incremental constraint satisfaction for equational logic programming abstract in this paper we are concerned with an instance of the constraint logic programming clp scheme specialized in solving equations with respect to a horn equational theory e the intended structure h e is given by the finest partition induced by e on the herbrand universe h over a finite one sorted alphabet this work deals with the description of an incremental constraint solver as the kernel of an operational semantics for the language clp h e the primary issues are how to verify the solvability of constraints in the structure h e by using some sound and complete semantic unification procedure such as narrowing how to simplify constraints in a computation sequence how to achieve incrementality in the computation process and how to profit from finitely failed derivations as a heuristic for optimizing the algorithms

a modular order sorted equational generalization algorithm generalization also called anti unification is the dual of unification given terms t and t a generalizer is a term t of which t and t are substitution instances the dual of a most general unifier mgu is that of least general generalizer lgg in this work we extend the known untyped generalization algorithm to first an order sorted typed setting with sorts subsorts and subtype polymorphism second we extend it to work modulo equational theories where function symbols can obey any combination of associativity commutativity and identity axioms including the empty set of such axioms and third to the combination of both which results in a modular order sorted equational generalization algorithm unlike the untyped case there is in general no single lgg in our framework due to order sortedness or to the equational axioms instead there is a finite minimal and complete set of lggs so that any other generalizer has at least one of them as an instance our generalization algorithms are expressed by means of inference systems for which we give proofs of correctness this opens up new applications to partial evaluation program synthesis and theorem proving for typed equational reasoning systems and typed rule based languages such as asf sdf elan obj cafe obj and maude

automatic color constancy algorithm selection and combination in this work we investigate how illuminant estimation techniques can be improved taking into account intrinsic low level properties of the images we show how these properties can be used to drive given a set of illuminant estimation algorithms the selection of the best algorithm for a given image the algorithm selection is made by a decision forest composed of several trees on the basis of the values of a set of heterogeneous features the features represent the image content in terms of low level visual properties the trees are trained to select the algorithm that minimizes the expected error in illuminant estimation we also designed a combination strategy that estimates the illuminant as a weighted sum of the different algorithms estimations experimental results on the widely used ciurea and funt dataset demonstrate the effectiveness of our approach

e generalization using grammars we extend the notion of anti unification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of e generalization sets we present a framework to combine inductive logic programming and e generalization that includes an extension of plotkin s lgg theorem to the equational case we demonstrate the potential power of e generalization by three example applications computation of suggestions for auxiliary lemmas in equational inductive proofs computation of construction laws for given term sequences and learning of screen editor command sequences

on the superlinear convergence of interior point algorithms for a general class of problems in this paper the authors extend the q superlinear convergence theory recently developed by zhang tapia and dennis for a class of interior point linear programming algorithms to similar interior point algorithms for quadratic programming and for linear complementarily problems this unified approach consists of viewing all these algorithms as a damped newton method applied to perturbations of a general problem a set of sufficient conditions for these algorithms to achieve q superlinear convergence is established the key ingredients consist of asymptotically taking the step to the boundary of the positive orthant and letting the centering parameter approach zero at a specific rate the construction of algorithms that have both the global property of polynomiality and the local property of superlinear convergence will be the subject of further research

color constancy by category correlation finding color representations that are stable to illuminant changes is still an open problem in computer vision until now most approaches have been based on physical constraints or statistical assumptions derived from the scene whereas very little attention has been paid to the effects that selected illuminants have on the final color image representation the novelty of this paper is to propose perceptual constraints that are computed on the corrected images we define the category hypothesis which weights the set of feasible illuminants according to their ability to map the corrected image onto specific colors here we choose these colors as the universal color categories related to basic linguistic terms which have been psychophysically measured these color categories encode natural color statistics and their relevance across different cultures is indicated by the fact that they have received a common color name from this category hypothesis we propose a fast implementation that allows the sampling of a large set of illuminants experiments prove that our method rivals current state of art performance without the need for training algorithmic parameters additionally the method can be used as a framework to insert top down information from other sources thus opening further research directions in solving for color constancy

order sorted algebra i equational deduction for multiple inheritance overloading exceptions and partial operations abstract this paper generalizes many sorted algebra msa to order sorted algebra osa by allowing a partial ordering relation on the set of sorts this supports abstract data types with multiple inheritance in roughly the sense of object oriented programming several forms of polymorphism and overloading partial operations as total on equationally defined subsorts exception handling and an operational semantics based on term rewriting we give the basic algebraic constructions for osa including quotient image product and term algebra and we prove their basic properties including quotient homomorphism and initiality theorems the paper s major mathematical results include a notion of osa deduction a completeness theorem for it and an osa birkhoff variety theorem we also develop conditional osa including initiality completeness and mckinsey malcev quasivariety theorems and we reduce osa to conditional msa which allows lifting many known msa results to osa retracts which intuitively are left inverses to subsort inclusions provide relatively inexpensive run time error handling we show that it is safe to add retracts to any osa signature in the sense that it gives rise to a conservative extension a final section compares and contrasts many different approaches to osa this paper also includes several examples demonstrating the flexibility and applicability of osa including some standard benchmarks like stack and list as well as a much more substantial example the number hierarchy from the naturals up to the quaternions

a superlinear infeasible interior point affine scaling algorithm for lcp we present an infeasible interior point algorithm for monotone linear complementarity problems in which the search directions are affine scaling directions and the step lengths are obtained from simple formulae that ensure both global and superlinear convergence by choosing the value of a parameter in appropriate ways polynomial complexity and convergence with q order up to but not including two can be achieved the only assumption made to obtain the superlinear convergence is the existence of a solution satisfying strict complementarily

a graph theoretic approach to statistical data security in this paper we study the problem of protecting sensitive data in an n by n two dimensional table of statistics when the nonsensitive data are made public along with the row and column sums for the table a sensitive cell is considered unprotected if its exact value can be deduced from the nonsensitive cell values and the row and column sums we give an efficient algorithm to identify all unprotected cells in a table the algorithm runs in linear time if the sensitive values are known and in o n 3 time if they are not known we then consider the problem of suppressing the fewest additional cell values to protect all the sensitive cells when some cells are initially unprotected we give a linear time algorithm for this problem in the useful special case that all cell values are strictly positive we next consider the problem of computing the tightest upper and lower bounds on the values of sensitive cells we show that each cell bound can be computed in o n 3 time but all theta n 2 value

elan from a rewriting logic point of view elan implements computational systems a concept that combines two first class entities rewrite rules and rewriting strategies elan can be used either as a logical framework or to describe and execute deterministic as well as non deterministic rule based processes with the general goal to make precise a rewriting logic based semantics of elan this paper has three contributions a presentation of the concepts of rules and strategies available in elan an expression of rewrite rules with matching conditions in conditional rewriting logic and finally an enrichment mechanism of a rewrite theory into a strategy theory in conditional rewriting logic

on the superlinear and quadratic convergence of primal dual interior point linear programming algorithms this paper presents a convergence rate analysis for interior point primal dual linear programming algorithms conditions that guarantee q superlinear convergence are identified in two distinct theories both state that under appropriate assumptions q superlinear convergence is achieved by asymptotically taking the step to the boundary of the positive orthant and letting the barrier parameter approach zero at a rate that is superlinearly faster than the convergence of the duality gap to zero the first theory makes no nondegeneracy assumption and explains why in recent numerical experimentation q superlinear convergence was always observed the second theory requires the restrictive assumption of primal nondegeneracy however it gives the surprising result that q superlinear convergence can still be attained even if centering is not phased out provided the iterates asymptotically approach the central path the latter theory is extended to produce a satisfactory q quadratic convergence theory it requir

statistical disclosure in two dimensional tables general tables abstract confidentiality protection of data published in tables is a major problem for statistical offices to obtain full cooperation of the respondents it is required that information of individual respondents with a confidential character is kept from being disclosed one method to avoid disclosure is the method of cell suppression in which the values of a number of statistical cells are not published but are suppressed from publication we discuss the method of cell suppression in general two dimensional tables in which row totals and column totals are always published the values of the sensitive cells are replaced by a cross x usually additional suppressions are necessary to prevent the values of the sensitive cells from being calculated from the row or column totals because of these additional suppressions useful information gets lost we want to minimize the loss of information by making the best choice for the additional suppressions therefore we introduce and compare the performance o

unranked second order anti unification abstract in this work we study anti unification for unranked terms and hedges permitting context and hedge variables hedges are sequences of unranked terms the anti unification problem of two hedges s and q is concerned with finding their generalization a hedge g such that both s and q are substitution instances of g second order power is gained by using context variables to generalize vertical differences at the input hedges hedge variables are used to generalize horizontal differences an anti unification algorithm is presented which computes a generalization of input hedges and records all the differences the algorithm is parametric by a skeleton computation function for instance we can compute a generalization of a skeleton which represents a constrained longest common subforest or an agreement subhedge subtree of the input hedges the computation of the generalization is done in quadratic time

evaluating combinational illumination estimation methods on real world images illumination estimation is an important component of color constancy and automatic white balancing a number of methods of combining illumination estimates obtained from multiple subordinate illumination estimation methods now appear in the literature these combinational methods aim to provide better illumination estimates by fusing the information embedded in the subordinate solutions the existing combinational methods are surveyed and analyzed here with the goals of determining 1 the effectiveness of fusing illumination estimates from multiple subordinate methods 2 the best method of combination 3 the underlying factors that affect the performance of a combinational method and 4 the effectiveness of combination for illumination estimation in multiple illuminant scenes the various combinational methods are categorized in terms of whether or not they require supervised training and whether or not they rely on high level scene content cues e g indoor versus outdoor extensive tests and enhanced analyzes using three data sets of real world images are conducted for consistency in testing the images were labeled according to their high level features 3d stages indoor outdoor and this label data is made available on line the tests reveal that the trained combinational methods direct combination by support vector regression in particular clearly outperform both the non combinational methods and those combinational methods based on scene content cues

a comparison of computational color constancy algorithms ii experiments with image data for pt i see ibid vol 11 no 9 p 972 84 2002 we test a number of the leading computational color constancy algorithms using a comprehensive set of images these were of 33 different scenes under 11 different sources representative of common illumination conditions the algorithms studied include two gray world methods a version of the retinex method several variants of forsyth s 1990 gamut mapping method cardei et al s 2000 neural net method and finlayson et al s color by correlation method finlayson et al 1997 2001 hubel and finlayson 2000 we discuss a number of issues in applying color constancy ideas to image data and study in depth the effect of different preprocessing strategies we compare the performance of the algorithms on image data with their performance on synthesized data all data used for this study are available online at http www cs sfu ca spl sim color data and implementations for most of the algorithms are also available http www cs sfu ca spl sim color code experiments with synthesized data part one of this paper suggested that the methods which emphasize the use of the input data statistics specifically color by correlation and the neural net algorithm are potentially the most effective at estimating the chromaticity of the scene illuminant unfortunately we were unable to realize comparable performance on real images here exploiting pixel intensity proved to be more beneficial than exploiting the details of image chromaticity statistics and the three dimensional 3 d gamut mapping algorithms gave the best performance

color constancy with spatio spectral statistics we introduce an efficient maximum likelihood approach for one part of the color constancy problem removing from an image the color cast caused by the spectral distribution of the dominating scene illuminant we do this by developing a statistical model for the spatial distribution of colors in white balanced images i e those that have no color cast and then using this model to infer illumination parameters as those being most likely under our model the key observation is that by applying spatial band pass filters to color images one unveils color distributions that are unimodal symmetric and well represented by a simple parametric form once these distributions are fit to training data they enable efficient maximum likelihood estimation of the dominant illuminant in a new image and they can be combined with statistical prior information about the illuminant in a very natural manner experimental evaluation on standard data sets suggests that the approach performs well

a comparison of computational color constancy algorithms i methodology and experiments with synthesized data we introduce a context for testing computational color constancy specify our approach to the implementation of a number of the leading algorithms and report the results of three experiments using synthesized data experiments using synthesized data are important because the ground truth is known possible confounds due to camera characterization and pre processing are absent and various factors affecting color constancy can be efficiently investigated because they can be manipulated individually and precisely the algorithms chosen for close study include two gray world methods a limiting case of a version of the retinex method a number of variants of forsyth s 1990 gamut mapping method cardei et al s 2000 neural net method and finlayson et al s color by correlation method finlayson et al 1997 2001 hubel and finlayson 2000 we investigate the ability of these algorithms to make estimates of three different color constancy quantities the chromaticity of the scene illuminant the overall magnitude of that illuminant and a corrected illumination invariant image we consider algorithm performance as a function of the number of surfaces in scenes generated from reflectance spectra the relative effect on the algorithms of added specularities and the effect of subsequent clipping of the data all data is available on line at http www cs sfu ca spl sim color data and implementations for most of the algorithms are also available http www cs sfu ca spl sim color code

fuzzy lattice operations on first order terms over signatures with similar constructors a constraint based approach abstract unification and generalization are operations on two terms computing respectively their greatest lower bound and least upper bound when the terms are quasi ordered by subsumption up to variable renaming i e t 1 t 2 iff t 1 t 2 for some variable substitution when term signatures are such that distinct functor symbols may be related with a fuzzy equivalence called a similarity these operations can be formally extended to tolerate mismatches on functor names and or arity or argument order we reformulate and extend previous work with a declarative approach defining unification and generalization as sets of axioms and rules forming a complete constraint normalization proof system these include the reynolds plotkin term generalization procedures maria sessa s weak unification with partially fuzzy signatures and its corresponding generalization as well as novel extensions of such operations to signatures with weaker functor similarities i e with possibly different arities one advantage of this approach is that it requires no modification of the conventional data structures for terms and substitutions this and the fact that these declarative specifications are efficiently executable conditional horn clauses offers great practical potential for fuzzy information handling applications

constant potential primal dual algorithms a framework we start with a study of the primal dual affine scaling algorithms for linear programs using ideas from kojima et al mizuno and nagasawa and new potential functions we establish a framework for primal dual algorithms that keep a potential function value fixed we show that if the potential function used in the algorithm is compatible with a corresponding neighborhood of the central path then the convergence proofs simplify greatly our algorithms have the property that all the iterates can be kept in a neighborhood of the central path without using any centering in the search directions

color constancy using natural image statistics and scene semantics existing color constancy methods are all based on specific assumptions such as the spatial and spectral characteristics of images as a consequence no algorithm can be considered as universal however with the large variety of available methods the question is how to select the method that performs best for a specific image to achieve selection and combining of color constancy algorithms in this paper natural image statistics are used to identify the most important characteristics of color images then based on these image characteristics the proper color constancy algorithm or best combination of algorithms is selected for a specific image to capture the image characteristics the weibull parameterization e g grain size and contrast is used it is shown that the weibull parameterization is related to the image attributes to which the used color constancy methods are sensitive an mog classifier is used to learn the correlation and weighting between the weibull parameters and the image attributes number of edges amount of texture and snr the output of the classifier is the selection of the best performing color constancy method for a certain image experimental results show a large improvement over state of the art single algorithms on a data set consisting of more than 11 000 images an increase in color constancy performance up to 20 percent median angular error can be obtained compared to the best performing single algorithm further it is shown that for certain scene categories one specific color constancy algorithm can be used instead of the classifier considering several algorithms

the bridge connectivity augmentation problem with a partition constraint in this paper we consider the augmentation problem of an undirected graph with k partitions of its vertices the main issue is how to add a set of edges with the smallest possible cardinality so that the resulting graph is 2 edge connected i e bridge connected while maintaining the original partition constraint to solve the problem we propose a simple linear time algorithm to the best of our knowledge the most efficient sequential algorithm runs in o n m nlogn logn time however we show that it can also run in o logn parallel time on an erew pram using a linear number of processors where n is the number of vertices in the input graph if a simple graph exists our main algorithm ensures that it is as simple as possible

large step interior point algorithms for linear complementarity problems recently kojima megiddo and mizuno showed theoretical convergence of primal dual interior point algorithms with the use of new step length rules for linear programs their rules which only rely on the lengths of steps from the current iterates in the primal and dual spaces to the respective boundaries of the primal and dual feasible regions allow taking large step lengths without performing any line search this paper extends and modifies their analysis to interior point algorithms for positive semidefinite linear complementarily problems global convergence and polynomial time convergence are presented under similar step length rules

superlinear primal dual affine scaling algorithms for lcp we describe an interior point algorithm for monotone linear complementarity problems in which primal dual affine scaling is used to generate the search directions the algorithm is shown to have global and superlinear convergence with q order up to but not including two the technique is shown to be consistent with a potential reduction algorithm yielding the first potential reduction algorithm that is both globally and superlinearly convergent

the reproduction angular error for evaluating the performance of illuminant estimation algorithms the angle between the rgbs of the measured illuminant and estimated illuminant colors the recovery angular error has been used to evaluate the performance of the illuminant estimation algorithms however we noticed that this metric is not in line with how the illuminant estimates are used normally the illuminant estimates are divided out from the image to hopefully provide image colors that are not confounded by the color of the light however even though the same reproduction results the same scene might have a large range of recovery errors in this work the scale of the problem with the recovery error is quantified next we propose a new metric for evaluating illuminant estimation algorithms called the reproduction angular error which is defined as the angle between the rgb of a white surface when the actual and estimated illuminations are divided out our new metric ties algorithm performance to how the illuminant estimates are used for a given algorithm adopting the new reproduction angular error leads to different optimal parameters further the ranked list of best to worst algorithms changes when the reproduction angular is used the importance of using an appropriate performance metric is established

all linear and integer programs are slim 3 way transportation programs we show that any rational convex polytope is polynomial time representable as a 3 way line sum transportation polytope of slim r c 3 format this universality theorem has important consequences for linear and integer programming and for confidential statistical data disclosure we provide a polynomial time embedding of arbitrary linear programs and integer programs in such slim transportation programs and in bitransportation programs our construction resolves several standing problems on 3 way transportation polytopes for example it demonstrates that unlike the case of 2 way contingency tables the range of values an entry can attain in any slim 3 way contingency table with specified 2 margins can contain arbitrary gaps our smallest such example has format 6 4 3 our construction provides a powerful automatic tool for studying concrete questions about transportation polytopes and contingency tables for example it automatically provides new proofs for some classical results including a well known real feasible but integer infeasible 6 4 3 transportation polytope of m vlach and bitransportation programs where any feasible bitransportation must have an arbitrarily large prescribed denominator

a novel algorithm for color constancy color constancy is the skill by which it is possible to tell the color of an object even under a colored light i interpret the color of an object as its color under a fixed canonical light rather than as a surface reflectance function this leads to an analysis that shows two distinct sets of circumstances under which color constancy is possible in this framework color constancy requires estimating the illuminant under which the image was taken the estimate is then used to choose one of a set of linear maps which is applied to the image to yield a color descriptor at each point this set of maps is computed in advance the illuminant can be estimated using image measurements alone because given a number of weak assumptions detailed in the text the color of the illuminant is constrained by the colors observed in the image this constraint arises from the fact that surfaces can reflect no more light than is cast on them for example if one observes a patch that excites the red receptor strongly the illuminant cannot have been deep blue two algorithms are possible using this constraint corresponding to different assumptions about the world the first algorithm crule will work for any surface reflectance crule corresponds to a form of coefficient rule but obtains the coefficients by using constraints on illuminant color the set of illuminants for which crule will be successful depends strongly on the choice of photoreceptors for narrowband photoreceptors crule will work in an unrestricted world the second algorithm mwext requires that both surface reflectances and illuminants be chosen from finite dimensional spaces but under these restrictive conditions it can recover a large number of parameters in the illuminant and is not an attractive model of human color constancy crule has been tested on real images of mondriaans and works well i show results for crule and for the retinex algorithm of land land 1971 land 1983 land 1985 operating on a number of real images the experimental work shows that for good constancy a color constancy system will need to adjust the gain of the receptors it employs in a fashion analagous to adaptation in humans

an analytical approach to the inference of summary data of additive type summary data take the form of a triple that consists of a summary attribute a category and a numeric value the inference problem of summary data consists in deciding whether or not a summary data of interest is evaluable i e can be computed from a given set of summary data we address the special case of the inference problem with homogeneous summary data i e summary data with the same summary attribute where the summary attribute is of additive nature owing to additivity one can model the information content of the given summary data by a linear equation system whose variables are constrained to take their values from the domain of the summary attribute we state two evaluability criteria one for a real or integral summary attribute and the other for a nonnegative real or nonnegative integral summary attribute using the two evaluability criteria we show that our inference problem can be solved in strongly polynomial time for a real or integral or nonnegative real summary attribute and is co i np complete for a nonnegative integral summary attribute moreover we prove that given a summary data of interest that is not evaluable even in the simplest case that the summary attribute is of a real type finding an evaluable summary data whose category is maximally contained in or minimally contains the category of the summary data of interest is an np hard problem

total protection of analytic invariant information in cross tabulated tables to protect sensitive information in a cross tabulated table it is a common practice to suppress some of the cells in the table an analytic invariant is a power series in terms of the suppressed cells that has a unique feasible value and a convergence radius equal to infty intuitively the information contained in an invariant is not protected even though the values of the suppressed cells are not disclosed this paper gives an optimal linear time algorithm for testing whether there exist nontrivial analytic invariants in terms of the suppressed cells in a given set of suppressed cells this paper also presents np completeness results and an almost linear time algorithm for the problem of suppressing the minimum number of cells in addition to the sensitive ones so that the resulting table does not leak analytic invariant information about a given set of suppressed cells

a linear algorithm for finding the invariant edges of an edge weighted graph given an edge weighted graph where all weights are nonnegative reals an edge reweighting is an assignment of nonnegative reals to edges such that for each vertex the sums of given and new weights assigned to the edges incident on the vertex do coincide an edge is then said to be invariant if its weight is the same for any edge reweighting we show that the set of invariant edges of an arbitrary edge weighted graph can be determined in time linear in the size of the underlying graph moreover an application to the security of statistical data is discussed

on the convergence of the affine scaling algorithm the affine scaling algorithm first proposed by dikin is presently enjoying great popularity as a potentially effective means of solving linear programs an outstanding question about this algorithm concerns its convergence in the presence of degeneracy in this paper we give new convergence results for this algorithm that do not require any non degeneracy assumption on the problem in particular we show that if the stepsize choice of either dikin or barnes or vanderbei et al is used then the algorithm generates iterates that converge at least linearly with a convergence ratio of 1 beta sqrt n wheren is the number of variables and 0 1 is a certain stepsize ratio for one particular stepsize choice which is an extension of that of barnes we show that the cost of the limit point is within o 1 of the optimal cost and for sufficiently small roughly proportional to how close the cost of the nonoptimal vertices are to the optimal cost is exactly optimal we prove the latter result by using an unusual proof technique that of analyzing the ergodic convergence of the corresponding dual vectors for the special case of network flow problems with integer data we show that it suffices to take 1 6mc wherem is the number of constraints andc is the sum of the cost coefficients to attain exact optimality

multi cue illumination estimation via a tree structured group joint sparse representation a multi cue illumination estimation method based on tree structured group joint sparse representation is proposed tests show that the proposed method works better than existing methods most of which are based on using only a single cue type for example a binarized color histogram or simple image statistic such as the mean rgb most existing illumination estimation methods make their estimates using only one of three kinds of cues they differ in which cue type they use but the chosen cue is either based on 1 properties of the low level rgb color distribution 2 mid level initial illuminant estimates provided by subordinate methods or 3 high level knowledge of scene content e g indoor versus outdoor scene the proposed multi cue method combines the information provided by cues of all three of these types within the framework of a tree structured group joint sparse representation tgjsr in tgjsr the training data is grouped into a tree of subgroups a test image under an unknown illuminant has its features reconstructed in terms of a joint sparse representation model derived from the grouped training data the test image s illumination is then estimated based on the weights involved in the joint sparse representation model as a general framework the proposed tgjsr framework can also easily be extended to incorporate any new features or cues that might be discovered in the future for illumination estimation

the complexity of three way statistical tables multiway tables with specified marginals arise in a variety of applications in statistics and operations research we provide a comprehensive complexity classification of three fundamental computational problems on tables existence counting and entry security one outcome of our work is that each of the following problems is intractable already for slim 3 tables with constant number 3 of rows 1 deciding existence of 3 tables with specified 2 marginals 2 counting all 3 tables with specified 2 marginals 3 deciding whether a specified value is attained in a specified entry by at least one of the 3 tables having the same 2 marginals as a given table this implies that a characterization of feasible marginals for such slim tables sought by much recent research is unlikely to exist another consequence of our study is a systematic efficient way of embedding the set of 3 tables satisfying any given 1 marginals and entry upper bounds in a set of slim 3 tables satisfying suitable 2 marginals with no entry bounds this provides a valuable tool for studying multi index transportation problems and multi index transportation polytopes remarkably it enables us to automatically recover a famous example due to vlach of a real feasible integer infeasible collection of 2 marginals for 3 tables of smallest possible size 3 4 6

models and algorithms for optimizing cell suppression in tabular data with linear constraints abstract cell suppression is a widely used technique for protecting sensitive information in statistical data presented in tabular form previous works on the subject mainly concentrate on two and three dimensional tables whose entries are subject to marginal totals in this article we address the problem of protecting sensitive data in a statistical table whose entries are linked by a generic system of linear constraints this very general setting covers among others k dimensional tables with marginals as well as hierarchical and linked tables in particular we address the optimization problem known in the literature as the complementary or secondary cell suppression problem in which the information loss due to suppression must be minimized we introduce a new integer linear programming model and outline an enumerative algorithm for its exact solution the algorithm can also be used as a heuristic procedure to find near optimal solutions extensive computational results on a test bed of 1 160 rea

a superlinearly convergent polynomial primal dual interior point algorithm for linear programming the choices of the centering parameter and the step length parameter are the fundamental issues in primal dual interior point algorithms for linear programming various choices for these two parameters that lead to polynomial algorithms have been proposed recently zhang tapia and dennis derived conditions for the choices of the two parameters that were sufficient for superlinear or quadratic convergence however prior to this work it had not been shown that these conditions for fast convergence are compatible with the choices that lead to polynomiality none of the existing polynomial primal dual interior point algorithms satisfy these fast convergence requirements this paper gives an affirmative answer to the question can a primal dual algorithm be both polynomial and superlinearly convergent for general problems a large step algorithm that possesses both polynomiality and under the assumption of the convergence of the iteration sequence q superlinear convergence is constructed and analyzed

a six stimulus theory for stochastic texture we report a six stimulus basis for stochastic texture perception fragmentation of the scene by a chaotic process causes the spatial scene statistics to conform to a weibull distribution the parameters of the weibull distribution characterize the spatial structure of uniform stochastic textures of many different origins completely in this paper we report the perceptual significance of the weibull parameters we demonstrate the parameters to be sensitive to orthogonal variations in the imaging conditions specifically to the illumination conditions camera magnification and resolving power and the texture orientation apparently the weibull parameters form a six stimulus basis for stochastic texture description the results indicate that texture perception can be approached like the experimental science of colorimetry

quadratic convergence in a primal dual method we show that the mizuno todd ye o nl iteration predictor corrector primal dual interior point algorithm for linear programming is quadratically convergent our proof does not assume that the problems be nondegenerate we do not assume that the iterate generated by the algorithm be convergent an assumption common to all previous asymptotic convergence analysis

potential reduction methods in mathematical programming we provide a survey of interior point methods for linear programming and its extensions that are based on reducing a suitable potential function at each iteration we give a fairly complete overview of potential reduction methods for linear programming focusing on the possibility of taking long steps and the properties of the barrier function that are necessary for the analysis we then describe briefly how the methods and results can be extended to certain convex programming problems following the approach of nesterov and todd we conclude with some open problems

a primal dual variant of the iri imai algorithm for linear programming a local acceleration method for primal dual potential reduction algorithms is introduced the method developed here uses modified newton search directions to minimize the tanabe todd ye tty potential function and can be regarded as a primal dual variant of the iri imai algorithm based on the multiplicative analogue of karmarkar s potential function when iterates are close to an optimal solution the tty potential function has negative curvature along the generated search directions therefore large reductions in the potential function can be obtained guaranteeing polynomial and quadratic convergence to nondegenerate solutions

anti unification and the theory of semirings abstract it was recently shown that anti unification over an equational theory consisting of only unit equations more than one is nullary such pure theories are artificial and are of little effect on practical aspects of anti unification in this work we extend these nullarity results to the theory of semirings a heavily studied theory with many practical applications furthermore our argument holds over semirings with commutative multiplication and or idempotent addition we also cover a few open questions discussed in previous work

primal dual affine scaling interior point methods for linear complementarity problems a first order affine scaling method and two m th order affine scaling methods for solving monotone linear complementarity problems lcps are presented all three methods produce iterates in a wide neighborhood of the central path the first order method has o nl 2 lognl 2 log lognl 2 iteration complexity if the lcp admits a strict complementary solution then both the duality gap and the iteration sequence converge superlinearly with q order two if m omega log sqrt n l then both higher order methods have o sqrt n l iteration complexity the q order of convergence of one of the methods is m 1 for problems that admit a strict complementarity solution while the q order of convergence of the other method is m 1 2 for general monotone lcps

superlinearly convergent o sqrt n l iteration interior point algorithms for linear programming and the monotone linear complementarity problem zhang and tapia have recently developed an interior point algorithm for the linear programming problem that has the property that the duality gap converges to zero q quadratically in the nondegenerate case and if the iterates converge q superlinearly in the degenerate case their algorithm also solves the integer model for lp in o nl iterations where l is the input length of the lp this paper presents an algorithm which maintains the quadratic superlinear convergence property but solves lp in o sqrt n l iterations in the integer model also the algorithm is generalized into an algorithm which solves lcp the lcp algorithm which is similar to an adaptive path following algorithm proposed by mizuno yoshise and kikuchi has similar local convergence properties if we assume that the iterates converge to a strictly complementary solution

color by correlation a simple unifying framework for color constancy the paper considers the problem of illuminant estimation how given an image of a scene recorded under an unknown light we can recover an estimate of that light obtaining such an estimate is a central part of solving the color constancy problem thus the work presented will have applications in fields such as color based object recognition and digital photography rather than attempting to recover a single estimate of the illuminant we instead set out to recover a measure of the likelihood that each of a set of possible illuminants was the scene illuminant we begin by determining which image colors can occur and how these colors are distributed under each of a set of possible lights we discuss how for a given camera we can obtain this knowledge we then correlate this information with the colors in a particular image to obtain a measure of the likelihood that each of the possible lights was the scene illuminant finally we use this likelihood information to choose a single light as an estimate of the scene illuminant computation is expressed and performed in a generic correlation framework which we develop we propose a new probabilistic instantiation of this correlation framework and show that it delivers very good color constancy on both synthetic and real images we further show that the proposed framework is rich enough to allow many existing algorithms to be expressed within it the gray world and gamut mapping algorithms are presented in this framework and we also explore the relationship of these algorithms to other probabilistic and neural network approaches to color constancy

edge based color constancy color constancy is the ability to measure colors of objects independent of the color of the light source a well known color constancy method is based on the gray world assumption which assumes that the average reflectance of surfaces in the world is achromatic in this paper we propose a new hypothesis for color constancy namely the gray edge hypothesis which assumes that the average edge difference in a scene is achromatic based on this hypothesis we propose an algorithm for color constancy contrary to existing color constancy algorithms which are computed from the zero order structure of images our method is based on the derivative structure of images furthermore we propose a framework which unifies a variety of known gray world max rgb minkowski norm and the newly proposed gray edge and higher order gray edge algorithms the quality of the various instantiations of the framework is tested and compared to the state of the art color constancy methods on two large data sets of images recording objects under a large number of different light sources the experiments show that the proposed color constancy algorithms obtain comparable results as the state of the art color constancy methods with the merit of being computationally more efficient

a self adjusting interior point algorithm for linear complementarity problems abstract based on the min max principle the standard centering equation in the interior point method is replaced by the optimality condition of a new proximity measure function thus a self adjusting mechanism is constructed in the new perturbed system the newton direction can be adjusted self adaptively according to the information of last iterates a self adjusting interior point method is given based on the new perturbed system numerical comparison is made between this algorithm and a primal dual interior point algorithm using standard perturbed system results demonstrate the efficiency and some advantages of the proposed algorithm

tree structured nuclear norm approximation with applications to robust face recognition structured sparsity as an extension of standard sparsity has shown the outstanding performance when dealing with some highly correlated variables in computer vision and pattern recognition however the traditional mixed l1 l2 or l1 text l infty group norm becomes weak in characterizing the internal structure of each group since they cannot alleviate the correlations between variables recently nuclear norm has been validated to be useful for depicting a spatially structured matrix variable it considers the global structure of the matrix variable but overlooks the local structure to combine the advantages of structured sparsity and nuclear norm this paper presents a tree structured nuclear norm approximation tsna model assuming that the representation residual with tree structured prior is a random matrix variable and follows a dependent matrix distribution the extended alternating direction method of multipliers is utilized to solve the proposed model an efficient bound condition based on the extended restricted isometry constants is provided to show the exact recovery of the proposed model under the given noisy case in addition tsna is connected with some newest methods such as sparse representation based classifier nuclear l1 norm joint regression and nuclear norm based matrix regression which can be regarded as the special cases of tsna experiments with face reconstruction and recognition demonstrate the benefits of tsna over other approaches

minimal invariant sets in a vertex weighted graph a weighting of vertices of a graph is admissible if there exists an edge weighting such that the weight of each vertex equals the sum of weights of its incident edges given an admissible vertex weighting of a graph an invariant set is an edge set such that the sum of the weights of its edges is the same for every edge weighting and a nonempty invariant set is minimal if none of its nonempty proper subsets is an invariant set it is easily seen that every nonempty invariant set is a disjoint union of minimal invariant sets a graphical characterisation of minimal invariant sets in a bipartite graph is known both in the case the vertex weights are reals and in the case the vertex weights are nonnegative reals we shall state a graphical characterisation of minimal invariant sets in an arbitrary vertex weighted graph moreover we give a linear algorithm to test an invariant set for minimality finally we state a complete axiomatisation of invariant sets and give a polynomial algorithm to find a set of minimal invariant sets that completely characterise the set of all invariant sets

lower bounding procedures for the 2 dimensional cell suppression problem abstract to protect confidential data from disclosure statistical offices use a technique called cell suppression which consists of suppressing data from the statistical tables they publish as some row and column subtotals are published omitting just the confidential values does not guarantee in every case that they cannot be disclosed or estimated within a narrow range therefore to protect confidential data it is often necessary to make complementary suppressions that is to suppress also values that are not confidential assigning a cost to every complementary suppression the cell suppression problem is that of finding a set of complementary suppressions with minimum total cost in this paper new necessary protection conditions are presented combining these new conditions with the ones known from the literature new lower bounding methods for the cell suppression problem are developed dominance theoretical results are proven and computational experience is reported for randomly generated tables

improving color constancy by photometric edge weighting edge based color constancy methods make use of image derivatives to estimate the illuminant however different edge types exist in real world images such as material shadow and highlight edges these different edge types may have a distinctive influence on the performance of the illuminant estimation therefore in this paper an extensive analysis is provided of different edge types on the performance of edge based color constancy methods first an edge based taxonomy is presented classifying edge types based on their photometric properties e g material shadow geometry and highlights then a performance evaluation of edge based color constancy is provided using these different edge types from this performance evaluation it is derived that specular and shadow edge types are more valuable than material edges for the estimation of the illuminant to this end the iterative weighted gray edge algorithm is proposed in which these edge types are more emphasized for the estimation of the illuminant images that are recorded under controlled circumstances demonstrate that the proposed iterative weighted gray edge algorithm based on highlights reduces the median angular error with approximately 25 percent in an uncontrolled environment improvements in angular error up to 11 percent are obtained with respect to regular edge based color constancy

color constancy for multiple light sources color constancy algorithms are generally based on the simplifying assumption that the spectral distribution of a light source is uniform across scenes however in reality this assumption is often violated due to the presence of multiple light sources in this paper we will address more realistic scenarios where the uniform light source assumption is too restrictive first a methodology is proposed to extend existing algorithms by applying color constancy locally to image patches rather than globally to the entire image after local patch based illuminant estimation these estimates are combined into more robust estimations and a local correction is applied based on a modified diagonal model quantitative and qualitative experiments on spectral and real images show that the proposed methodology reduces the influence of two light sources simultaneously present in one scene if the chromatic difference between these two illuminants is more than 1 the proposed framework outperforms algorithms based on the uniform light source assumption with error reduction up to approximately 30 otherwise when the chromatic difference is less than 1 and the scene can be considered to contain one approximately uniform light source the performance of the proposed method framework is similar to global color constancy methods

feedback vertex sets on restricted bipartite graphs a feedback vertex set fvs in a graph is a subset of vertices whose complement induces a forest finding a minimum fvs is np complete on bipartite graphs but tractable on convex bipartite graphs and on chordal bipartite graphs a bipartite graph is called tree convex if a tree is defined on one part of the vertices such that for every vertex in the other part its neighborhood induces a subtree when the tree is a path a triad or a star the bipartite graph is called convex bipartite triad convex bipartite or star convex bipartite respectively we show that 1 fvs is tractable on triad convex bipartite graphs 2 fvs is np complete on star convex bipartite graphs and on tree convex bipartite graphs where the maximum degree of vertices on the tree is at most three