influence in principal components analysis summary in linear regression the theoretical influence function and the various sample versions of it have an established place as diagnostic tools these same functions are developed here to provide methods for the detection of influential observations in principal components analysis the perturbation theory of real symmetric matrices unifies this development some interesting points of contrast with the regression case are noted and explained theoretically

renyi divergence and kullback leibler divergence renyi divergence is related to renyi entropy much like kullback leibler divergence is related to shannon s entropy and comes up in many settings it was introduced by renyi as a measure of information that satisfies almost the same axioms as kullback leibler divergence and depends on a parameter that is called its order in particular the renyi divergence of order 1 equals the kullback leibler divergence we review and extend the most important properties of renyi divergence and kullback leibler divergence including convexity continuity limits of sigma algebras and the relation of the special order 0 to the gaussian dichotomy and contiguity we also show how to generalize the pythagorean inequality to orders different from 1 and we extend the known equivalence between channel capacity and minimax redundancy to continuous channel inputs for all orders and present several other minimax results

fluctuation theorems for quantum master equations a quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation i e a quantum master equation qme quantum trajectories and their associated entropy heat and work appear naturally by transforming the qme to a time dependent liouville space basis that diagonalizes the instantaneous reduced density matrix of the subsystem a quantum integral fluctuation theorem a steady state fluctuation theorem and the jarzynski relation are derived in a similar way as for classical stochastic dynamics

a new method of feature fusion and its application in image recognition a new method of feature extraction based on feature fusion is proposed in this paper according to the idea of canonical correlation analysis cca at first the theory framework of cca used in pattern recognition and its reasonable description are discussed the process can be explained as follows extract two groups of feature vectors with the same pattern establish the correlation criterion function between the two groups of feature vectors and extract their canonical correlation features to form effective discriminant vector for recognition then the problem of canonical projection vectors is solved when two total scatter matrixes are singular such that it fits for the case of high dimensional space and small sample size in this sense the applicable range of cca is extended at last the inherent essence of this method used in recognition is analyzed further in theory experimental results on concordia university cenparmi database of handwritten arabic numerals and yale face database show that recognition rate is far higher than that of the algorithm adopting single feature or the existing fusion algorithm

the influence function of principal component analysis by self organizing rule this article is concerned with a neural network approach to principal component analysis pca an algorithm for pca by the self organizing rule has been proposed and its robustness observed through the simulation study by xu and yuille 1995 in this article the robustness of the algorithm against outliers is investigated by using the theory of influence function the influence function of the principal component vector is given in an explicit form through this expression the method is shown to be robust against any directions orthogonal to the principal component vector in addition a statistic generated by the self organizing rule is proposed to assess the influence of data in pca

growth rates and critical exponents of classes of binary combinatorial geometries estimation par exces du nombre de points d une geometrie binaire de rang n n 2 ne contenant pas comme mineur m k 5 et f 7 m k 5 et c 10 resp

code enumerators and tutte polynomials it is proved that the set of higher weight enumerators of a linear code over a finite field is equivalent to the tutte polynomial associated to the code an explicit expression for the tutte polynomial is given in terms of the subcode weights generalizations of these results are proved and are applied to codeword m tuples these general results are used to prove a very general macwilliams type identity for linear codes that generalizes most previous extensions of the macwilliams identity in addition a general and very useful matrix framework for manipulating weight and support enumerators of linear codes is presented

local influence analysis of nonlinear structural equation models by regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete data log likelihood function in the em algorithm we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model the basic building blocks of local influence analysis are computed via observations of the latent variables generated by the metropolis hastings algorithm while the diagnostic measures are obtained via the conformal normal curvature seven perturbation schemes including some perturbation schemes on latent vectors are investigated the proposed procedure is illustrated by a simulation study and a real example

assessing local influence for specific restricted likelihood application to factor analysis in restricted statistical models since the first derivatives of the likelihood displacement are often nonzero the commonly adopted formulation for local influence analysis is not appropriate however there are two kinds of model restrictions in which the first derivatives of the likelihood displacement are still zero general formulas for assessing local influence under these restrictions are derived and applied to factor analysis as the usually used restriction in factor analysis satisfies the conditions various influence schemes are introduced and a comparison to the influence function approach is discussed it is also shown that local influence for factor analysis is invariant to the scale of the data and is independent of the rotation of the factor loadings

local influence in principal components analysis summary based on the definition of generalised influence function and generalised cook statistic local influence of small perturbations on the eigenvalues and eigenvectors of a covariance matrix are studied for population and sample versions the results based on the correlation matrix are also derived and some related topics are discussed finally an example is used for illustration bations although this method has been applied to many models beckman nachtsheim cook 1987 lawrance 1988 thomas cook 1990 assessing the local influence for multivariate data is still an unexplored area in this paper a method based on a generalised influence function and generalised cook statistic is introduced to assess the local influence of small perturbations on a statistic of interest and we prove that this method is equivalent to cook s work based on normal curvature in the likelihood framework since local influence on some statistics in multivariate analysis is not easy to study using the likelihood displacement of cook 1986 this method is expected to have wider applications in this paper we employ the generalised cook statistic to assess local influence in principal components analysis in 2 we introduce the definition of the generalised influ ence function and generalised cook statistic in 3 the perturbation theory of eigenvalues and eigenvectors of a real symmetric matrix is studied in 4 the local influence of small perturbations of observations on eigenvalues and the eigenvectors of sample covariance

the standardized influence matrix and its applications abstract in this article we introduce the standardized influence matrix sim of parameter estimators as a conjugate of the sample covariance matrix of standardized influence functions sifs evaluated at the data points we propose principal component analysis for the sim and its complement sim analysis as a diagnostic tool for regression or other statistical inference and provide theoretical insight to the local influence defined by cook we show that sim analysis reveals the multivariate structure of outlying and or influential points specifically sim analysis uncovers hidden structures of influence such as clustering that cannot be identified by the lengths of the standardized influences finally examples in linear regression show that a diagnostic method using sim is more effective if robust parameter estimates are used in calculating the sample sim

discriminative learning and recognition of image set classes using canonical correlations we address the problem of comparing sets of images for object recognition where the sets may represent variations in an object s appearance due to changing camera pose and lighting conditions canonical correlations also known as principal or canonical angles which can be thought of as the angles between two d dimensional subspaces have recently attracted attention for image set matching canonical correlations offer many benefits in accuracy efficiency and robustness compared to the two main classical methods parametric distribution based and nonparametric sample based matching of sets here this is first demonstrated experimentally for reasonably sized data sets using existing methods exploiting canonical correlations motivated by their proven effectiveness a novel discriminative learning method over sets is proposed for set classification specifically inspired by classical linear discriminant analysis lda we develop a linear discriminant function that maximizes the canonical correlations of within class sets and minimizes the canonical correlations of between class sets image sets transformed by the discriminant function are then compared by the canonical correlations classical orthogonal subspace method osm is also investigated for the similar purpose and compared with the proposed method the proposed method is evaluated on various object recognition problems using face image sets with arbitrary motion captured under different illuminations and image sets of 500 general objects taken at different views the method is also applied to object category recognition using eth 80 database the proposed method is shown to outperform the state of the art methods in terms of accuracy and efficiency

excluding the cycle geometries of the kuratowski graphs from binary geometries etude des geometries binaires ne contenant pas comme mineur la geometrie des cycles m k 5 du graphe complet k 5

the second laws of quantum thermodynamics the second law of thermodynamics places constraints on state transformations it applies to systems composed of many particles however we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath is there a second law of thermodynamics in this regime here we find that for processes which are approximately cyclic the second law for microscopic systems takes on a different form compared to the macroscopic scale imposing not just one constraint on state transformations but an entire family of constraints we find a family of free energies which generalize the traditional one and show that they can never increase the ordinary second law relates to one of these with the remainder imposing additional constraints on thermodynamic transitions we find three regimes which determine which family of second laws govern state transitions depending on how cyclic the process is in one regime one can cause an apparent violation of the usual second law through a process of embezzling work from a large system which remains arbitrarily close to its original state these second laws are relevant for small systems and also apply to individual macroscopic systems interacting via long range interactions by making precise the definition of thermal operations the laws of thermodynamics are unified in this framework with the first law defining the class of operations the zeroth law emerging as an equivalence relation between thermal states and the remaining laws being monotonicity of our generalized free energies

generalized channels channels for convex subsets of the state space let k be a convex subset of the state space of a finite dimensional c algebra we study the properties of channels on k which are defined as affine maps from k into the state space of another algebra extending to completely positive maps on the subspace generated by k we show that each such map is the restriction of a completely positive map on the whole algebra called a generalized channel we characterize the set of generalized channels and also the equivalence classes of generalized channels having the same value on k moreover if k contains the tracial state the set of generalized channels forms again a convex subset of a multipartite state space this leads to a definition of a generalized supermap which is a generalized channel with respect to this subset we prove a decomposition theorem for generalized supermaps and describe the equivalence classes the set of generalized supermaps having the same value on equivalent generalized channels is also characterized special cases include quantum

cross validation in principal component analysis summary this paper describes a form of cross validation in the context of principal component analysis which has a number of useful aspects as regards multivariate data inspection and description topics covered include choice of dimensionality identification of influential observations and selection of important variables the methods are motivated by and illustrated on a well known data set 1 data set and objectives jeffers 1967 described two detailed multivariate case studies one of which concerned 19 variables measured on each of 40 winged aphids alatee adelges that had been caught in a light trap the 19 variables are listed in table 1 principal component analysis pca was used to examine the structure in the data and if possible to answer the following questions i how many dimensions of the individuals are being measured ii how many distinct taxa are present in the habitat iii which variables among the 19 are redundant for distinguishing between taxa and which must be retained in future work of the 19 variables 14 are length or width measurements four are counts and one anal fold is a presence absence variable scored 0 or 1 in view of this disparity in variable type jeffers elected to standardise the data and thus effect the pca by finding the latent roots and vectors of the correlation rather than covariance matrix of the data the elements of each latent vector provide the coefficients of one of 19 linear combinations of the standardised original variables that successively maximise sample variance subject to being orthogonal with each other and the corresponding latent root is the sample variance of that linear combination the 19 observations for each aphid were subjected to each of these 19 linear transformations to form the 19 principal component scores for that aphid the above questions were then answered as follows i the latent roots of the correlation matrix were as given in table 1 the four largest comprise 73 0 12 5 3 9 and 2 6 respectively of the total variance 19 0 of the standardised variables the dimensionality of the data was therefore taken to be 2 ii when the scores of the first two principal components for the 40 aphids were plotted against orthogonal axes the resulting 40 points divided into four groups as shown in figure 1 hence four distinct species were identified for the aphids iii from consideration of the size of coefficients in the first three principal components it was concluded that only the four variables length of tibia number of ovipositor

estimation of subspace arrangements with applications in modeling and segmenting mixed data recently many scientific and engineering applications have involved the challenging task of analyzing large amounts of unsorted high dimensional data that have very complicated structures from both geometric and statistical points of view such unsorted data are considered mixed as different parts of the data have significantly different structures which cannot be described by a single model in this paper we propose to use subspace arrangements a union of multiple subspaces for modeling mixed data each subspace in the arrangement is used to model just a homogeneous subset of the data thus multiple subspaces together can capture the heterogeneous structures within the data set in this paper we give a comprehensive introduction to a new approach for the estimation of subspace arrangements this is known as generalized principal component analysis gpca in particular we provide a comprehensive summary of important algebraic properties and statistical facts that are crucial for making the inference of subspace arrangements both efficient and robust even when the given data are corrupted by noise or contaminated with outliers this new method in many ways improves and generalizes extant methods for modeling or clustering mixed data there have been successful applications of this new method to many real world problems in computer vision image processing and system identification in this paper we will examine several of those representative applications this paper is intended to be expository in nature however in order that this may serve as a more complete reference for both theoreticians and practitioners we take the liberty of filling in several gaps between the theory and the practice in the existing literature

discriminative feature extraction by a neural implementation of canonical correlation analysis the canonical correlation analysis cca aims at measuring linear relationships between two sets of variables views that can be used for feature extraction in classification problems with multiview data however the correlated features extracted by the cca may not be class discriminative since cca does not utilize the class labels in its traditional formulation although there is a method called discriminative cca dcca that aims to increase the discriminative ability of cca inspired from the linear discriminant analysis lda it has been shown that the extracted features with this method are identical to those by the lda with respect to an orthogonal transformation therefore dcca is simply equivalent to applying single view regular lda to each one of the views separately besides dcca and the other similar dcca approaches have generalization problems due to the sample covariance matrices used in their computation which are sensitive to outliers and noisy samples in this paper we propose a method called discriminative alternating regression d ar to explore correlated and also discriminative features d ar utilizes two alternating multilayer perceptrons each with a linear hidden layer learning to predict both the class labels and the outputs of each other we show that the features found by d ar on training sets significantly accomplish higher classification accuracies on test sets of facial expression recognition object recognition and image retrieval experimental data sets

on local influence analysis of full information item factor models the full information item factor fiif model is very useful for analyzing relations of dichotomous variables in this article we present a feasible procedure to assess local influence of minor perturbations for identifying influence aspects of the fiif model the development is based on a q displacement function which is closely related with the monte carlo em algorithm in the ml estimation in the e step of this algorithm the conditional expectations are approximated by sample means of observations simulated by the gibbs sampler from the appropriate conditional distributions it turns out that these observations can be utilized for computing the building blocks of the proposed diagnostic measures the diagnoses are based on the conformal normal curvature that can be computed easily a number of interesting perturbation schemes are considered the methodology is illustrated with two real examples

influence in canonical correlation analysis the perturbation theory of the generalized eigenproblem is used to derive influence functions of each squared canonical correlation coefficient and the corresponding canonical vector pair three sample versions of these functions are described and some properties are noted as particular applications the influence function of the squared multiple correlation coefficient and influence functions of eigenvalues and eigenvectors in correspondence analysis are obtained three numerical examples are briefly discussed

completely positive divisibility does not mean markovianity in the classical domain it is well known that divisibility does not imply that a stochastic process is markovian however for quantum processes divisibility is often considered to be synonymous with markovianity we show that completely positive divisible quantum processes can still involve non markovian temporal correlations that we then fully classify using the recently developed process tensor formalism which generalizes the theory of stochastic processes to the quantum domain

sensitivity analysis of structural equation models the main purpose of this paper is to investigate the sensitivity analysis of structural equation model when minor perturbation is introduced some influence measure that based on the general case weight perturbation is derived for the generalized least squares estimation an influence measure that related to the cook s distance is also developed for the special case deletion perturbation scheme using the proposed methodology the influential observation in a data set can be detected moreover the general theory can be applied to detect the influential parameters in a model finally some illustrative artificial and real examples are presented

influential observations in principal factor analysis we propose a method for detecting influential observations in iterative principal factor analysis for this purpose we derive the influence functionsi x llt andi x for the common variance matrixt llt and the unique variance matrix respectively in the common factor decomposition llt a numerical example is given for illustration

using conditional bias in principal component analysis for the evaluation of joint influence on the eigenvalues of the covariance matrix abstract influence analysis in principal component analysis has usually been tackled using the influence function 1 or local influence 2 approaches the main objective of this paper is that of proposing influence diagnostics for the eigenvalues of the covariance matrix that is for the variance explained by the principal components from a different angle that of the conditional bias 3 an approximation of the conditional bias of the simple eigenvalues of the sample covariance matrix is calculated under normality and some influence diagnostics are proposed the study is carried by considering joint influence

robust kernel principal component analysis this letter discusses the robustness issue of kernel principal component analysis a class of new robust procedures is proposed based on eigenvalue decomposition of weighted covariance the proposed procedures will place less weight on deviant patterns and thus be more resistant to data contamination and model deviation theoretical influence functions are derived and numerical examples are presented as well both theoretical and numerical results indicate that the proposed robust method outperforms the conventional approach in the sense of being less sensitive to outliers our robust method and results also apply to functional principal component analysis

multiset canonical correlations using globality preserving projections with applications to feature extraction and recognition multiset features extracted from the same patterns always represent different characteristics of data thus it is very valuable to perform the extraction on multiple feature sets this paper addresses the issue of multiset correlation feature extraction mcfe in multiple feature representations a novel method is proposed to carry out the mcfe for classification called multiset canonical correlations using globality preserving projections mcc gps which can perform joint dimensionality reduction for high dimensional data mcc gp integrates correlational characteristics of feature pairs and global geometric information of data in the transformed low dimensional space this makes mcc gps have better discriminant ability than a previous method proposed by the authors called multiset integrated canonical correlation analysis micca which only considers correlations for recognition tasks furthermore mcc gp can subsume two popular feature extraction methods into its framework under some constraints this also provides a new insight for these two methods the proposed method is applied to pattern recognition and examined using the coil 100 and eth 80 object databases and ar cmu pie and yale face databases extensive experimental results show that mcc gp outperforms micca and multiset canonical correlation analysis in terms of classification accuracy and efficiency

kernel component analysis using an epsilon insensitive robust loss function kernel principal component analysis pca is a technique to perform feature extraction in a high dimensional feature space which is nonlinearly related to the original input space the kernel pca formulation corresponds to an eigendecomposition of the kernel matrix eigenvectors with large eigenvalues correspond to the principal components in the feature space starting from the least squares support vector machine ls svm formulation to kernel pca we extend it to a generalized form of kernel component analysis kca with a general underlying loss function made explicit for classical kernel pca the underlying loss function is l 2 in this generalized form one can plug in also other loss functions in the context of robust statistics it is known that the l 2 loss function is not robust because its influence function is not bounded therefore outliers can skew the solution from the desired one another issue with kernel pca is the lack of sparseness the principal components are dense expansions in terms of kernel functions in this paper we introduce robustness and sparseness into kernel component analysis by using an epsilon insensitive robust loss function we propose two different algorithms the first method solves a set of nonlinear equations with kernel pca as starting points the second method uses a simplified iterative weighting procedure that leads to solving a sequence of generalized eigenvalue problems simulations with toy and real life data show improvements in terms of robustness together with a sparse representation

principal component analysis with external information on both subjects and variables a method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis in this method the original data are first decomposed into several components according to external information the components are then subjected to principal component analysis to explore structures within the components it is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices the numerical method based on the qr decomposition is described which simplifies the computation considerably the proposed method includes a number of interesting special cases whose relations to existing methods are discussed examples are given to demonstrate practical uses of the method

extending quantum operations for a given set of input output pairs of quantum states or observables we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output the physical maps on quantum states are trace preserving completely positive maps but we also consider variants of these requirements we generalize the definition of complete positivity to linear maps defined on arbitrary subspaces then formulate this notion as a semidefinite program and relate it by duality to approximative extensions of this map this gives a characterization of the maps which can be approximated arbitrarily well as the restriction of a map that is completely positive on the whole algebra also yielding the familiar extension theorems on operator spaces for quantum channel extensions and extensions by probabilistic operations we obtain semidefinite characterizations and we also elucidate the special case of abelian inputs or outputs finally revisiting a theorem by alberti and uhlmann we provide simpler and more widely applicable conditions for certain extension problems on qubits and by using a semidefinite programming formulation we exhibit counterexamples to seemingly reasonable but false generalizations of the alberti uhlmann theorem

a simple theorem on 3 connectivity abstract it is well known that for any element of a connected matroid either the deletion or the contraction of that element preserves connectivity we prove a simple and natural generalization to 3 connected matroids this result is used to prove seymour s generalization of a theorem of kelmans

implications of influence function analysis for sliced inverse regression and sliced average variance estimation sliced inverse regression sliced inverse regression ii and sliced average variance estimation are three related dimension reduction methods that require relatively mild model assumptions as an approximation for the relative influence of single observations from large samples the influence function is used to compare the sensitivity of the three methods to particular observational types the analysis carried out here helps to explain why there is a lack of agreement concerning the preferability of these dimension reduction procedures in general an efficient sample version of the influence function is also developed and evaluated

connected hyperplanes in binary matroids abstract for a 3 connected binary matroid m let dim a m be the dimension of the subspace of the cocycle space spanned by the non separating cocircuits of m avoiding a where a e m when a bixby and cunningham in 1979 showed that dim a m r m in 2004 when a 1 lemos proved that dim a m r m 1 in this paper we characterize the 3 connected binary matroids having a pair of elements that meets every non separating cocircuit using this result we show that 2 dim a m r m 3 when m is regular and a 2 for a 3 we exhibit a family of cographic matroids with a 3 element set intersecting every non separating cocircuit we also construct the matroids that attains mcnulty and wu s bound for the number of non separating cocircuits of a simple and cosimple connected binary matroid

the second order approximation to sample influence curve in canonical correlation analysis a second order approximation to the sample influence curve sic in canonical correlation analysis has been derived in the literature however it does not seem satisfactory for some cases in this paper we present a more accurate second order approximation as a particular case the proposed method is exact for the sic of the squared multiple correlation coefficient an example is given

the binary matroids with no 4 wheel minor on caracterise les matroides binaires sans mineurs isomorphes a une roue de rang 4 on resout pour cette classe de matrices le probleme critique et on etend les resultats de kung walton welsh pour les classes associees de matroides binaires

the influence of observations on misclassification probability estimates in linear discriminant analysis summary the influence of observations upon misclassification probability estimates in linear discriminant analysis is examined for a single observation an exact expression is given confirming two surprising results of campbell 1978 it also shows that the influence of an observation is governed by two quantities a the difference between its linear discriminant score and that for its sample mean and b its atypicality estimate for its own population this is analogous to linear model results where an observation s influence depends upon its residual and its leverage however important differences from the regression situation are noted contours of this one at a time influence can be superimposed on the plot introduced by critchley ford 1985 examining the joint influence of several observations is complicated by the computational burden and by possible masking effects a quadratic approximation is developed for this problem using pregibon s 1981 case weights scheme this approximation has an error of order n 3 where n denotes the assumed common order of the sample sizes an example is given

canonical correlation analysis on data with censoring and error information we developed a probabilistic model for canonical correlation analysis in the case when the associated datasets are incomplete this case can arise where data entries either contain measurement errors or are censored i e nonignorable missing due to uncertainties in instrument calibration and physical limitations of devices and experimental conditions the aim of our model is to estimate the true correlation coefficients through eliminating the effects of measurement errors and abstracting helpful information from censored data as exact inference is not possible for the proposed model a modified variational expectation maximization em algorithm was developed in the algorithm developed we approximated the posteriors of the latent variables as normal distributions in the experiment the modified e step approximation accuracy is first empirically demonstrated by being compared to hybrid monte carlo hmc sampling the following experiments were carried out on synthetic datasets with different numbers of censored data and different correlation coefficient settings to compare the proposed algorithm with a maximum a posteriori map solution and a markov chain em solution experimental results showed that the variational em solution compares favorably against the map solution approaching the accuracy of the markov chain em while maintaining computational simplicity we finally applied the proposed algorithm to finding the mostly correlated properties of galaxy group with the x ray luminosity

dividing quantum channels we investigate the possibility of dividing quantum channels into concatenations of other channels thereby studying the semigroup structure of the set of completely positive trace preserving maps we show the existence of indivisible channels which can not be written as non trivial products of other channels and study the set of infinitesimal divisible channels which are elements of continuous completely positive evolutions for qubit channels we obtain a complete characterization of the sets of indivisible and infinitesimal divisible channels moreover we identify those channels which are solutions of time dependent master equations for both positive and completely positive evolutions for arbitrary finite dimension we prove a representation theorem for elements of continuous completely positive evolutions based on new results on determinants of quantum channels and markovian approximations

the weights in mds codes the weights in maximum distance separable mds codes of length n and dimension k over the finite field gf q are studied up to some explicit exceptional cases the mds codes with parameters given by the mds conjecture are shown to contain all k weights in the range n k 1 to n the proof uses the covering radius of the dual code

divisibility and information flow notions of quantum markovianity for noninvertible dynamical maps we analyze the relation between completely positive cp divisibility and the lack of information backflow for an arbitrary not necessarily invertible dynamical map it is well known that cp divisibility always implies a lack of information backflow moreover these two notions are equivalent for invertible maps in this letter it is shown that for a map which is not invertible the lack of information backflow always implies the existence of a completely positive propagator which however needs not be trace preserving interestingly for a wide class of image nonincreasing dynamical maps this propagator becomes trace preserving as well and hence the lack of information backflow implies cp divisibility this result sheds new light into the structure of the time local generators giving rise to cp divisible evolutions we show that if the map is not invertible then positivity of dissipation decoherence rates is no longer necessary for cp divisibility

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

asymptotic distributions of principal components based on robust dispersions algebraically principal components can be defined as the eigenvalues and eigenvectors of a covariance or correlation matrix but they are statistically meaningful as successive projections of the multivariate data in the direction of maximal variability an attractive alternative in robust principal component analysis is to replace the classical variability measure i e variance by a robust dispersion measure this projection pursuit approach was first proposed in li chen 1985 as a method of constructing a robust scatter matrix recent unpublished work of c croux and a ruiz gazen provided the influence functions of the resulting principal components the present paper focuses on the asymptotic distributions of robust principal components in particular we obtain the asymptotic normality of the principal components that maximise a robust dispersion measure we also explain the need to use a dispersion functional with a continuous influence function

robust principal component analysis by self organizing rules based on statistical physics approach this paper applies statistical physics to the problem of robust principal component analysis pca the commonly used pca learning rules are first related to energy functions these functions are generalized by adding a binary decision field with a given prior distribution so that outliers in the data are dealt with explicitly in order to make pca robust each of the generalized energy functions is then used to define a gibbs distribution from which a marginal distribution is obtained by summing over the binary decision field the marginal distribution defines an effective energy function from which self organizing rules have been developed for robust pca under the presence of outliers both the standard pca methods and the existing self organizing pca rules studied in the literature of neural networks perform quite poorly by contrast the robust rules proposed here resist outliers well and perform excellently for fulfilling various pca like tasks such as obtaining the first principal component vector the first k principal component vectors and directly finding the subspace spanned by the first k vector principal component vectors without solving for each vector individually comparative experiments have been made and the results show that the authors robust rules improve the performances of the existing pca algorithms significantly when outliers are present

the development and comparison of robust methodsfor estimating the fundamental matrix this paper has two goals the first is to develop a variety of robust methods for the computation of the fundamental matrix the calibration free representation of camera motion the methods are drawn from the principal categories of robust estimators viz case deletion diagnostics m estimators and random sampling and the paper develops the theory required to apply them to non linear orthogonal regression problems although a considerable amount of interest has focussed on the application of robust estimation in computer vision the relative merits of the many individual methods are unknown leaving the potential practitioner to guess at their value the second goal is therefore to compare and judge the methods comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery in contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth a variety of error measures are examined the experiments allow a statistically satisfying and quasi optimal method to be synthesized which is shown to be stable with up to 50 percent outlier contamination and may still be used if there are more than 50 percent outliers performance bounds are established for the method and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined the results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers

two graphical displays for outlying and influential observations in regression summary the paper describes two procedures for detecting observations with outlying values either in the response variable or in the explanatory variables in multiple regression these procedures are presented as half normal plots with envelopes derived from simulation in order to avoid overinterpretation of the data analysis of a well known data set leads to the use of a data transformation a simple test for which is commended and to some comments on the relationship with robust regression the widespread availability of sophisticated computer software has made the fitting of multiple regression equations painless but the very ease of these procedures may cause insufficient care to be given to checking and scrutiny of the data transcription punching and data manipulation errors may lead to bad values both of the observations y and of the independent or explanatory variables x it is the purpose of the present paper to describe and exemplify two plots which provide checks against such bad values it is argued that these plots and a test for transformations should accompany any thorough regression analysis bad values of the response or outliers have long been detected by a variety of plots of residuals bad values of the explanatory variables are less easily detected even when they lead to an extreme point in the design space since the fitted equation will pass close to such an influential observation the residual may not be especially large even after allowance has been made for the small variance of the fitted value at such a point to detect such behaviour a quantity is needed which exhibits the dependence of the fitted model on each point or group of points discussions of such quantities are given by hoaglin welsch 1978 and more recently by belsley kuh welsch 1980 2 1 by cook weisberg 1980 and by pregibon 1981 the quantity used here is a modification of a statistic proposed by cook 1977 which is derived in 2 two half normal plots are presented in 3 as an aid to interpretation envelopes to the plots are generated by simulation examples of the plots are given in 4 both for simulated data and for the stack loss data given by brownlee 1965 p 454 transformations of this data set are discussed in 5 the paper concludes with some comments on the relationship with robust

constructive method for detecting the information backflow of non markovian dynamics we investigate the relation between two approaches to the characterization of quantum markovianity divisibility and lack of information backflow we show that a bijective dynamical map is completely positive divisible if and only if a monotonic nonincrease of distinguishability is observed for two equiprobable states of the evolving system and an ancilla moreover our proof is constructive given any such map that is not completely positive divisible we give an explicit construction of two states that when taken with the same a priori probability exhibit information backflow finally while an ancilla is necessary for the equivalence to hold in general we show that it is always possible to witness the non markovianity of bijective maps without using any entanglement between the system and ancilla

a family of fuzzy learning algorithms for robust principal component analysis neural networks in this paper we analyze xu and yuille s robust principal component analysis rpca learning algorithms by means of the distance measurement in space based on the analysis a family of fuzzy rpca learning algorithms is proposed which is robust against outliers these algorithms can explicitly be understood from the viewpoint of fuzzy set theory though xu and yuille s algorithms were proposed based on a statistical physics approach in the proposed algorithms an adaptive learning procedure overcomes the difficulty of selection of learning parameters in xu and yuille s algorithms furthermore the robustness of proposed algorithms is investigated by using the theory of influence functions simulations are carried out to illustrate the robustness of these algorithms

sensitivity analysis in factor analysis difference between using covariance and correlation matrices influence curves of some parameters under various methods of factor analysis have been given in the literature these influence curves depend on the influence curves for either the covariance or the correlation matrix used in the analysis the differences between the influence curves based on the covariance and the correlation matrices are derived in this paper simple formulas for the differences of the influence curves based on the two matrices for the unique variance matrix factor loadings and some other parameter are obtained under scale invariant estimation methods though the influence curves themselves are in complex forms

a unified approach to exploratory factor analysis with missing data nonnormal data and in the presence of outliers factor analysis is regularly used for analyzing survey data missing data data with outliers and consequently nonnormal data are very common for data obtained through questionnaires based on covariance matrix estimates for such nonstandard samples a unified approach for factor analysis is developed by generalizing the approach of maximum likelihood under constraints statistical properties of the estimates for factor loadings and error variances are obtained a rescaled bartlett corrected statistic is proposed for evaluating the number of factors equivariance and invariance of parameter estimates and their standard errors for canonical varimax and normalized varimax rotations are discussed numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures

quantum non markovian processes break conditional past future independence for classical markovian stochastic systems past and future events become statistically independent when conditioned to a given state at the present time memory non markovian effects break this condition inducing a nonvanishing conditional past future correlation here this classical memory indicator is extended to a quantum regime which provides an operational definition of quantum non markovianity based on a minimal set of three time ordered quantum system measurements and postselection the detection of memory effects through the measurement scheme is univocally related to departures from born markov and white noise approximations in quantum and classical environments respectively

probabilistic principal component analysis principal component analysis pca is a ubiquitous technique for data analysis and processing but one which is not based upon a probability model in this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model closely related to factor analysis we consider the properties of the associated likelihood function giving an em algorithm for estimating the principal subspace iteratively and discuss the advantages conveyed by the definition of a probability density function for pca

on the covering dimension of a linear code this paper introduces the covering dimension of a linear code over a finite field which is analogous to the critical exponent of a representable matroid and thus generalizes invariants that lie at the heart of several fundamental problems in a coding theory an upper bound on the covering dimension is proved improving kung s classical bound for the critical exponent in addition a construction is given for linear codes that attain equality in this covering dimension bound

operational characterization of divisibility of dynamical maps in this work we show the operational characterization to the divisibility of dynamical maps in terms of the distinguishability of quantum channels it is proven that the distinguishability of any pair of quantum channels does not increase under divisible maps in which the full hierarchy of divisibility is isomorphic to the structure of entanglement between system and environment this shows that i channel distinguishability is the operational quantity signifying detecting divisibility indivisibility of dynamical maps and ii the decision problem for the divisibility of maps is as hard as the separability problem in entanglement theory we also provide the information theoretic characterization to the divisibility of maps with conditional min entropy

fluctuation theorems for non markovian quantum processes exploiting previous results on markovian dynamics and fluctuation theorems we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach the entropy production along single trajectories for forward and backward processes is obtained with the help of a recently proposed classical like non markovian stochastic unravelling which is demonstrated to lead to a correction of the standard entropic fluctuation theorem this correction is interpreted as resulting from the interplay between the information extracted from the system through measurements and the flow of information from the environment to the open system due to memory effects single realizations of a dynamical process are no longer independent and their correlations fundamentally affect the behavior of entropy fluctuations

thermodynamics of non markovian reservoirs and heat engines we show that non markovian effects of the reservoirs can be used as a resource to extract work from an otto cycle the state transformation under non markovian dynamics is achieved via a two step process namely an isothermal process using a markovian reservoir followed by an adiabatic process from second law of thermodynamics we show that the maximum amount of extractable work from the state prepared under the non markovian dynamics quantifies a lower bound of non markovianity we illustrate our ideas with an explicit example of non markovian evolution

complete description of a quantum system at a given time a generalization of the description of a quantum system in the time interval between two measurements is presented a new concept of a generalized state is introduced generalized states yield a complete description of a quantum system when information about the system is available both from the past snd from the future the formalism of generalized states provides a natural language for describing many peculiar situations in particular situations in which one can ascertain the result of a measurement of any one of several non commuting variables are analysed weak measurements on quantum systems described by generalized states are discussed the relation belween weak and strong measurements is investigated

influence functions and outlier detection under the common principal components model a robust approach summary the common principal components model for several groups of multivariate observations assumes equal principal axes but different variances along these axes among the groups influence functions for plug in and projection pursuit estimates under a common principal component model are obtained asymptotic variances are derived from them outlier detection is possible using partial influence functions

influence functions for a linear subspace method a linear subspace method which is one of discriminant methods was proposed as a pattern recognition method and was studied because the method and its extensions do not encounter the situation of singular covariance matrix we need not consider extensions such as generalized ridge discrimination even when treating a high dimensional and sparse dataset in addition classifiers based on a multi class discrimination method can function faster because of the simple decision procedure therefore they have been widely used for face and speech recognition however it seems that sufficient studies have not been conducted about the statistical assessment of training data performance for classifier in terms of prediction accuracy in statistics influence functions for statistical discriminant analysis were derived and the assessments for analysis result were performed these studies indicate that influence functions are useful for detecting large influential observations for analysis results by using discrimination methods and they contribute to enhancing the performance of a target classifier in this paper we propose the statistical diagnostics of a classifier on the basis of an influence function by using the linear subspace method we first propose the discriminant score for the linear subspace method next we derive the sample and empirical influence functions for the average of the discriminant scores to detect large influential observations for the misclassification rate finally through a simulation study and a real data analysis we detect the outliers in the training dataset using the derived influence function and develop a highly sophisticated classifier in the linear subspace method highlightswe propose the discriminant score for a clafic method we derive the influence functions for the score and its average because we can enhance the classifier in the clafic method with them we show the effectiveness of our approach through a clear simulation study

facial expression recognition using kernel canonical correlation analysis kcca in this correspondence we address the facial expression recognition problem using kernel canonical correlation analysis kcca following the method proposed by lyons et al and zhang et al we manually locate 34 landmark points from each facial image and then convert these geometric points into a labeled graph lg vector using the gabor wavelet transformation method to represent the facial features on the other hand for each training facial image the semantic ratings describing the basic expressions are combined into a six dimensional semantic expression vector learning the correlation between the lg vector and the semantic expression vector is performed by kcca according to this correlation we estimate the associated semantic expression vector of a given test image and then perform the expression classification according to this estimated semantic expression vector moreover we also propose an improved kcca algorithm to tackle the singularity problem of the gram matrix the experimental results on the japanese female facial expression database and the ekman s pictures of facial affect database illustrate the effectiveness of the proposed method