bayesian approaches to gaussian mixture modeling a bayesian based methodology is presented which automatically penalizes overcomplex models being fitted to unknown data we show that with a gaussian mixture model the approach is able to select an optimal number of components in the model and so partition data sets the performance of the bayesian method is compared to other methods of optimal model selection and found to give good results the methods are tested on synthetic and real data sets

parametric and non parametric unsupervised cluster analysis much work has been published on methods for assessing the probable number of clusters or structures within unknown data sets this paper aims to look in more detail at two methods a broad parametric method based around the assumption of gaussian clusters and the other a non parametric method which utilises methods of scale space filtering to extract robust structures within a data set it is shown that whilst both methods are capable of determining cluster validity for data sets in which clusters tend towards a multivariate gaussian distribution the parametric method inevitably fails for clusters which have a non gaussian structure whilst the scale space method is more robust

multiobject behavior recognition by event driven selective attention method this paper presents a multiobject behaviour recognition approach based on assumption generation and verification i e feasible assumptions about the present behaviors consistent with the input image and behavior models are dynamically generated and verified by finding their supporting evidence in input images this can be realized by an architecture called the selective attention model which consists of a state dependent event detector and an event sequence analyzer the former detects image variation event in a limited image region focusing region which is not affected by occlusions and outliers the latter analyzes sequences of detected events and activates all feasible states representing assumptions about multiobject behaviors we further extend the system by introducing colored token propagation to discriminate different objects in state space and integration of multiviewpoint image sequences to disambiguate the single view recognition results extensive experiments of human behavior recognition in real world environments demonstrate the soundness and robustness of our architecture

boosted multi class semi supervised learning for human action recognition human action recognition is a challenging task due to significant intra class variations occlusion and background clutter most of the existing work use the action models based on statistic learning algorithms for classification to achieve good performance on recognition a large amount of the labeled samples are therefore required to train the sophisticated action models however collecting labeled samples is labor intensive to tackle this problem we propose a boosted multi class semi supervised learning algorithm in which the co em algorithm is adopted to leverage the information from unlabeled data three key issues are addressed in this paper firstly we formulate the action recognition in a multi class semi supervised learning problem to deal with the insufficient labeled data and high computational expense secondly boosted co em is employed for the semi supervised model construction to overcome the high dimensional feature space weighted multiple discriminant analysis wmda is used to project the features into low dimensional subspaces in which the gaussian mixture models gmm are trained and boosting scheme is used to integrate the subspace models thirdly we present the upper bound of the training error in multi class framework which is able to guide the novel classifier construction in theory the proposed solution is proved to minimize this upper error bound experimental results have shown good performance on public datasets

exponential dichotomies almost periodic structurally stable differential systems and an example abstract in this paper we introduce concepts of almost periodic topological in short apt equivalence and almost periodic structural in short aps stability of differential systems and a necessary and sufficient condition for aps stability of differential systems furthermore we discuss the inheritability of the aps stability and density of aps stable differential systems in a certain space of uniformly almost periodic differential systems

riccati differential inequalities and dichotomies for linear systems a general notion of dichotomy for linear differential systems is investigated it is well known that a system x a t x in which the matrix a t is bounded and diagonally dominant by rows or columns has an invariant splitting of its solution space into two subspaces each uniformly asymptotically stable one for increasing time and the other for decreasing time similar results are obtained here where the concept of diagonal dominance is weakened using riccati inequalities

lyapunov type characterization of hyperbolic behavior abstract we give a complete characterization of the uniform hyperbolicity and nonuniform hyperbolicity of a cocycle with values in the space of bounded linear operators acting on a hilbert space in terms of the existence of appropriate quadratic forms our work unifies and extends many results in the literature by considering the general case of not necessarily invertible cocycles acting on a hilbert space over an arbitrary invertible dynamics as a nontrivial application of we study the persistence of hyperbolicity under small linear perturbations

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

view invariant representation and recognition of actions analysis of human perception of motion shows that information for representing the motion is obtained from the dramatic changes in the speed and direction of the trajectory in this paper we present a computational representation of human action to capture these dramatic changes using spatio temporal curvature of 2 d trajectory this representation is compact view invariant and is capable of explaining an action in terms of meaningful action units called dynamic instants and intervals a dynamic instant is an instantaneous entity that occurs for only one frame and represents an important change in the motion characteristics an interval represents the time period between two dynamic instants during which the motion characteristics do not change starting without a model we use this representation for recognition and incremental learning of human actions the proposed method can discover instances of the same action performed by different people from different view points experiments on 47 actions performed by 7 individuals in an environment with no constraints shows the robustness of the proposed method

unsupervised learning of finite mixture models this paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data the adjective unsupervised is justified by two properties of the algorithm 1 it is capable of selecting the number of components and 2 unlike the standard expectation maximization em algorithm it does not require careful initialization the proposed method also avoids another drawback of em for mixture fitting the possibility of convergence toward a singular estimate at the boundary of the parameter space the novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models instead we seamlessly integrate estimation and model selection in a single algorithm our technique can be applied to any type of parametric mixture model for which it is possible to write an em algorithm in this paper we illustrate it with experiments involving gaussian mixtures these experiments testify for the good performance of our approach

assessing a mixture model for clustering with the integrated completed likelihood we propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood for this purpose the observed data are assigned to unknown clusters using a maximum a posteriori operator then the integrated completed likelihood icl is approximated using the bayesian information criterion bic numerical experiments on simulated and real data of the resulting icl criterion show that it performs well both for choosing a mixture model and a relevant number of clusters in particular icl appears to be more robust than bic to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data

singular multicontact structures abstract we describe the automorphisms of a singular multicontact structure that is a generalisation of the martinet distribution such a structure is interpreted as a para cr structure on a hypersurface m of a direct product space r 2 r 2 we introduce the notion of a finite type singularity analogous to cr geometry and along the way we prove extension results for para cr functions and mappings on embedded para cr manifolds into the ambient space

abnormal minimizers this paper constructs the first example of a singular abnormal minimizer for the lagrange problem with linear velocity constraints and quadratic definite lagrangian or equivalently for an optimal control system of linear controls with k controls n states and a running cost function that is quadratic positive definite in the controls in the example k 2 n 3 and the system is completely controllable the example is stable if both the control law and cost are perturbed the singular minimizer persists its importance is due in part to the fact that it is a counterexample to a theorem that has appeared several times in the differential geometry literature there the problem is called the problem of finding minimizing sub riemannian geodesics and it has been claimed that all minimizers are normal pontryagin extremals the mathematical theory of optimal processes wiley interscience new york 1962 if the number of states equals the number of controls then the problem is that of finding riemannian geodesics the main difficulty is proving minimality to do this the length cost of the abnormal is compared with all competing normal extremals a detailed asymptotic analysis of the differential equations governing the normals shows that they are all longer

modeling and classifying human activities from trajectories using a class of space varying parametric motion fields many approaches to trajectory analysis such as clustering or classification use probabilistic generative models thus not requiring trajectory alignment registration switched linear dynamical models e g hmms have been used in this context due to their ability to describe different motion regimes however these models are not suitable for handling space dependent dynamics that are more naturally captured by nonlinear models as is well known these are more difficult to identify in this paper we propose a new way of modeling trajectories based on a mixture of parametric motion vector fields that depend on a small number of parameters switching among these fields follows a probabilistic mechanism characterized by a field of stochastic matrices this approach allows representing a wide variety of trajectories and modeling space dependent behaviors without using global nonlinear dynamical models experimental evaluation is conducted in both synthetic and real scenarios the latter concerning with human trajectory modeling for activity classification a central task in video surveillance

beyond tracking modelling activity and understanding behaviour in this work we present a unified bottom up and top down automatic model selection based approach for modelling complex activities of multiple objects in cluttered scenes an activity of multiple objects is represented based on discrete scene events and their behaviours are modelled by reasoning about the temporal and causal correlations among different events this is significantly different from the majority of the existing techniques that are centred on object tracking followed by trajectory matching in our approach object independent events are detected and classified by unsupervised clustering using expectation maximisation em and classified using automatic model selection based on schwarz s bayesian information criterion bic dynamic probabilistic networks dpns are formulated for modelling the temporal and causal correlations among discrete events for robust and holistic scene level behaviour interpretation in particular we developed a dynamically multi linked hidden markov model dml hmm based on the discovery of salient dynamic interlinks among multiple temporal processes corresponding to multiple event classes a dml hmm is built using bic based factorisation resulting in its topology being intrinsically determined by the underlying causality and temporal order among events extensive experiments are conducted on modelling activities captured in different indoor and outdoor scenes our experimental results demonstrate that the performance of a dml hmm on modelling group activities in a noisy and cluttered scene is superior compared to those of other comparable dynamic probabilistic networks including a multi observation hidden markov model mohmm a parallel hidden markov model pahmm and a coupled hidden markov model chmm

riccati inequality and functional properties of differential operators on the half line abstract given a piecewise continuous function a r l c n and a projection p 1 onto a subspace x 1 of c n we investigate the injectivity surjectivity and more generally the fredholm properties of the ordinary differential operator with boundary condition u a u p 1 u 0 this operator acts from the natural space w a 1 2 u u l 2 a u l 2 into l 2 x 1 a main novelty is that it is not assumed that a is bounded or that u a u 0 has any dichotomy except to discuss the impact of the results on this special case we show that all the functional properties of interest including the characterization of the fredholm index can be related to the existence of a selfadjoint solution h of the riccati differential inequality h a a h h a a h 2 special attention is given to the simple case when h a a satisfies this inequality when h is known all the other hypotheses and criteria are easily verifiable in most concrete problems

spectral clustering with eigenvector selection the task of discovering natural groupings of input patterns or clustering is an important aspect of machine learning and pattern analysis in this paper we study the widely used spectral clustering algorithm which clusters data using eigenvectors of a similarity affinity matrix derived from a data set in particular we aim to solve two critical issues in spectral clustering 1 how to automatically determine the number of clusters and 2 how to perform effective clustering given noisy and sparse data an analysis of the characteristics of eigenspace is carried out which shows that a not every eigenvectors of a data affinity matrix is informative and relevant for clustering b eigenvector selection is critical because using uninformative irrelevant eigenvectors could lead to poor clustering results and c the corresponding eigenvalues cannot be used for relevant eigenvector selection given a realistic data set motivated by the analysis a novel spectral clustering algorithm is proposed which differs from previous approaches in that only informative relevant eigenvectors are employed for determining the number of clusters and performing clustering the key element of the proposed algorithm is a simple but effective relevance learning method which measures the relevance of an eigenvector according to how well it can separate the data set into different clusters our algorithm was evaluated using synthetic data sets as well as real world data sets generated from two challenging visual learning problems the results demonstrated that our algorithm is able to estimate the cluster number correctly and reveal natural grouping of the input data patterns even given sparse and noisy data

a dynamical approach to the sard problem in carnot groups abstract we introduce a dynamical systems approach for the study of the sard problem in sub riemannian carnot groups we show that singular curves can be obtained by concatenating trajectories of suitable dynamical systems as an application we positively answer the sard problem in some classes of carnot groups

dichotomies in terms of lyapunov functions for linear difference equations abstract necessary and sufficient conditions that a linear difference equation have an exponential dichotomy on the set of the integer numbers are given in terms of lyapunov functions

the sard conjecture on martinet surfaces given a totally nonholonomic distribution of rank two on a three dimensional manifold we investigate the size of the set of points that can be reached by singular horizontal paths starting from a same point in this setting the sard conjecture states that that set should be a subset of the so called martinet surface of 2 dimensional hausdorff measure zero we prove that the conjecture holds in the case where the martinet surface is smooth moreover we address the case of singular real analytic martinet surfaces and show that the result holds true under an assumption of non transversality of the distribution on the singular set of the martinet surface our methods rely on the control of the divergence of vector fields generating the trace of the distribution on the martinet surface and some techniques of resolution of singularities