visual object recognition using probabilistic kernel subspace similarity probabilistic subspace similarity based face matching is an efficient face recognition algorithm proposed by moghaddam et al it makes one basic assumption the intra class face image set spans a linear space however there are yet no rational geometric interpretations of the similarity under that assumption this paper investigates two subjects first we present one interpretation of the intra class linear subspace assumption from the perspective of manifold analysis and thus discover the geometric nature of the similarity second we also note that the linear subspace assumption does not hold in some cases and generalize it to nonlinear cases by introducing kernel tricks the proposed model is named probabilistic kernel subspace similarity pkss experiments on synthetic data and real visual object recognition tasks show that pkss can achieve promising performance and outperform many other current popular object recognition algorithms

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

a probabilistic fuzzy logic system for modeling and control in this paper a probabilistic fuzzy logic system pfls is proposed for the modeling and control problems similar to the ordinary fuzzy logic system fls the pfls consists of the fuzzification inference engine and defuzzification operation to process the fuzzy information different to the fls it uses the probabilistic modeling method to improve the stochastic modeling capability by using a three dimensional membership function mf the pfls is able to handle the effect of random noise and stochastic uncertainties existing in the process a unique defuzzification method is proposed to simplify the complex operation finally the proposed pfls is applied to a function approximation problem and a robotic system it shows a better performance than an ordinary fls in stochastic circumstance

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

extended fuzzy logic sets and systems the concepts of sets and approximate reasoning within extended fuzzy logic fle provide a systematic procedure for transforming unprecisiated knowledge into a nonlinear mapping over what we define here as f sets an f set differs from a fuzzy set in that it is associated with the restriction of validity in addition to that of possibility therefore by f set we can simultaneously deal with two different types of uncertainties one that is related to ill known objects represented by incomplete information information with its one or more aspects being imprecise vague partial nonspecific undetermined and another that is related to truth values considering gradualness here we define new concepts of vartheta cuts and alpha vartheta cuts introduce the f extension principle and consider arithmetic computations within fle we then address other aspects of the proposed fle system such as fuzzification and validification operations in input processing stage set conversion and defuzzification in output processing stage and inferencing in fact in this paper we intend to develop fle theoretically and practically from the stands of sets and systems to extend the concept of approximate reasoning as a consequence of this development we assert that considering the validity degree of methods and information can lead to more reasonable and trustworthy results through capturing more uncertainty

linear neighborhood propagation and its applications in this paper a novel graph based transductive classification approach called linear neighborhood propagation is proposed the basic idea is to predict the label of a data point according to its neighbors in a linear way this method can be cast into a second order intrinsic gaussian markov random field framework its result corresponds to a solution to an approximate inhomogeneous biharmonic equation with dirichlet boundary conditions different from existing approaches our approach provides a novel graph structure construction method by introducing multiple wise edges instead of pairwise edges and presents an effective scheme to estimate the weights for such multiple wise edges to the best of our knowledge these two contributions are novel for semi supervised classification the experimental results on image segmentation and transductive classification demonstrate the effectiveness and efficiency of the proposed approach

on the concept of possibility probability consistency both probability and possibility may be seen as information about an experiment it is conceivable to have at some time these two forms of information about a same experiment and then the question of the relation between them arises at once in this paper some aspects of the concept of possibility probability consistency are studied the consistency is considered as a fuzzy property relative to the coherence between possibilistic and probabilistic information we analyse several measures of the degree of consistency and introduce an axiomatic to characterize them

analysis of factorial survival experiments several new methodological issues that arise within two way factorial designs for survival experiments are discussed within the framework of asymptotic theory for the proportional hazards model with two binary treatment covariates these issues include the proper formulation of null hypotheses and alternatives the choice among log rank and adjusted or stratified log rank statistics the asymptotic correlation between test statistics for the separate main effects the asymptotic power under the various possible methods of analysis of tests to detect main effects and interactions the comparison of power to detect main effects within a 2 x 2 factorial design with power in a three group trial where no patients are randomized simultaneously to both treatments and the problems of analysis arising when accrual or exposure to one of the treatments is terminated early for ethical reasons

an efficient configuration for probabilistic fuzzy logic system a novel inference configuration is proposed to improve the computational efficiency and information loss in the probabilistic fuzzy inference process the probabilistic inference and the fuzzy inference are unified in one operation based on the continuous form of the probabilistic fuzzy set besides the faster inference operation it is able to produce fuzzy outputs in a complete probabilistic distribution that in turn will provide information about the approximation bound the computational analyses of six different fuzzy systems demonstrate the inference efficiency of the proposed method its effectiveness can be further demonstrated on the application to modeling of an industrial curing process the robust modeling performance discloses its potential in process modeling under complex environment

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

label information guided graph construction for semi supervised learning in the literature most existing graph based semi supervised learning methods only use the label information of observed samples in the label propagation stage while ignoring such valuable information when learning the graph in this paper we argue that it is beneficial to consider the label information in the graph learning stage specifically by enforcing the weight of edges between labeled samples of different classes to be zero we explicitly incorporate the label information into the state of the art graph learning methods such as the low rank representation lrr and propose a novel semi supervised graph learning method called semi supervised low rank representation this results in a convex optimization problem with linear constraints which can be solved by the linearized alternating direction method though we take lrr as an example our proposed method is in fact very general and can be applied to any self representation graph learning methods experiment results on both synthetic and real data sets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data and therefore is more effective for semi supervised learning tasks

rule acquisition and adjustment based on set valued mapping based on the theory of set valued mapping a new approach on how to acquire fuzzy rule sets from the corresponding relations between the group of data on the two universes of discourse is presented moreover some theories and methods on how to adjust fuzzy rule sets with the change of the group of data are established finally a recurrence theorem of the group of data is also given

random walks for image segmentation a novel method is proposed for performing multilabel interactive image segmentation given a small number of pixels with user defined or predefined labels one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels by assigning each pixel to the label for which the greatest probability is calculated a high quality image segmentation may be obtained theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits this algorithm is formulated in discrete space i e on a graph using combinatorial analogues of standard operators and principles from continuous potential theory allowing it to be applied in arbitrary dimension on arbitrary graphs

semantic preserving distance metric learning and applications how do we accurately browse a large set of images or efficiently annotate the images from an image library image clustering methods are invaluable tools for applications such as content based image retrieval and image annotation to perform these tasks it is critical to have proper features to describe the visual and semantic content of images and to define an accurate distance metric to measure the dissimilarity between any two images however existing methods which adopt the features of color histograms edge direction histograms and shape context lack the ability to describe semantic content to solve this problem we propose a new approach that utilizes user provided pairwise constraints to describe the semantic relationship between two images a semantic preserving distance metric learning sp dml algorithm is developed to explore the complementary characteristics of the visual features and pairwise constraints in a unified feature space in this space the learned distance metric can be used to measure the dissimilarity between two images specifically the manifold structure adopted in sp dml is revealed by the image s visual features to integrate semantic contents in distance metric learning sp dml utilizes pairwise constraints to build semantic patches and align these patches to obtain the optimal distance metric for the new feature space experimental results in image clustering demonstrate that the performance of sp dml is appealing

power and sample size for dose finding studies with survival endpoints under model uncertainty multiple comparison procedures combined with modeling techniques mcp mod bretz et al 2005 is an efficient and robust statistical methodology for the model based design and analysis of dose finding studies with an unknown dose response model with this approach multiple comparison methods are used to identify statistically significant contrasts corresponding to a set of candidate dose response models and the best model is then used to estimate the target dose power and sample size calculations for this methodology require knowledge of the covariance matrix for the estimators of the placebo adjusted mean responses among the dose groups in this article we consider survival endpoints and derive an analytic form of the covariance matrix for the estimators of the log hazard ratios as a function of the total number of events in the study we then use this closed form expression of the covariance matrix to derive the power and sample size formulas we discuss practical considerations in the application of these formulas in addition we provide an illustration with a motivating example on chronic obstructive pulmonary disease finally we demonstrate through simulation studies that the proposed formulas are accurate enough for practical use

simultaneous inference on treatment effects in survival studies with factorial designs a clinical trial with a 2 2 factorial design involves randomization of subjects to treatment a or a and within each group further randomization to treatment b or b under this design one can assess the effects of treatments a and b on a clinical endpoint using all patients one may additionally compare treatment a treatment b or combination therapy ab to a b with multiple comparisons however it may be desirable to control the overall type i error especially for regulatory purposes because the subjects overlap in the comparisons the test statistics are generally correlated by accounting for the correlations one can achieve higher statistical power compared to the conventional bonferroni correction herein we derive the correlation between any two stratified or unstratified log rank statistics for a 2 2 factorial design with a survival time endpoint such that the overall type i error for multiple treatment comparisons can be properly controlled in addition we allow for adjustment of prognostic factors in the treatment comparisons and conduct simultaneous inference on the effect sizes we use simulation studies to show that the proposed methods perform well in realistic situations we then provide an application to a recently completed randomized controlled clinical trial on alcohol dependence finally we discuss extensions of our approach to other factorial designs and multiple endpoints

systems control with generalized probabilistic fuzzy reinforcement learning reinforcement learning rl is a valuable learning method when the systems require a selection of control actions whose consequences emerge over long periods for which input output data are not available in most combinations of fuzzy systems and rl the environment is considered to be deterministic in many problems however the consequence of an action may be uncertain or stochastic in nature in this paper we propose a novel rl approach to combine the universal function approximation capability of fuzzy systems with consideration of probability distributions over possible consequences of an action the proposed generalized probabilistic fuzzy rl gpfrl method is a modified version of the actor critic ac learning architecture the learning is enhanced by the introduction of a probability measure into the learning structure where an incremental gradient descent weight updating algorithm provides convergence our results show that the proposed approach is robust under probabilistic uncertainty while also having an enhanced learning speed and good overall performance

the analysis of multiple endpoints in clinical trials treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall type i error rate one option is to select a single primary endpoint for formal statistical inference but this is not always feasible another approach is to apply bonferroni correction i e multiply each p value by the total number of endpoints its conservatism for correlated endpoints is examined for multivariate normal data a third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics quantitative binary and survival endpoints are all considered within this general framework two examples are presented and the relative merits of the proposed strategies are discussed

nonparametric inference in factorial designs with censored data a method is proposed for testing the hypotheses of no main effects and no interaction in factorial designs with several observations per cell the method uses the fact that these hypotheses can be expressed in terms of a vector of contrasts it is based on the observation that nonparametric estimation of these contrasts is no more difficult than estimation of the location difference in the two sample problem to implement the method with censored data a new extension of the hodges lehmann estimator is proposed the estimator is simple to compute and its variance is easily evaluated a simulation study examines the performance of the proposed estimation and testing method in the context of a two by two design and a real data set from a three way layout with heavy censoring is analyzed

semi supervised classification and betweenness computation on large sparse directed graphs this work addresses graph based semi supervised classification and betweenness computation in large sparse networks several millions of nodes the objective of semi supervised classification is to assign a label to unlabeled nodes using the whole topology of the graph and the labeling at our disposal two approaches are developed to avoid explicit computation of pairwise proximity between the nodes of the graph which would be impractical for graphs containing millions of nodes the first approach directly computes for each class the sum of the similarities between the nodes to classify and the labeled nodes of the class as suggested initially in 1 2 along this approach two algorithms exploiting different state of the art kernels on a graph are developed the same strategy can also be used in order to compute a betweenness measure the second approach works on a trellis structure built from biased random walks on the graph extending an idea introduced in 3 these random walks allow to define a biased bounded betweenness for the nodes of interest defined separately for each class all the proposed algorithms have a linear computing time in the number of edges while providing good results and hence are applicable to large sparse networks they are empirically validated on medium size standard data sets and are shown to be competitive with state of the art techniques finally we processed a novel data set which is made available for benchmarking for multi class classification in a large network the u s patents citation network containing 3m nodes of six different classes and 38m edges the three proposed algorithms achieve competitive results around 85 classification rate on this large network they classify the unlabeled nodes within a few minutes on a standard workstation

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

knowledge distance measure in multigranulation spaces of fuzzy equivalence relations abstract hierarchical quotient space structure hqss which is a typical representation of multigranulation spaces serves as the essential description tool of fuzzy equivalence relations however current studies on hqss have three main limitations i the inability to reflect the relationship between any two quotient spaces in an hqss ii classification isomorphism cannot characterize the degree of subdivision that exists in an hqss with changing granularities and iii the difficulty in characterizing the difference between two hqsss that are classification isomorphic in this paper we address these issues from the perspective of knowledge distance first we propose a partition based knowledge distance based on the earth mover s distance emd and we prove that our knowledge distance is equivalent to the binary granule based knowledge distance bgkd but is more intuitive than the bgkd then by studying the hierarchy of hqss we conclude that the granularity difference between any two quotient spaces in an hqss is equal to the knowledge distance between them in the view of knowledge distance the concepts of classification isomorphism and subdivision isomorphism are defined and discussed finally we define the concept of the knowledge difference sequence pair which not only discriminates whether two fuzzy equivalence relations are isomorphic but also characterizes the difference between any two hqsss with respect to them theoretical analysis shows that our work is valuable for advancing the application of the hierarchy granular computing theory

laplacian regularized low rank representation and its applications low rank representation lrr has recently attracted a great deal of attention due to its pleasing efficacy in exploring low dimensional subspace structures embedded in data for a given set of observed data corrupted with sparse errors lrr aims at learning a lowest rank representation of all data jointly lrr has broad applications in pattern recognition computer vision and signal processing in the real world data often reside on low dimensional manifolds embedded in a high dimensional ambient space however the lrr method does not take into account the non linear geometric structures within data thus the locality and similarity information among data may be missing in the learning process to improve lrr in this regard we propose a general laplacian regularized low rank representation framework for data representation where a hypergraph laplacian regularizer can be readily introduced into i e a non negative sparse hyper laplacian regularized lrr model nshlrr by taking advantage of the graph regularizer our proposed method not only can represent the global low dimensional structures but also capture the intrinsic non linear geometric information in data the extensive experimental results on image clustering semi supervised image classification and dimensionality reduction tasks demonstrate the effectiveness of the proposed method

regularized tree partitioning and its application to unsupervised image segmentation in this paper we propose regularized tree partitioning approaches we study normalized cut ncut and average cut acut criteria over a tree forming two approaches 1 normalized tree partitioning ntp and 2 average tree partitioning atp we give the properties that result in an efficient algorithm for ntp and atp in addition we present the relations between the solutions of ntp and atp over the maximum weight spanning tree of a graph and ncut and acut over this graph to demonstrate the effectiveness of the proposed approaches we show its application to image segmentation over the berkeley image segmentation data set and present qualitative and quantitative comparisons with state of the art methods

what does a probabilistic interpretation of fuzzy sets mean in this paper we propose a statistics model to better understand the probabilistic interpretation for fuzzy sets the model shows the relationship between the two kinds of statistics the set valued statistics for fuzzy sets and the conventional probability statistics for membership functions our model overcomes the shortcomings in previous approaches the results of this paper provide a theoretical interpretation to zadeh s insight that possibility relates to soft constraints restricting the values of language variables

fuzzy sets and statistical data abstract specific features of probability and possibility theories are discussed with emphasis on semantical aspects instead of putting forward the acknowledged usefulness of possibility theory for the non statistical modelling of subjective categories we try to figure out how statistical data and possibility theory could be matched as a result procedures for constructing weak possibilistic substitutes of probability measures and for processing imprecise statistical data are outlined they provide new insights on relationship between fuzzy sets and probability theories

concepts of probabilistic sets abstract in the field of pattern recognition or decision making theory the important subjects are as follows 1 ambiguity of property of objects 2 variety of character of objects 3 subjectivity of observers 4 evolution of knowledge of observers i e learning considering these points the concept of probabilistic set is proposed it is based on both probability theory and fuzzy concepts a probabilistic set on a total space is defined by a point wise measurable function from a parameter space which is a probability space to a characteristic space which is a measurable space it is shown that the family of all probabilistic sets constitutes a complete pseudo boolean algebra moment analysis is possible by using a probability measure of the parameter space other useful concepts are also mentioned such as probabilistic mappings and expected cardinal numbers

deformed graph laplacian for semisupervised learning graph laplacian has been widely exploited in traditional graph based semisupervised learning ssl algorithms to regulate the labels of examples that vary smoothly on the graph although it achieves a promising performance in both transductive and inductive learning it is not effective for handling ambiguous examples shown in fig 1 this paper introduces deformed graph laplacian dgl and presents label prediction via dgl lpdgl for ssl the local smoothness term used in lpdgl which regularizes examples and their neighbors locally is able to improve classification accuracy by properly dealing with ambiguous examples theoretical studies reveal that lpdgl obtains the globally optimal decision function and the free parameters are easy to tune the generalization bound is derived based on the robustness analysis experiments on a variety of real world data sets demonstrate that lpdgl achieves top level performance on both transductive and inductive settings by comparing it with popular ssl algorithms such as harmonic functions anchorgraph regularization linear neighborhood propagation laplacian regularized least square and laplacian support vector machine

nonparametric methods for factorial designs with censored data abstract nonparametric hypotheses of no main effects no simple effects and no interaction effects are considered in the context of factorial designs with censored observations to test these hypotheses the asymptotic distribution of quadratic forms of rank statistics is derived using the methodology of martingales for counting processes the weights used reduce to the usual logistic scores with uncensored data but are different from the weights commonly used for testing the equality of k samples the formulation of all results includes tied observations approximations to the small sample distributions of the test statistics are given the performance of the tests is examined via simulation studies the procedures are illustrated on a real dataset

structure constrained low rank representation benefiting from its effectiveness in subspace segmentation low rank representation lrr and its variations have many applications in computer vision and pattern recognition such as motion segmentation image segmentation saliency detection and semisupervised learning it is known that the standard lrr can only work well under the assumption that all the subspaces are independent however this assumption cannot be guaranteed in real world problems this paper addresses this problem and provides an extension of lrr named structure constrained lrr sc lrr to analyze the structure of multiple disjoint subspaces which is more general for real vision data we prove that the relationship of multiple linear disjoint subspaces can be exactly revealed by sc lrr with a predefined weight matrix as a nontrivial byproduct we also illustrate that sc lrr can be applied for semisupervised learning the experimental results on different types of vision problems demonstrate the effectiveness of our proposed method

learning from normalized local and global discriminative information for semi supervised regression and dimensionality reduction semi supervised dimensionality reduction is one of the important topics in pattern recognition and machine learning during the past decade laplacian regularized least square laprls and semi supervised discriminant analysis sda are the two widely used semi supervised dimensionality reduction methods in this paper we show that sda and laprls can be unified into a constrained manifold regularized least square framework the manifold term however cannot fully utilize the underlying discriminative information we thus introduce a new and effective semi supervised dimensionality reduction method called learning from local and global information llgdi to solve the problem the proposed llgdi method adopts a set of local classification functions to preserve both local geometrical and discriminative information of dataset it also adopts a global classification function to preserve the global discriminative information and an uncorrelated constraint to calculate the projection matrix for simultaneously solving regression and dimensionality reduction problem as a result the llgdi method is able to preserve local discriminative manifold information as well as the global discriminative information theoretical analysis and extensive simulations presented in the paper show the effectiveness of the llgdi algorithm the results also demonstrate llgdi can achieve superior performance compared with other existing methods

a nonparametric classification method based on k associated graphs graph is a powerful representation formalism that has been widely employed in machine learning and data mining in this paper we present a graph based classification method consisting of the construction of a special graph referred to as k associated graph which is capable of representing similarity relationships among data cases and proportion of classes overlapping the main properties of the k associated graphs as well as the classification algorithm are described experimental evaluation indicates that the proposed technique captures topological structure of the training data and leads to good results on classification task particularly for noisy data in comparison to other well known classification techniques the proposed approach shows the following interesting features 1 a new measure called purity is introduced not only to characterize the degree of overlap among classes in the input data set but also to construct the k associated optimal graph for classification 2 nonlinear classification with automatic local adaptation according to the input data contrasting to k nearest neighbor classifier which uses a fixed k the proposed algorithm is able to automatically consider different values of k in order to best fit the corresponding overlap of classes in different data subspaces revealing both the local and global structure of input data 3 the proposed classification algorithm is nonparametric implicating high efficiency and no need for model selection in practical applications