on newton raphson iteration for multiplicative inverses modulo prime powers we study algorithms for the fast computation of modular inverses newton raphson iteration over p adic numbers gives a recurrence relation computing modular inverse modulo p m that is logarithmic in m we solve the recurrence to obtain an explicit formula for the inverse then we study different implementation variants of this iteration and show that our explicit formula is interesting for small exponent values but slower or large exponent say of more than 700 bits overall we thus propose a hybrid combination of our explicit formula and the best asymptotic variants this hybrid combination yields then a constant factor improvement also for large exponents

a complete axiomatization of fuzzy functional dependencies using fuzzy function the notion of functional dependency in classical relational databases corresponds to a partial function therefore it appears natural that the notion of fuzzy functional dependency should correspond to the notion of partial fuzzy function following this approach we introduce the notion of fuzzy functional dependency in fuzzy relational databases and show that the classical inference rules for functional dependencies form a sound and complete formal system in our case

a computational approach to approximate and plausible reasoning with applications to expert systems the intended purpose of this paper is twofold proposing a common basis for the modeling of uncertainty and imprecision and discussing various kinds of approximate and plausible reasoning schemes in this framework together with probability different kinds of uncertainty measures credibility and plausibility functions in the sense of shafer possibility measures in the sense of zadeh and the dual measures of necessity sugeno s g fuzzy measures are introduced in a unified way the modeling of imprecision in terms of possibility distribution is then presented and related questions such as the measure of the uncertainty of fuzzy events the probability and possibility qualification of statements the concept of a degree of truth and the truth qualification of propositions are discussed at length deductive inference from premises weighted by different kinds of measures by uncertainty or by truth values in the framework of various multivalued logics is fully investigated then deductive inferences from imprecise or fuzzy premises are dealt with patterns of reasoning where both uncertainty and imprecision are present are also addressed the last section is devoted to the combination of uncertain or imprecise pieces of information given by different sources on the whole this paper is a tentative survey of quantitative approaches in the modeling of uncertainty and imprecision including recent theoretical proposals as well as more empirical techniques such as the ones developed in expert systems such as mycin or prospector the management of uncertainty and imprecision in reasoning patterns being a key issue in artificial intelligence

data mining by attribute generalization with fuzzy hierarchies in fuzzy databases in this paper we examine the soft computing issues involving data generalization on fuzzy information the attribute induction process is formalized for these three cases crisp hierarchy fuzzy data fuzzy hierarchy crisp data fuzzy hierarchy fuzzy data each case is exemplified by applications of the algorithm to a prototype database

local rademacher complexity for multi label learning we analyze the local rademacher complexity of empirical risk minimization based multi label learning algorithms and in doing so propose a new algorithm for multi label learning rather than using the trace norm to regularize the multi label predictor we instead minimize the tail sum of the singular values of the predictor in multi label learning benefiting from the use of the local rademacher complexity our algorithm therefore has a sharper generalization error bound compared with methods that minimize over all singular values concentrating on the tail singular values results in better recovery of the low rank structure of the multi label predictor which plays an important role in exploiting label correlations we propose a new conditional singular value thresholding algorithm to solve the resulting objective function moreover a variance control strategy is employed to reduce the variance of variables in optimization empirical studies on real world data sets validate our theoretical results and demonstrate the effectiveness of the proposed algorithm for multi label learning

the complex zeros of random polynomials mark kac gave an explicit formula for the expectation of the number vn a of zeros of a random polynomial n i pn z e tj j o in any measurablc subset q of the reals here in i are independent standard normal random variables in fact for each n 1 he obtained an explicit intensity function gn for which e vn l jgn x dx here we extend this formula to obtain an explicit formula for the expected number of zeros in any measurable subset q of the complex plane c namely we show that e vn ki j hn x y dxdy j gn x dx where hn is an explicit intensity function we also study the asymptotics of hn showing that for large n its mass lies close to and is uniformly distributed around the unit circle

a fast optimization method for general binary code learning hashing or binary code learning has been recognized to accomplish efficient near neighbor search and has thus attracted broad interests in recent retrieval vision and learning studies one main challenge of learning to hash arises from the involvement of discrete variables in binary code optimization while the widely used continuous relaxation may achieve high learning efficiency the pursued codes are typically less effective due to accumulated quantization error in this paper we propose a novel binary code optimization method dubbed discrete proximal linearized minimization dplm which directly handles the discrete constraints during the learning process specifically the discrete thus nonsmooth nonconvex problem is reformulated as minimizing the sum of a smooth loss term with a nonsmooth indicator function the obtained problem is then efficiently solved by an iterative procedure with each iteration admitting an analytical discrete solution which is thus shown to converge very fast in addition the proposed method supports a large family of empirical loss functions which is particularly instantiated in this paper by both a supervised and an unsupervised hashing losses together with the bits uncorrelation and balance constraints in particular the proposed dplm with a supervised ell 2 loss encodes the whole nus wide database into 64 b binary codes within 10 s on a standard desktop computer the proposed approach is extensively evaluated on several large scale data sets and the generated binary codes are shown to achieve very promising results on both retrieval and classification tasks

global hashing system for fast image search hashing methods have been widely investigated for fast approximate nearest neighbor searching in large data sets most existing methods use binary vectors in lower dimensional spaces to represent data points that are usually real vectors of higher dimensionality we divide the hashing process into two steps data points are first embedded in a low dimensional space and the global positioning system method is subsequently introduced but modified for binary embedding we devise dataindependent and data dependent methods to distribute the satellites at appropriate locations our methods are based on finding the tradeoff between the information losses in these two steps experiments show that our data dependent method outperforms other methods in different sized data sets from 100k to 10m by incorporating the orthogonality of the code matrix both our data independent and data dependent methods are particularly impressive in experiments on longer bits

the montgomery inverse and its applications the montgomery inverse of b module a is b sup 1 2 sup n mod a where n is the number of bits in a the right shifting binary algorithm for modular inversion is shown naturally to compute the new inverse in fewer operations than the ordinary modular inverse the new inverse facilitates recent work by koc on modular exponentiation and has other applications in cryptography

data summarization in relational databases through fuzzy dependencies in this paper we deal with the problem of treating with dependencies in relational databases which do not hold in an exact manner as classical functional dependencies but in a weaker sense i e we face with relations which satisfy dependencies such that people with similar age and height have similar weight we model this relationship through the concept of fuzzy dependency we see that these dependencies imply some kind of fuzzy redundancy and in order to avoid it we propose to use a projection operator which leads us to partition a relation r into two projections say r1 and r2 with a less amount of information then we proceed to replace the original relation by these projections in this process we must guarantee that we can recover the data we had in the original relation this will be possible by using a special join operator applied to r1 and r2 we must also guarantee that we can test the fuzzy dependency for new entries to the database in the same way either if we consider the original relation r or if we work with the projections r1 and r2 we also show that this definition of dependency maintains the good properties of completeness of the classical case 1999 elsevier science inc all rights reserved

numerical decomposition of the solution sets of polynomial systems into irreducible components in engineering and applied mathematics polynomial systems arise whose solution sets contain components of different dimensions and multiplicities in this article we present algorithms based on homotopy continuation that compute much of the geometric information contained in the primary decomposition of the solution set in particular ignoring multiplicities our algorithms lay out the decomposition of the set of solutions into irreducible components by finding at each dimension generic points on each component as by products the computation also determines the degree of each component and an upper bound on its multiplicity the bound is sharp i e equal to one for reduced components the algorithms make essential use of generic projection and interpolation and can if desired describe each irreducible component precisely as the common zeroes of a finite number of polynomials

extending the fuzzy database with fuzzy numbers abstract the fuzzy relational database model originated by the authors permits fuzzy domain values from a discrete finite universe the model is extended here by demonstrating that fuzzy numbers may be employed as domain values without loss of consistency with respect to representation or the relational algebra where equivalence is required in an ordinary relational database similarity is employed in a fuzzy relational database for discrete finite universes similarity between atomic elements is described via a fuzzy similarity relation with max min transitivity two or more fuzzy numbers are defined to be similar if their union forms a continuous level set over the real line this convention effects the partitioning of fuzzy number domains that is necessary to assure the well definedness of the fuzzy relational algebra

some properties of extended fuzzy preference relations using modalities abstract a fuzzy preference relation is extended to six kinds of relations between fuzzy sets the properties of the six extended relations are investigated especially a sufficient condition for reducing the extended relations to four kinds is discussed when fuzzy sets are bounded and normal and some examples are given to illustrate it further a sufficient condition for the extended negative relations to coincide with the extended inverse relations is described

fuzzy loss less decompositions in databases in this paper we deal with the problem of defining projection and join operators in the framework of a fuzzy relational database we study the properties of such operators relating to the concept of fuzzy functional dependency there are two main properties to achieve on the one hand if a relation r satisfies a dependency between two sets of attributes x and y then we want to preserve this dependency in the fuzzy projection over xy of r on the other hand we want to test a fuzzy dependency just by looking at this projection therefore such a projection operator must allow us to store the information conveyed in r into a separate relation with fewer tuples in order to define the criterion for fuzzy dependency we shall need to extend a resemblance relation defined for crisp data to the fuzzy case finally we shall introduce a fuzzy join operator which will allow us to recover the information given in a relation from its projections

the montgomery modular inverse revisited we modify an algorithm given by kaliski to compute the montgomery inverse of an integer modulo a prime number we also give a new definition of the montgomery inverse and introduce efficient algorithms for computing the classical modular inverse the kaliski montgomery inverse and the new montgomery inverse the proposed algorithms are suitable for software implementations on general purpose microprocessors

a fast learning algorithm for deep belief nets we show how to use complementary priors to eliminate the explaining away effects that make inference difficult in densely connected belief nets that have many hidden layers using complementary priors we derive a fast greedy algorithm that can learn deep directed belief networks one layer at a time provided the top two layers form an undirected associative memory the fast greedy algorithm is used to initialize a slower learning procedure that fine tunes the weights using a contrastive version of the wake sleep algorithm after fine tuning a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels this generative model gives better digit classification than the best discriminative learning algorithms the low dimensional manifolds on which the digits lie are modeled by long ravines in the free energy landscape of the top level associative memory and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind

on fuzzy bags and their application to flexible querying an issue in extending database management functionalities is to increase the expressiveness of query languages flexible querying enables users to express preferences inside requirements and priorities inside compound queries the answers are then qualified and sorted out the fuzzy sets theory offers a general framework for dealing with flexible queries moreover the bag type plays an important role in databases systems taking into account both flexible queries and bags define fuzzy bags a new approach of this concept based on the notion of fuzzy cardinalities is presented in this paper fuzzy cardinalities provide a general framework in which different collection types set fuzzy set bag and fuzzy bag are treated in a uniform way and can then be composed we show how they can be used to build up flexible queries and to manipulate both quantitative and qualitative information on the elements of collections

evaluating flexible criteria on uncertain data abstract modern information management systems and databases are rapidly becoming better equipped for handling data imperfections a common imperfection is uncertainty indicating that a property s exact value is not known ideally such systems can be queried uniformly using flexible criteria regardless of whether the underlying data are uncertain or not the result thereof should always be informative and intuitive and should reflect to what degree the data satisfy the criteria and to which degree this is uncertain in this work we present a novel way to evaluate flexible criteria on uncertain data the result thereof is a distribution of uncertainty over degrees of satisfaction these so called suitability distributions are first constructed for possibilistic data it is shown that they can be used in all scenarios going from regular crisp criteria on certain data to flexible criteria on uncertain data and that they seamlessly generalize other alternatives importantly their interpretation is always the same so they can be used without needing to have prior knowledge regarding the quality of the data afterwards their properties and supported operations are given next it is shown that they can also be applied more broadly for example for probabilistic data examples illustrate their rich semantics ease of use and broad applicability

the study of joins in fuzzy relational databases abstract it is often necessary to join naturally two or more fuzzy relations to answer a user s query however the result of a join may not be what one expects in this paper we study the decomposition problem of fuzzy relation schemes we show that the algorithm proposed by aho et al 1 to test lossless join decomposition for classical relations can be applied in the fuzzy domain when particularizations are induced by functional dependencies

generalizing database relational algebra for the treatment of incomplete or uncertain information and vague queries abstract this paper deals with relational databases which are extended in the sense that fuzzily known values are allowed for attributes precise as well as partial imprecise uncertain knowledge concerning the value of the attributes are represented by means of 0 1 valued possibility distributions in zadeh s sense thus we have to manipulate ordinary relations on cartesian products of sets of fuzzy subsets rather than fuzzy relations besides vague queries whose contents are also represented by possibility distributions can be taken into account the basic operations of relational algebra union intersection cartesian product projection and selection are extended in order to deal with partial information and vague queries approximate equalities and inequalities modeled by fuzzy relations can also be taken into account in the selection operation then the main features of a query language based on the extended relational algebra are presented an illustrative example is provided this approach which enables a very general treatment of relational databases with fuzzy attribute values makes an extensive use of dual possibility and necessity measures

multiple feature kernel hashing for large scale visual search recently hashing has become attractive in large scale visual search owing to its theoretical guarantee and practical success however most of the state of the art hashing methods can only employ a single feature type to learn hashing functions related research on image search clustering and other domains has proved the advantages of fusing multiple features in this paper we propose a novel multiple feature kernel hashing framework where hashing functions are learned to preserve certain similarities with linearly combined multiple kernels corresponding to different features the framework is not only compatible with general types of data and diverse types of similarities indicated by different visual features but also general for both supervised and unsupervised scenarios we present efficient alternating optimization algorithms to learn both the hashing functions and the optimal kernel combination experimental results on three large scale benchmarks cifar 10 nus wide and a trecvid show that the proposed approach can achieve superior accuracy and efficiency over state of the art methods highlightswe propose a generic multiple feature hashing framework using multiple kernels visual features are implicitly mapped and concatenated to reduce complexity we formulate both supervised and unsupervised hashing problems in the framework alternating optimization ways efficiently learn hashing functions and the kernel space experiments validate the superior performances and efficiency of the proposed approach

newton s method with deflation for isolated singularities of polynomial systems we present a modification of newton s method to restore quadratic convergence for isolated singular solutions of polynomial systems our method is symbolic numeric we produce a new polynomial system which has the original multiple solution as a regular root using standard bases a tool for the symbolic computation of multiplicities we show that the number of deflation stages is bounded by the multiplicity of the isolated root our implementation performs well on a large class of applications

relaxing constraints in enhanced entity relationship models using fuzzy quantifiers while various articles about fuzzy entity relationship er and enhanced entity relationship eer models have recently been published not all examine how the constraints expressed in the model may be relaxed in this paper our aim is to relax the constraints which can be expressed in a conceptual model using the modeling tool so that these constraints can be made more flexible we will also study new constraints that are not considered in classic eer models we use the fuzzy quantifiers which have been widely studied in the context of fuzzy sets and fuzzy query systems for databases in addition we shall examine the representation of these constraints in an eer model and their practical repercussions the following constraints are studied the fuzzy participation constraint the fuzzy cardinality constraint the fuzzy completeness constraint to represent classes and subclasses the fuzzy cardinality constraint on overlapping specializations fuzzy disjoint and fuzzy overlapping constraints on specializations fuzzy attribute defined specializations fuzzy constraints in union types or categories and fuzzy constraints in shared subclasses we shall also demonstrate how fuzzy min max notation can substitute the fuzzy cardinality constraint but not the fuzzy participation constraint all these fuzzy constraints have a new meaning they offer greater expressiveness in conceptual design and are included in the so called fuzzy eer model

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

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

measuring properties of fuzzy sets a general technique and its use in fuzzy query evaluation abstract a fuzzy set can be viewed as a weighted max combination or as a convex combination of a family of nested ordinary sets the latter point of view allows the interpretation of a fuzzy set as a consonant random set then any numerical set function applied to a fuzzy set leads to a result which is a random number the expectation attached to this random number provides a scalar evaluation of the fuzzy set with respect to the considered set function this approach is very general and can be used for various kinds of measurements cardinality confidence measures attached to the occurrence of events diameter or perimeter of a fuzzy region distance between two sets etc also the fuzziness of the set to evaluate naturally induces a fuzzy set of possible evaluations and expected values of the lower and upper bounds of this fuzzy set of numbers can be computed the weighted max combination view which leads to another type of scalar evaluation is also briefly discussed in this paper the above approach is more particularly applied to the treatment of queries asking for some global evaluation of a set of items specified by means of a fuzzy property this kind of query can be managed by languages like sql in case of a crisp set of items when this set is fuzzily specified a scalar answer can still be provided as well as a fuzzy valued or interval valued one if we want to keep track of the effect of the fuzziness of the query the case where the data base contains precise information but also the more general case of fuzzy information data bases are considered

sampling algebraic sets in local intrinsic coordinates numerical data structures for positive dimensional solution sets of polynomial systems are sets of generic points cut out by random planes of complementary dimension we may represent the linear spaces defined by those planes either by explicit linear equations or in parametric form these descriptions are respectively called extrinsic and intrinsic representations while intrinsic representations lower the cost of the linear algebra operations we observe worse condition numbers in this paper we describe the local adaptation of intrinsic coordinates to improve the numerical conditioning of sampling algebraic sets local intrinsic coordinates also lead to a better step size control we illustrate our results with maple experiments and computations with phcpack on some benchmark polynomial systems

iterative quantization a procrustean approach to learning binary codes for large scale image retrieval this paper addresses the problem of learning similarity preserving binary codes for efficient similarity search in large scale image collections we formulate this problem in terms of finding a rotation of zero centered data so as to minimize the quantization error of mapping this data to the vertices of a zero centered binary hypercube and propose a simple and efficient alternating minimization algorithm to accomplish this task this algorithm dubbed iterative quantization itq has connections to multiclass spectral clustering and to the orthogonal procrustes problem and it can be used both with unsupervised data embeddings such as pca and supervised embeddings such as canonical correlation analysis cca the resulting binary codes significantly outperform several other state of the art methods we also show that further performance improvements can result from transforming the data with a nonlinear kernel mapping prior to pca or cca finally we demonstrate an application of itq to learning binary attributes or classemes on the imagenet data set

an extended version of the fuzzy relational database model abstract the fuzzy relational database model proposed by buckles and petry is a formal method for organizing and using fuzzy information in relational databases the model possesses two key properties that hold for classical relational databases no two tuples have identical interpretations and each relational algebra operation has a unique result the original fuzzy relational database model was based on similarity relations which were defined on finite scalar domains buckles and petry later extended the model to incorporate fuzzy number domains this extension was done without loss of consistency with the representation or the relational algebra in a recent paper we have extended the original model to proximity relations which generalize similarity relations the key properties of buckles and petry s model are preserved in the extension in this work we demonstrate that the existence of partitions on finite scalar domains in the fuzzy relational model is the key to preserving the important properties of the classical relational model we explain how proximity relations defined on finite scalar domains are used to partition the domains further we show that normal fuzzy sets can be employed as domain values these fuzzy sets become members of fi nite scalar domains and their characteristic functions are employed in generating the proximity relations of the fuzzy relational database model

fuzzy division in fuzzy relational databases an approach an approach to calculate the relational division in fuzzy databases is presented starting with the gefred model the tuples of the division are obtained with a possibility degree that indicates the extent to which they comply with the relational division requisites the results obtained are those expected a priori furthermore in order to formalize this method of fuzzy relational division two new operators are defined which may be useful in other operations the qualified fuzzy intersection and the generalized fuzzy projection with group functions some examples are included in order to clarify the method proposed here and the defined operators a comparison with other fuzzy division approaches that appear in the literature is included too

tolerant division queries and possibilistic database querying this article is situated in the framework of the relational model of data and it focuses on two quite orthogonal issues even if one may reasonably think that they can be mixed together the first topic is concerned with non traditional queries called flexible or fuzzy queries the key idea here is to introduce preferences inside queries addressed to a database thanks to fuzzy predicates so doing the user can express that some values are preferred to others but also that some criteria are more important than others this idea of preferences is especially illustrated with several extensions of the division operation the second question tackled is about the handling and querying of possibilistic databases basically a possibilistic database is similar to a regular one except that some attribute values are ill known and represented as possibility distributions in such a case it turns out that the set of queries that can be posed to the database with acceptable performances is significantly reduced with respect to the usual relational algebra however it is shown that diverse types of queries of interest against possibilistic databases can be envisaged

on calculating multiplicative inverses modulo 2 m this paper presents a procedure for calculating multiplicative inverses modulo 2m based on a novel mathematical approach the procedure is suitable for software implementation on a general purpose processor when counting the total number of word level processor multiplications the computational effort involved in calculating a multiplicative inverse is 2 3 that of a single multiplication of m bit values in addition to a few word level multiplications for standard processor word sizes the number of these additional multiplications does not exceed 12 this introduces a clear advantage of the proposed method when compared to other known methods presented in the literature

the condition number of equivalence transformations that block diagonalize matrix pencils how ill conditioned must a matrix s be if its columns are constrained to span certain subspaces we answer this question in order to find nearly best conditioned matrices sr and sl that block diagonalize a given matrix pencil t a b i e s l 1 tsr is bloc diagonal we show that the best conditioned sr has a condition number approximately equal to the cosecant of the smallest angle between right subspaces belonging to different diagonal blocks of thus the more nearly the right subspaces overlap the more ill conditioned sr must be the same is true of sl and the left subspaces for the standard eigenproblem t a i sl sr and the cosecant of the angle between subspaces turns out equal to an earlier estimate of the smallest condition number namely the norm of the projection matrix associated with one of the subspaces we apply this result to bound the error in an algorithm to compute analytic functions of matrices for instance exp t

adaptive multiprecision path tracking this article treats numerical methods for tracking an implicitly defined path the numerical precision required to successfully track such a path is difficult to predict a priori and indeed it may change dramatically through the course of the path in current practice one must either choose a conservatively large numerical precision at the outset or rerun paths multiple times in successively higher precision until success is achieved to avoid unnecessary computational cost it would be preferable to adaptively adjust the precision as the tracking proceeds in response to the local conditioning of the path we present an algorithm that can be set to either reactively adjust precision in response to step failure or proactively set the precision using error estimates we then test the relative merits of reactive and proactive adaptation on several examples arising as homotopies for solving systems of polynomial equations

spline regression hashing for fast image search techniques for fast image retrieval over large databases have attracted considerable attention due to the rapid growth of web images one promising way to accelerate image search is to use hashing technologies which represent images by compact binary codewords in this way the similarity between images can be efficiently measured in terms of the hamming distance between their corresponding binary codes although plenty of methods on generating hash codes have been proposed in recent years there are still two key points that needed to be improved 1 how to precisely preserve the similarity structure of the original data and 2 how to obtain the hash codes of the previously unseen data in this paper we propose our spline regression hashing method in which both the local and global data similarity structures are exploited to better capture the local manifold structure we introduce splines developed in sobolev space to find the local data mapping function furthermore our framework simultaneously learns the hash codes of the training data and the hash function for the unseen data which solves the out of sample problem extensive experiments conducted on real image datasets consisting of over one million images show that our proposed method outperforms the state of the art techniques

product quantization for nearest neighbor search this paper introduces a product quantization based approach for approximate nearest neighbor search the idea is to decompose the space into a cartesian product of low dimensional subspaces and to quantize each subspace separately a vector is represented by a short code composed of its subspace quantization indices the euclidean distance between two vectors can be efficiently estimated from their codes an asymmetric version increases precision as it computes the approximate distance between a vector and a code experimental results show that our approach searches for nearest neighbors efficiently in particular in combination with an inverted file system results for sift and gist image descriptors show excellent search accuracy outperforming three state of the art approaches the scalability of our approach is validated on a data set of two billion vectors

unsupervised feature selection via nonnegative spectral analysis and redundancy control in many image processing and pattern recognition problems visual contents of images are currently described by high dimensional features which are often redundant and noisy toward this end we propose a novel unsupervised feature selection scheme namely nonnegative spectral analysis with constrained redundancy by jointly leveraging nonnegative spectral clustering and redundancy analysis the proposed method can directly identify a discriminative subset of the most useful and redundancy constrained features nonnegative spectral analysis is developed to learn more accurate cluster labels of the input images during which the feature selection is performed simultaneously the joint learning of the cluster labels and feature selection matrix enables to select the most discriminative features row wise sparse models with a general ell 2 p norm 0 are leveraged to make the proposed model suitable for feature selection and robust to noise besides the redundancy between features is explicitly exploited to control the redundancy of the selected subset the proposed problem is formulated as an optimization problem with a well defined objective function solved by the developed simple yet efficient iterative algorithm finally we conduct extensive experiments on nine diverse image benchmarks including face data handwritten digit data and object image data the proposed method achieves encouraging the experimental results in comparison with several representative algorithms which demonstrates the effectiveness of the proposed algorithm for unsupervised feature selection

fuzzy databases modeling design and implementation j galindo a urrutia m piattini eds idea group publishing 2006 321pp isbn 1 59140 325 1

a flexible bipolar querying approach with imprecise data and guaranteed results in this paper we propose an approach to query a database when the user preferences are bipolar i e express both constraints and wishes about the desired result and the data stored in the database are imprecise results are then completely ordered with respect to these bipolar preferences giving priority to constraints over wishes additionally we propose a treatment that allows us to guarantee that any query will return a result even if no element satisfies all constraints specified by the user such a treatment may be useful when user s constraints are unrealistic i e cannot be all satisfied simultaneously and when the user desires a guaranteed result the approach is illustrated on a real world problem concerning the selection of optimal packaging for fresh fruits and vegetables

fuzzy information in extended fuzzy relational databases abstract the queries on type 2 fuzzy relational databases may get non reasonable answers and as pointed out by buckles a tuple s membership value is not static but is a measure of the appropriateness of that tuple to a given query here we use two supplementary attributes r and i e to model the concepts of fuzziness and uncertainty respectively we also use these two attribute values to compute the appropriateness of a tuple to a given query in this paper the proposed fuzzy relational model is defined by first order logical in our proposed model the classical properties of the database which are 1 database interpretation being redundant free being uniquely determined and 2 the well definedness of relational algebra are preserved for the fuzzy relational algebra therefore the proposed fuzzy relational model can capture more meaning than the conventional approaches and is more suitable to handle the real life application

flexible queries on relational databases using fuzzy logic and ontologies combines fuzzy logic and semantic techniques to perform flexible queries in a relational database alternative method to fuzzy logic to execute flexible queries on non scalar attributes answers are ordered according with the accomplishment degree to the query ontologies are used as an attribute domain frame to return semantically similar information to the query fuzzy logic are used on scalar attributes nowadays there are many proposals that allow users to perform fuzzy queries on relational databases regardless of these proposals fuzzy queries are really useful on scalar values where fuzzy sets can be adjusted to the user needs and domains but non scalar values are a more complex task here we extend non scalar attribute management in fuzzy queries with the use of ontologies thus we allow to compute this kind of queries not only with the similarity relationships defined explicitly on a fuzzy set but with semantically interrelated terms modeled as a domain ontology as well moreover we present the architecture of a novel system that combines both techniques to return an answer as much complete as possible and ordered by a degree of accomplishment finally a qualitative and quantitative study about the use of flexible queries on relational databases is included in this work as well

fast similarity search for learned metrics we introduce a method that enables scalable similarity search for learned metrics given pairwise similarity and dissimilarity constraints between some examples we learn a mahalanobis distance function that captures the examples underlying relationships well to allow sublinear time similarity search under the learned metric we show how to encode the learned metric parameterization into randomized locality sensitive hash functions we further formulate an indirect solution that enables metric learning and hashing for vector spaces whose high dimensionality makes it infeasible to learn an explicit transformation over the feature dimensions we demonstrate the approach applied to a variety of image data sets as well as a systems data set the learned metrics improve accuracy relative to commonly used metric baselines while our hashing construction enables efficient indexing with learned distances and very large databases

retrieving images in fuzzy object relational databases using dominant color descriptors in this paper a fuzzy approach for image retrieval on the basis of color features is presented the proposal deals with vagueness in the color description and introduces the use of fuzzy database models to store and retrieve imprecise data to face the color description the concept of dominant fuzzy color is proposed using linguistic labels for representing the color information in terms of hue saturation and intensity to deal with fuzzy data in our database model we use a general approach which can support the manipulation of fuzzy objects in an object relational database system this allows the retrieval of images by performing flexible queries on the database

neighborhood discriminant hashing for large scale image retrieval with the proliferation of large scale community contributed images hashing based approximate nearest neighbor search in huge databases has aroused considerable interest from the fields of computer vision and multimedia in recent years because of its computational and memory efficiency in this paper we propose a novel hashing method named neighborhood discriminant hashing ndh for short to implement approximate similarity search different from the previous work we propose to learn a discriminant hashing function by exploiting local discriminative information i e the labels of a sample can be inherited from the neighbor samples it selects the hashing function is expected to be orthogonal to avoid redundancy in the learned hashing bits as much as possible while an information theoretic regularization is jointly exploited using maximum entropy principle as a consequence the learned hashing function is compact and nonredundant among bits while each bit is highly informative extensive experiments are carried out on four publicly available data sets and the comparison results demonstrate the outperforming performance of the proposed ndh method over state of the art hashing techniques

web image search re ranking with click based similarity and typicality in image search re ranking besides the well known semantic gap intent gap which is the gap between the representation of users query demand and the real intent of the users is becoming a major problem restricting the development of image retrieval to reduce human effects in this paper we use image click through data which can be viewed as the implicit feedback from users to help overcome the intention gap and further improve the image search performance generally the hypothesis visually similar images should be close in a ranking list and the strategy images with higher relevance should be ranked higher than others are widely accepted to obtain satisfying search results thus image similarity and the level of relevance typicality are determinate factors correspondingly however when measuring image similarity and typicality conventional re ranking approaches only consider visual information and initial ranks of images while overlooking the influence of click through data this paper presents a novel re ranking approach named spectral clustering re ranking with click based similarity and typicality first to learn an appropriate similarity measurement we propose click based multi feature similarity learning algorithm which conducts metric learning based on click based triplets selection and integrates multiple features into a unified similarity space via multiple kernel learning then based on the learnt click based image similarity measure we conduct spectral clustering to group visually and semantically similar images into same clusters and get the final re rank list by calculating click based clusters typicality and within clusters click based image typicality in descending order our experiments conducted on two real world query image data sets with diverse representative queries show that our proposed re ranking approach can significantly improve initial search results and outperform several existing re ranking approaches

reconstruction of structurally incomplete matrices with reweighted low rank and sparsity priors most matrix reconstruction methods assume that missing entries randomly distribute in the incomplete matrix and the low rank prior or its variants are used to well pose the problem however in practical applications missing entries are structurally rather than randomly distributed and cannot be handled by the rank minimization prior individually to remedy this this paper introduces new matrix reconstruction models using double priors on the latent matrix named reweighted low rank and sparsity priors relasp in the proposed relasp models the matrix is regularized by a low rank prior to exploit the inter column and inter row correlations and its columns rows are regularized by a sparsity prior under a dictionary to exploit intra column row correlations both the low rank and sparse priors are reweighted on the fly to promote low rankness and sparsity respectively numerical algorithms to solve our relasp models are derived via the alternating direction method under the augmented lagrangian multiplier framework results on synthetic data image restoration tasks and seismic data interpolation show that the proposed relasp models are quite effective in recovering matrices degraded by highly structural missing and various types of noise complementing the classic matrix reconstruction models that handle random missing only

incomplete conjunctive information abstract many information systems capable of handling incomplete or fuzzy information manipulate objects with single valued attributes information is then said to be disjunctive information is said to be conjunctive when pertaining to many valued attributes while a piece of incomplete disjunctive information is easily represented by means of a set of mutually exclusive possible values modeling incomplete conjunctive information theoretically leads to consider families of sets since attributes are then set valued under complete information some proposals are made in order to efficiently and rigorously represent incomplete conjunctive information and deal with query evaluation especially in the case where only upper and or lower bounds of the set of values of a many valued attribute are known applications of this approach can be expected for the processing of time intervals as well as spatial reasoning among other topics in knowledge base management

ldahash improved matching with smaller descriptors sift like local feature descriptors are ubiquitously employed in computer vision applications such as content based retrieval video analysis copy detection object recognition photo tourism and 3d reconstruction feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations in particular affine and intensity scale transformations however real transformations that an image can undergo can only be approximately modeled in this way and thus most descriptors are only approximately invariant in practice second descriptors are usually high dimensional e g sift is represented as a 128 dimensional vector in large scale retrieval and matching problems this can pose challenges in storing and retrieving descriptor data we map the descriptor vectors into the hamming space in which the hamming metric is used to compare the resulting representations this way we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples we show extensive experimental validation demonstrating the advantage of the proposed approach

multivalued dependencies in fuzzy relational databases and lossless join decomposition abstract the fuzzy multivalued dependency is defined on the lines of classical multivalued dependency to resolve the redundancy and inconsistency in fuzzy databases the implication problem of fmvd s has been examined and a set of sound and complete inference axioms has been proposed we next examine lossless join problem of fuzzy relations in the presence of fuzzy functional depandencies and fuzzy multivalued dependencies and obtain decomposition of relation schemes

point location in arrangements of hyperplanes we present a solution to the point location problem in arrangements of hyperplanes in ed with running time o d5 log n and space o nd for arbitrary 0 where n is the number of hyperplanes the main result is the d5 factor in the expression for the running time all previously known algorithms are exponential in d or log n this leads to nonuniform polynomial algorithms for np complete problems

proximity relations in the fuzzy relational database model abstract the fuzzy relational model of buckles and petry is a rigorous scheme for incorporating non ideal or fuzzy information in a relational database in addition to providing a consistent scheme for representing fuzzy information in the relational structure the model possesses two critical properties that hold for classical relational databases these properties are that no two tuples have identical interpretations and each relational operation has a unique result the fuzzy relational model relies on similarity relations for each scalar domain in the fuzzy database these relations are reflexive symmetric and max min transitive in addition to introducing fuzziness into the relational model each similarity relation induces equivalence classes in its domain it is the existence of these equivalence classes that provides the model with the important properties possessed by classical relational databases in this paper we extend the fuzzy relational database model of buckles and petry to deal with proximity relations for scalar domains since reflexivity and symmetry are the only constraints placed on proximity relations they generalize the notion of similarity relations we show that it is possible to induce equivalence classes from proximity relations thus the nice properties of the fuzzy relational model of buckles and petry are preserved furthermore the removal of the max min transitivity restriction also provides database users with more freedom to express their value structures

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

gefred a generalized model of fuzzy relational databases abstract in this paper we present a fuzzy relational databases model whose main characteristics are the integration of previous models in the same framework representation capabilities for a wide series of fuzzy information and a coherent and flexible handling of it this model aims to solve each problem of representation and handling of fuzzy information taking into account its specific nature and hence it allows the user to choose the comparison operator and the fuzzy compatibility measure to be used in a query besides it permits the user to specify the precision with which the conditions involved in a query are satisfied

algorithms for inversion mod p k p k this article describes and analyzes all existing algorithms for computing x a 1 pmod p k x a 1 mod p k for a prime p p and also introduces a new algorithm based on the exact solution of linear equations using p p adic expansions the algorithm starts with the initial value c a 1 pmod p c a 1 mod p and iteratively computes the digits of the inverse x a 1 pmod p k x a 1 mod p k in base p p the mod 2 version of the algorithm is more efficient than all existing algorithms for small values of k k moreover it stands out as being the only one that works for any p p any k k and digit by digit while the new algorithm is asymptotically worse off it requires the minimal number of arithmetic operations just a single addition per step as compared to all existing algorithms

a domain calculus for fuzzy relational databases abstract a complete relational calculus is introduced for similarity based fuzzy relational databases the ordinary domain calculus is chosen as the basis from which to develop the fuzzy counterpart because it tends to be closer to natural language than tuple calculus a constructive proof is used to show that the fuzzy relational algebra can be mapped into the calculus the proof is significant from the standpoint of demonstrating implementability of the calculus as a query language

modular multiplication without trial division let n 1 we present a method for multiplying two integers called n residues modulo n while avoiding division by n n residues are represented in a nonstandard way so this method is useful only if several computations are done modulo one n the addition and subtraction algorithms are unchanged 1 description some algorithms 1 2 4 5 require extensive modular arith metic we propose a representation of residue classes so as to speed modular multiplication without affecting the modular addition and subtraction algorithms other recent algorithms for modular arithmetic appear in 3 6 fix n 1 define an a residue to be a residue class modulo n select a radix r coprime to n possibly the machine word size or a power thereof such that r n and such that computations modulo r are inexpensive to process let r l and n be integers satisfying 0 n then return t n else return t to validate redc observe mn tn n tmod r so t is an integer also tr tmod n so t tr x mod n thirdly 0 t mn rn rn so 0 t 2n if r and n are large then t mn may exceed the largest double precision value one can circumvent this by adjusting m so r m 0 given two numbers x and y between 0 and n 1 inclusive let z redc xy then z xy r x mod n so xr l yr x zrx mod n also 0 z n so z is the product of x and y in this representation other algorithms for operating on n residues in this representation can be derived from the algorithms normally used the addition algorithm is unchanged since xr x yr x zr x mod n if and only if x y z mod n also unchanged are

non transitive fuzzy dependencies i in this work we deal with the problem of defining projection and join operators in a fuzzy database so that they allow us to compress the information given in a relation r of such a database such a compression is possible when a relation satisfies one kind of fuzzy functional dependency f f d such projection and join operators allow us to decompose the original relation r into two new relations in such a way that the amount of information to store is less than originally with r in this process of decomposition there are two main properties to be achieved on the one hand we must be able to test the fuzzy dependency just by looking at one of the projections as it has less records than r this represents a computational advantage on the other hand the join of both projections is such that we can recover the information we had in r but with fuzzier values in order to measure the degree of increasing fuzziness the concept of granularity level is used the definition of fuzzy dependency does not verify the transitivity inference axiom

homotopies for intersecting solution components of polynomial systems we show how to use numerical continuation to compute the intersection c a cap b of two algebraic sets a and b where a b and c are numerically represented by witness sets en route to this result we first show how to find the irreducible decomposition of a system of polynomials restricted to an algebraic set the intersection of components a and b then follows by considering the decomposition of the diagonal system of equations u v 0 restricted to u v in a times b an offshoot of this new approach is that one can solve a large system of equations by finding the solution components of its subsystems and then intersecting these it also allows one to find the intersection of two components of the two polynomial systems which is not possible with any previous numerical continuation approach

upper and lower images of a fuzzy set induced by a fuzzy relation applications to fuzzy inference and diagnosis in fuzzy set theory the image of a fuzzy set induced by a fuzzy relation is usually obtained by a sup t norm composition this corresponds to the upper image which gathers the elements in relation with at least one element of the fuzzy set however the dual point of view leading to the definition of the lower image as the fuzzy set of elements in relation with all the elements of the fuzzy set whose image is computed is not often considered fuzzy sets and fuzzy relations depending on the situations can be interpreted either in a conjunctive manner or as subsets of mutually exclusive possible values for variables whose precise values are ill known disjunctive view the applications of upper and lower images are investigated in both interpretations the generalized modus ponens used in fuzzy rule based systems corresponds to the disjunctive view the interest of upper and lower images is also emphasized for diagnosis problems where the conjunctive interpretation is encountered

twofold fuzzy sets and rough sets some issues in knowledge representation abstract this paper deals with the representation of sets where the membership of some elements may be ill known rather than just a matter of degree as in a fuzzy set the notion of a twofold fuzzy set is introduced when the relevant information for determining the membership status is incomplete a twofold fuzzy set is made of a nested pair of fuzzy sets the one which gathers the elements which more or less necessarily belong and the one which gathers the elements which more or less possibly belong twofold fuzzy sets are compared from a frontal and from a semantical point of view with other proposals and particularly with the notion of a rough set recently introduced by pawlak set operations of twofold fuzzy sets are discussed and the cardinality of a twofold fuzzy set is defined twofold fuzzy relations are also introduced finally various applications of twofold fuzzy sets in knowledge representation are briefly discussed

efficient refinement of uncertain data by fuzzy integrity constraints abstract fuzzy data models were proposed to handle uncertain data based on a set of fuzzy functional dependencies the fuzzy values in a fuzzy relation may be refined into clearer ones in this paper we develop efficient algorithms for the refinement process a dependency graph is defined for a set of fuzzy functional dependencies by this graph an efficient refinement sequence can be determined these algorithms are proved correct and efficient

on the impact of regular functional dependencies when moving to a possibilistic database framework this paper is situated in the area of fuzzy databases i e databases containing imprecise information more precisely it deals with the notion of a functional dependency when data involved in this type of property are possibly imprecise contrary to previous works the idea is not to fuzzify the concept of a functional dependency in the view suggested here we rather consider regular functional dependencies and we study the impact of the presence of such fds on the insertion and handling of imprecise data