump in the order parameters the spin spin correlation function is used to partition the spins and the corresponding data points into clusters we demonstrate on three synthetic and three real data sets how the method works detailed comparison to the performance of other techniques clearly indicates the relative success of our method

mandatory leaf node prediction in hierarchical multilabel classification in hierarchical classification the output labels reside on a tree or directed acyclic graph dag structured hierarchy on testing the prediction paths of a given test example may be required to end at leaf nodes of the label hierarchy this is called mandatory leaf node prediction mlnp and is particularly useful when the leaf nodes have much stronger semantic meaning than the internal nodes however while there have been a lot of mlnp methods in hierarchical multiclass classification performing mlnp in hierarchical multilabel classification is difficult in this paper we propose novel mlnp algorithms that consider the global label hierarchy structure we show that the joint posterior probability over all the node labels can be efficiently maximized by dynamic programming for label trees or greedy algorithm for label dags in addition both algorithms can be further extended for the minimization of the expected symmetric loss experiments are performed on real world mlnp data sets with label trees and label dags the proposed method consistently outperforms other hierarchical and flat multilabel classification methods

unsupervised learning by minimal entropy encoding following basic principles of information theoretic learning in this paper we propose a novel approach to data clustering referred to as minimal entropy encoding mee which is based on a set of functions features projecting each input onto a minimum entropy configuration code inspired by traditional parsimony principles we seek solutions in reproducing kernel hilbert spaces and then we prove that the encoding functions are expressed in terms of kernel expansion in order to avoid trivial solutions the developed features must be as different as possible by means of a soft constraint on the empirical estimation of the entropy associated with the encoding functions this leads to an unconstrained optimization problem that can be efficiently solved by conjugate gradient we also investigate an optimization strategy based on concave convex algorithms the relationships with maximum margin clustering are studied showing that mee overcomes some of its critical issues such as the lack of a multiclass extension and the need to face problems with a large number of constraints a massive evaluation on several benchmarks of the proposed approach shows improvements over state of the art techniques both in terms of accuracy and computational complexity

a novel clustering method based on hybrid k nearest neighbor graph abstract most of the existing clustering methods have difficulty in processing complex nonlinear data sets to remedy this deficiency in this paper a novel data model termed hybrid k nearest neighbor hknn graph which combines the advantages of mutual k nearest neighbor graph and k nearest neighbor graph is proposed to represent the nonlinear data sets moreover a clustering method based on the hknn graph chknn is proposed the chknn first generates several tight and small subclusters then merges these subclusters by exploiting the connectivity among them in order to select the optimal parameters for chknn we further propose an internal validity index termed k nearest neighbor index knni which can also be used to evaluate the validity of nonlinear clustering results by varying a control parameter experimental results on synthetic and real world data sets as well as that on the video clustering have demonstrated the significant improvement on performance over existing nonlinear clustering methods and internal validity indices

mercer kernel based clustering in feature space the article presents a method for both the unsupervised partitioning of a sample of data and the estimation of the possible number of inherent clusters which generate the data this work exploits the notion that performing a nonlinear data transformation into some high dimensional feature space increases the probability of the linear separability of the patterns within the transformed space and therefore simplifies the associated data structure it is shown that the eigenvectors of a kernel matrix which defines the implicit mapping provides a means to estimate the number of clusters inherent within the data and a computationally simple iterative procedure is presented for the subsequent feature space partitioning of the data

level dependent sugeno integral in this paper a new concept of level dependent sugeno integral is introduced and it is used to represent comonotone maxitive aggregation functions acting on a complete scale k the relationship between the level dependent sugeno integral and some other types of fuzzy integrals is shown and properties of the level dependent sugeno integral are discussed several examples show that the level dependent sugeno integral can have different aggregation attitudes for low input values than for high input values and thus overcome problems that arise while using the sugeno integral

a survey of kernel and spectral methods for clustering clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines the focus of this paper is the partitioning clustering problem with a special interest in two recent approaches kernel and spectral methods the aim of this paper is to present a survey of kernel and spectral clustering methods two approaches able to produce nonlinear separating hypersurfaces between clusters the presented kernel clustering methods are the kernel version of many classical clustering algorithms e g k means som and neural gas spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized an explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation besides fuzzy kernel clustering methods are presented as extensions of kernel k means clustering algorithm

support vector clustering we present a novel clustering method using the approach of support vector machines data points are mapped by means of a gaussian kernel to a high dimensional feature space where we search for the minimal enclosing sphere this sphere when mapped back to data space can separate into several components each enclosing a separate cluster of points we present a simple algorithm for identifying these clusters the width of the gaussian kernel controls the scale at which the data is probed while the soft margin constant helps coping with outliers and overlapping clusters the structure of a dataset is explored by varying the two parameters maintaining a minimal number of support vectors to assure smooth cluster boundaries we demonstrate the performance of our algorithm on several datasets

incorporating the loss function into discriminative clustering of structured outputs clustering using the hilbert schmidt independence criterion cluhsic is a recent clustering algorithm that maximizes the dependence between cluster labels and data observations according to the hilbert schmidt independence criterion hsic it is unique in that structure information on the cluster outputs can be easily utilized in the clustering process however while the choice of the loss function is known to be very important in supervised learning with structured outputs we will show in this paper that cluhsic is implicitly using the often inappropriate zero one loss we propose an extension called cluhsical which stands for clustering using hsic and loss which explicitly considers both the output dependency and loss function its optimization problem has the same form as cluhsic except that its partition matrix is constructed in a different manner experimental results on a number of datasets with structured outputs show that cluhsical often outperforms cluhsic in terms of both structured loss and clustering accuracy

choquet integral and fuzzy measures on locally compact space the concept of outer regular fuzzy measures is proposed and it is shown that a functional of certain type on the cone of positive continuous functions with compact supports is represented as a choquet integral with respect to a outer regular fuzzy measure it is also shown that the choquet integral of positive continuous functions with compact supports is represented as a lebesgue integral with the same integrands this representation is a generalization of certain previous results of others which are useful for computation of the upper and lower expected value

finknn a fuzzy interval number k nearest neighbor classifier for prediction of sugar production from populations of samples this work introduces finknn a k nearest neighbor classifier operating over the metric lattice of conventional interval supported convex fuzzy sets we show that for problems involving populations of measurements data can be represented by fuzzy interval numbers fins and we present an algorithm for constructing fins from such populations we then present a lattice theoretic metric distance between fins with arbitrary shaped membership functions which forms the basis for finknn s similarity measurements we apply finknn to the task of predicting annual sugar production based on populations of measurements supplied by hellenic sugar industry we show that finknn improves prediction accuracy on this task and discuss the broader scope and potential utility of these techniques

efficient algorithms for exact inference in sequence labeling svms the task of structured output prediction deals with learning general functional dependencies between arbitrary input and output spaces in this context two loss sensitive formulations for maximum margin training have been proposed in the literature which are referred to as margin and slack rescaling respectively the latter is believed to be more accurate and easier to handle nevertheless it is not popular due to the lack of known efficient inference algorithms therefore margin rescaling which requires a similar type of inference as normal structured prediction is the most often used approach focusing on the task of label sequence learning we here define a general framework that can handle a large class of inference problems based on hamming like loss functions and the concept of decomposability for the underlying joint feature map in particular we present an efficient generic algorithm that can handle both rescaling approaches and is guaranteed to find an optimal solution in polynomial time

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

clustering irregular shapes using high order neurons this article introduces a method for clustering irregularly shaped data arrangements using high order neurons complex analytical shapes are modeled by replacing the classic synaptic weight of the neuron by high order tensors in homogeneous coordinates in the first and second order cases this neuron corresponds to a classic neuron and to an ellipsoidalmetric neuron we show how high order shapes can be formulated to follow the maximum correlation activation principle and permit simple local hebbian learning we also demonstrate decomposition of spatial arrangements of data clusters including very close and partially overlapping clusters which are difficult to distinguish using classic neurons superior results are obtained for the iris data

policy iteration based feedback control it is well known that stochastic control systems can be viewed as markov decision processes mdps with continuous state spaces in this paper we propose to apply the policy iteration approach in mdps to the optimal control problem of stochastic systems we first provide an optimality equation based on performance potentials and develop a policy iteration procedure then we apply policy iteration to the jump linear quadratic problem and obtain the coupled riccati equations for their optimal solutions the approach is applicable to linear as well as nonlinear systems and can be implemented on line on real world systems without identifying all the system structure and parameters

an examination of procedures for determining the number of clusters in a data set a monte carlo evaluation of 30 procedures for determining the number of clusters was conducted on artificial data sets which contained either 2 3 4 or 5 distinct nonoverlapping clusters to provide a variety of clustering solutions the data sets were analyzed by four hierarchical clustering methods external criterion measures indicated excellent recovery of the true cluster structure by the methods at the correct hierarchy level thus the clustering present in the data was quite strong the simulation results for the stopping rules revealed a wide range in their ability to determine the correct number of clusters in the data several procedures worked fairly well whereas others performed rather poorly thus the latter group of rules would appear to have little validity particularly for data sets containing distinct clusters applied researchers are urged to select one or more of the better criteria however users are cautioned that the performance of some of the criteria may be data dependent

lebesgue sampling based optimal control problems with time aggregation we formulate the lebesgue sampling based optimal control problem we show that the problem can be solved by the time aggregation approach in markov decision processes mdp theory policy iteration based and reinforcement learning based methods are developed for the optimal policies both analytical solutions and sample path based algorithms are given compared to the periodic sampling scheme the lebesgue sampling scheme improves system performance

smoothly approximated support vector domain description support vector domain description svdd is a well known tool for pattern analysis when only positive examples are reliable the svdd model is often fitted by solving a quadratic programming problem which is time consuming this paper attempts to fit svdd in the primal form directly however the primal objective function of svdd is not differentiable which prevents the well behaved gradient based optimization methods from being applicable as such we propose to approximate the primal objective function of svdd by a differentiable function and a conjugate gradient method is applied to minimize the smoothly approximated objective function extensive experiments on pattern classification were conducted and compared to the quadratic programming based svdd the proposed approach is much more computationally efficient and yields similar classification performance on these problems highlightssmoothly approximates the objective function of support vector domain description gradient based optimization method could be applied to the smoothed model the proposed algorithms have asymptotic training complexity n 2 the algorithm is easy to implement without requiring any optimization package

generalized transformed t conorm integral and multifold integral fuzzy integrals are commonly used as aggregation operators in this paper we present new composite models based on fuzzy integrals with several t conorms these models permit to further increase the computational power of the previous models basic properties of new composite models are studied in particular it is shown that for composite models the only meaningful case is when not all the t conorms are the same

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

an approximation approach for the deviation matrix of continuous time markov processes with application to markov decision theory we present an update formula that allows the expression of the deviation matrix of a continuous time markov process with denumerable state space having generator matrix q through a continuous time markov process with generator matrix q we show that under suitable stability conditions the algorithm converges at a geometric rate by applying the concept to three different examples namely the m m 1 queue with vacations the m g 1 queue and a tandem network we illustrate the broad applicability of our approach for a problem in admission control we apply our approximation algorithm to markov decision theory for computing the optimal control policy numerical examples are presented to highlight the efficiency of the proposed algorithm

an interpretation of fuzzy measures and the choquet integral as an integral with respect to a fuzzy measure abstract in this paper the non additivity of sugeno s fuzzy measures is interpreted in terms of addition and the rationality of the choquet integral is discussed it is pointed out that a fuzzy measure on a set x expresses the interaction between the subsets of x and can be represented by an additive measure it is shown through concrete examples that the choquet integral is reasonable as an integral with respect to a fuzzy measure it is also found that the choquet integral is closely related with the representation of a fuzzy measure

fuzzy t conorm integral with respect to fuzzy measures generalization of sugeno integral and choquet integral abstract this article discusses integrals with respect to sugeno s fuzzy measures sugeno integrals and choquet integrals with respect to general fuzzy measures are generalized in the setting of a t conorm algebraic system first t conorm integrals with respect to decomposable measures based on t conorm algebraic system are defined they are a modification of the weber integral secondly they are extended to fuzzy t conorm integrals with respect to general fuzzy measures the extension is made in the same way as the extension of the lebesgue integral to the choquet integral the class of fuzzy t conorm integrals includes choquet integrals and sugeno integrals properties of the integrals especially their representation are discussed

policy iteration algorithm for singular controlled diffusion processes in this paper the infinite horizon optimal control problems for singular diffusion processes are considered from the viewpoints of markov decision processes and perturbation analysis where the singularity of diffusion means that the covariance matrix of the system noise is allowed to be degenerate a formula of performance difference under two different controls is derived and leads to a comparison theorem by the comparison theorem starting from a control a so called better control can be selected therefore a control policy iteration algorithm is developed by which the performance improves step by step and converges to the optimal one when this applies to the stochastic affine nonlinear regulator and stochastic linear quadratic optimal control problems better control can be constructed in a closed form it is also shown that when the considered stochastic systems degenerate to the deterministic ones the proposed algorithm reduces to the adaptive dynamic programming algorithm j j murray c j

cognitive integrals with its generalized and adapted forms motivated by some cognition styles this study first proposes a new type of preaggregation functions called cognitive integrals with its generalized forms rather than being affected only by selected capacity generalized cognitive integrals consider other two parameters the cognitive strength and the involved semicopula our main focus is on cognitive strength by which the integrals values will be monotonically decreasing with respect to our cognitive strength after some appropriated adaptations we later propose the concept of adapted cognitive integrals with two equivalent forms of itself not only being a type of the preaggregation functions we prove that adapted cognitive integrals are indeed one new type of aggregation functions still equipped with the two new parameters like in cognitive integrals