fast algorithms for computing tree lcs the lcs of two rooted ordered and labeled trees f and g is the largest forest that can be obtained from both trees by deleting nodes we present algorithms for computing tree lcs which exploit the sparsity inherent to the tree lcs problem assuming g is smaller than f our first algorithm runs in time o email protected height f height g lglg g where r is the number of pairs email protected f email protected g such that v and w have the same label our second algorithm runs in time o email protected lglg g where l is the size of the lcs of f and g for this algorithm we present a novel three dimensional alignment graph our third algorithm is intended for the constrained variant of the problem in which only nodes with zero or one children can be deleted for this case we obtain an o rhlglg g time algorithm where h height f height g

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

existence of some extremal self dual codes two new singly even extremal self dual codes are constructed a 52 26 10 code and a 54 27 10 code

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

duality for modules over finite rings and applications to coding theory this paper sets a foundation for the study of linear codes over finite rings the finite frobenius rings are singled out as the most appropriate for coding theoretic purposes because two classical theorems of mac williams the extension theorem and the mac williams identities generalize from finite fields to finite frobenius rings it is over frobenius rings that certain key identifications can be made between the ring and its complex characters

on the algebraic structure of quasi cyclic codes i finite fields a new algebraic approach to quasi cyclic codes is introduced the key idea is to regard a quasi cyclic code over a field as a linear code over an auxiliary ring by the use of the chinese remainder theorem crt or of the discrete fourier transform dft that ring can be decomposed into a direct product of fields that ring decomposition in turn yields a code construction from codes of lower lengths which turns out to be in some cases the celebrated squaring and cubing constructions and in other cases the u spl upsi u spl upsi and vandermonde constructions all binary extended quadratic residue codes of length a multiple of three are shown to be attainable by the cubing construction quinting and septing constructions are introduced other results made possible by the ring decomposition are a characterization of self dual quasi cyclic codes and a trace representation that generalizes that of cyclic codes

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

a space efficient algorithm for the longest common subsequence in k length substrings abstract two space efficient algorithms to solve the l c s k problem and l c s k problem are presented in this paper the algorithms improve the time and space complexities of the algorithms of benson et al 4 the space cost of the first algorithm to solve the l c s k problem is reduced from o n 2 to o k n if the size of the two input sequences are both n the time and space costs of the second algorithm to solve the l c s k problem are both improved the time cost is reduced from o k n 2 to o n 2 and the space cost is reduced from o n 2 to o k n in the case of k o 1 the two algorithms are both linear space algorithms

finding similar consensus between trees an algorithm and a distance hierarchy abstract the problem of finding this similar consensus also known as the largest approximately common substructures of two trees arises in many pattern recognition applications this paper presents a dynamic programming algorithm to solve the problem based on the distance measure originated from tanaka and tanaka the algorithm runs as fast as the best known algorithm for comparing two trees using tanaka s distance measure when the allowed distance between the common substructures is a constant independent of the input trees in addition we establish a hierarchy among tanaka s distance measure and three other edit based distance measures published in the literature

ordered and unordered tree inclusion the following tree matching problem is considered given labeled trees p and t can p be obtained from t by deleting nodes deleting a node u entails removing all edges incident to u and if u has a parent v replacing the edge from v to u by edges from v to the children of u the problem is motivated by the study of query languages for structured text databases simple solutions to this problem require exponential time for ordered trees an algorithm is presented that requires o p t time and space the corresponding problem for unordered trees is also considered and a proof of its np completeness is given an algorithm is presented for the unordered problem this algorithm works in o p t time if the out degrees of the nodes in p are bounded by a constant and in polynomial time if they are o log t

krawtchouk polynomials and universal bounds for codes and designs in hamming spaces universal bounds for the cardinality of codes in the hamming space f sub r sup n with a given minimum distance d and or dual distance d are stated a self contained proof of optimality of these bounds in the framework of the linear programming method is given the necessary and sufficient conditions for attainability of the bounds are found the parameters of codes satisfying these conditions are presented in a table a new upper bound for the minimum distance of self dual codes and a new lower bound for the crosscorrelation of half linear codes are obtained

on the 24 12 10 quaternary code and binary codes with an automorphism having two cycles a general decomposition theorem is given for codes over finite fields which have an automorphism of a given type such codes can be decomposed as direct sums of subcodes which may be viewed as shorter length codes over extension fields if such a code is self dual sometimes the subcodes are also this decomposition is applied to prove that the self dual 24 12 10 quaternary code has no automorphism of order 3 this decomposition is also applied to count the number of equivalent 2r r and 2r 2r 1 self dual binary codes with an automorphism of prime order r

rapid and brief communication a note on kernel uncorrelated discriminant analysis in this paper we give a theoretical analysis on kernel uncorrelated discriminant analysis kuda and point out the drawbacks underlying the current kuda algorithm which was recently introduced by liang and shi pattern recognition 38 2 2005 307 310 then we propose an effective algorithm to overcome these drawbacks the effectiveness of the proposed method was confirmed by experiments

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

classification of quaternary hermitian self dual codes of length 20 a classification of quaternary hermitian self dual codes of length 20 is given using this classification a classification of extremal quaternary hermitian self dual codes of length 22 is also given

mblda a novel multiple between class linear discriminant analysis abstract linear discriminant analysis lda with its extensions is a group of classical methods in dimensionality reduction for supervised learning however when some classes are far away from the others it may be difficult to find the optimal direction by lda because of the average between class scatter moreover ldas are always time consuming for high dimensional problem since the involved generalized eigenvalue problem is needed to be solved in this paper a multiple between class linear discriminant analysis mblda is proposed for dimensionality reduction mblda finds the transformation directions by approximating the solution to a min max programming problem leading to well separability in the reduced space with a fast learning speed on the high dimensional problem it is proved theoretically that the proposed method can deal with the special generalized eigenvalue problem by solving a underdetermined homogeneous system of linear equations experimental results on the artificial and benchmark datasets show that mblda can not only reduce the dimension to a powerful linear discriminant level but also have a fast learning speed

ell_ 1 norm heteroscedastic discriminant analysis under mixture of gaussian distributions fisher s criterion is one of the most popular discriminant criteria for feature extraction it is defined as the generalized rayleigh quotient of the between class scatter distance to the within class scatter distance consequently fisher s criterion does not take advantage of the discriminant information in the class covariance differences and hence its discriminant ability largely depends on the class mean differences if the class mean distances are relatively large compared with the within class scatter distance fisher s criterion based discriminant analysis methods may achieve a good discriminant performance otherwise it may not deliver good results moreover we observe that the between class distance of fisher s criterion is based on the ell 2 norm which would be disadvantageous to separate the classes with smaller class mean distances to overcome the drawback of fisher s criterion in this paper we first derive a new discriminant criterion expressed as a mixture of absolute generalized rayleigh quotients based on a bayes error upper bound estimation where mixture of gaussians is adopted to approximate the real distribution of data samples then the criterion is further modified by replacing ell 2 norm with ell 1 one to better describe the between class scatter distance such that it would be more effective to separate the different classes moreover we propose a novel ell 1 norm heteroscedastic discriminant analysis method based on the new discriminant analysis l1 hda gm for heteroscedastic feature extraction in which the optimization problem of l1 hda gm can be efficiently solved by using the eigenvalue decomposition approach finally we conduct extensive experiments on four real data sets and demonstrate that the proposed method achieves much competitive results compared with the state of the art methods

decompositions and extremal type ii codes over z sub 4 in previous work by huffman and by yorgov 1983 a decomposition theory of self dual linear codes c over a finite field f sub q was given when c has a permutation automorphism of prime order r relatively prime to q we extend these results to linear codes over the galois ring z sub 4 and apply the theory to z sub 4 codes of length 24 in particular we obtain 42 inequivalent 24 12 z sub 4 codes of minimum euclidean weight 16 which lead to 42 constructions of the leech lattice

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

circulant based extremal additive self dual codes over gf 4 it is well known that the problem of finding stabilizer quantum error correcting codes qecc is transformed into the problem of finding additive self orthogonal codes over the galois field gf 4 under a trace inner product our purpose is to classify the extremal additive circulant self dual codes of lengths up to 15 and construct good codes for lengths 16 spl les n spl les 27 we also classify the extremal additive 4 circulant self dual codes of lengths 4 6 8 12 14 and 16 and most codes of length 10 and construct good codes of even lengths up to 22 furthermore we classify the extremal additive bordered 4 circulant self dual codes of lengths 3 5 7 9 11 13 15 and 17 and construct good codes for lengths 19 21 23 and 25 we give the current status of known extremal or optimal additive self dual codes of lengths 12 to 27

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

on the automorphism group of a doubly even 72 36 16 code we prove that a putative doubly even 72 36 16 code has no automorphism of order 3 with fixed points moreover such a code has no automorphism of an odd order greater than 7 eventually we prove that 25 and 49 do not divide the order of its automorphism group

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

lcsk a refined similarity measure abstract in this paper we define a new similarity measure lcsk aiming at finding the maximal number of k length substrings matching in both input strings while preserving their order of appearance for which the traditional lcs is a special case where k 1 we examine this generalization in both theory and practice we first describe its basic solution and give an experimental evidence in real data for its ability to differentiate between sequences that are considered similar according to the lcs measure we then examine extensions of the lcsk definition to lcs in at least k length substrings lcs k and 2 dimensional lcsk and also define complementary edk and ed k distances

feature extraction using constrained maximum variance mapping in this paper an efficient feature extraction method named as constrained maximum variance mapping cmvm is developed the proposed algorithm can be viewed as a linear approximation of multi manifolds learning based approach which takes the local geometry and manifold labels into account the cmvm and the original manifold learning based approaches have a point in common that the locality is preserved moreover the cmvm is globally maximizing the distances between different manifolds after the local scatters have been characterized the proposed method focuses on developing a linear transformation that can maximize the dissimilarities between all the manifolds under the constraint of locality preserving compared to most of the up to date manifold learning based methods this trick makes contribution to pattern classification from two aspects on the one hand the local structure in each manifold is still kept on the other hand the discriminant information between manifolds can be explored finally feret face database cmu pie face database and usps handwriting data are all taken to examine the effectiveness and efficiency of the proposed method experimental results validate that the proposed approach is superior to other feature extraction methods such as linear discriminant analysis lda locality preserving projection lpp unsupervised discriminant projection udp and maximum variance projection mvp

there is no 24 12 10 self dual quaternary code an attempt at directly constructing a 24 12 10 extremal quaternary code is reported the attempt at directly constructing the generator matrix of the code is detailed it was found that no such code exists

scatter balance an angle based supervised dimensionality reduction subspace selection is widely applied in data classification clustering and visualization the samples projected into subspace can be processed efficiently in this paper we research the linear discriminant analysis lda and maximum margin criterion mmc algorithms intensively and analyze the effects of scatters to subspace selection meanwhile we point out the boundaries of scatters in lda and mmc algorithms to illustrate the differences and similarities of subspace selection in different circumstances besides the effects of outlier classes on subspace selection are also analyzed according to the above analysis we propose a new subspace selection method called angle linear discriminant embedding alde on the basis of angle measurement alde utilizes the cosine of the angle to get new within class and between class scatter matrices and avoids the small sample size problem simultaneously to deal with high dimensional data we extend alde to a two stage alde ts alde the synthetic data experiments indicate that alde can balance the within class and between class scatters and be robust to outlier classes the experimental results based on uci machine learning repository and image databases show that ts alde has a lower time complexity than alde while processing high dimensional data

classification of extremal self dual quaternary codes of lengths 30 and 32 we classify extremal hermitian self dual quaternary codes of lengths 30 and 32 with an automorphism of odd prime order we prove that there exists exactly one extremal hermitian self dual 30 15 12 quaternary code with a nontrivial automorphism of odd prime order up to equivalence the order of its automorphism group is 36 540 in fact this code is equivalent to the extended quadratic residue code we also prove that there exists no extremal hermitian self dual 32 16 12 quaternary code with a nontrivial automorphism of odd prime order

on 3 elements in monomial automorphism groups of quaternary codes a general theory is given for examining quaternary self dual codes having monomial automorphisms of orders that are a power of 3 a theory of decomposing such codes is given and applications of this theory are described this work extends similar work when the codes have nontrivial odd order permutation automorphisms

type ii codes even unimodular lattices and invariant rings we study self dual codes over the ring z sub 2k of the integers modulo 2k with relationships to even unimodular lattices modular forms and invariant rings of finite groups we introduce type ii codes over z sub 2k which are closely related to even unimodular lattices as a remarkable class of self dual codes and a generalization of binary type ii codes a construction of even unimodular lattices is given using type ii codes several examples of type ii codes are given in particular the first extremal type ii code over z sub 6 of length 24 is constructed which gives a new construction of the leech lattice the complete and symmetrized weight enumerators in genus g of codes over z sub 2k are introduced and the macwilliams identities for these weight enumerators are given we investigate the groups which fix these weight enumerators of type ii codes over z sub 2k and we give the molien series of the invariant rings of the groups for small cases we show that modular forms are constructed from complete and symmetrized weight enumerators of type ii codes shadow codes over z sub 2k are also introduced

new extremal self dual codes of lengths 36 and 38 there are two distinct weight enumerators for extremal singly even self dual 36 18 8 codes for each weight enumerator only one extremal self dual code is previously known in this correspondence we construct several new extremal singly even self dual 36 18 8 codes for each weight enumerator we also construct a number of new extremal singly even self dual 38 19 8 codes

type iv self dual codes over rings we study type iv self dual codes over the commutative rings of order 4 gleason type theorems of type iv codes and their shadow codes are investigated a mass formula of type iv codes over these rings are given we give a classification of type tv codes over z sub 4 and f2 uf sub 2 for reasonable lengths we also construct a number of optimal type tv codes

face recognition based on the uncorrelated discriminant transformation abstract the extraction of discriminant features is the most fundamental and important problem in face recognition this paper presents a method to extract optimal discriminant features for face images by using the uncorrelated discriminant transformation and kl expansion experiments on the orl database and the nust603 database have been performed experimental results show that the uncorrelated discriminant transformation is superior to the foley sammon discriminant transformation and the new method to extract uncorrelated discriminant features for face images is very effective an error rate of 2 5 is obtained with the experiments on the orl database an average error rate of 1 2 is obtained with the experiments on the nust603 database experiments show that by extracting uncorrelated discriminant features face recognition could be performed with higher accuracy on lower than 16 16 resolution mosaic images it is suggested that for the uncorrelated discriminant transformation the optimal face image resolution can be regarded as the resolution m n which makes the dimensionality n mn of the original image vector space be larger and closer to the number of known face classes

locally linear discriminant embedding an efficient method for face recognition in this paper an efficient feature extraction method named as locally linear discriminant embedding llde is proposed for face recognition it is well known that a point can be linearly reconstructed by its neighbors and the reconstruction weights are under the sum to one constraint in the classical locally linear embedding lle so the constrained weights obey an important symmetry for any particular data point they are invariant to rotations rescalings and translations the latter two are introduced to the proposed method to strengthen the classification ability of the original lle the data with different class labels are translated by the corresponding vectors and those belonging to the same class are translated by the same vector in order to cluster the data with the same label closer they are also rescaled to some extent so after translation and rescaling the discriminability of the data will be improved significantly the proposed method is compared with some related feature extraction methods such as maximum margin criterion mmc as well as other supervised manifold learning based approaches for example ensemble unified lle and linear discriminant analysis en ullelda locally linear discriminant analysis llda experimental results on yale and cmu pie face databases convince us that the proposed method provides a better representation of the class information and obtains much higher recognition accuracies

faster scaling algorithms for network problems this paper presents algorithms for the assignment problem the transportation problem and the minimum cost flow problem of operations research the algorithms find a minimum cost solution yet run in time close to the best known bounds for the corresponding problems without costs for example the assignment problem equivalently minimum cost matching in a bipartite graph can be solved in o sqrt nm log nn time where n m and n denote the number of vertices number of edges and largest magnitude of a cost costs are assumed to be integral the algorithms work by scaling as in the work of goldberg and tarjan in each scaled problem an approximate optimum solution is found rather than an exact optimum

cubic self dual binary codes we study binary self dual codes with a fixed point free automorphism of order three all binary codes of that type can be obtained by a cubic construction that generalizes turyn s we regard such cubic codes of length 3 spl lscr as codes of length spl lscr over the ring f sub 2 spl times f sub 4 classical notions of type ii codes shadow codes and weight enumerators are adapted to that ring two infinite families of cubic codes are introduced new extremal binary codes in lengths spl les 66 are constructed by a randomized algorithm necessary conditions for the existence of a cubic 72 36 16 type ii code are derived

there exists no hermitian self dual quaternary 26 13 10 sub 4 code hermitian self dual quaternary codes exist for all even lengths the smallest length for which the maximum possible minimum distance of such codes is undetermined is 26 it is then either 8 or 10 by exhaustive computer search this case is settled it is shown that minimum distance 10 is impossible for these parameters

monomials of orders 7 and 11 cannot be in the group of a 24 12 10 self dual quaternary code corresp it is an interesting open question whether a self dual quaternary 24 12 10 code c exists it was shown by conway and pless that the only primes which can be orders of permutations in the group of c are 11 7 and 3 in this correspondence we eliminate 11 and 7 not only as permutations but also as orders of monomials in the group of c this is done by reducing the problems to the consideration of several codes and finding low weight vectors in these codes

a method for constructing inequivalent self dual codes with applications to length 56 necessary and sufficient conditions are presented for two doubly even codes with an automorphism of odd prime order to be equivalent under certain assumptions for the codes as an application we obtain all extremal doubly even codes of length 56 with an automorphism of order 13 sixteen such codes are inequivalent

an efficient algorithm to solve the small sample size problem for lda in this paper we present an efficient algorithm to solve the most discriminant vectors of lda for high dimensional data set the experiments on orl face database confirm the effectiveness of the proposed method

classification of extremal and s extremal binary self dual codes of length 38 in this paper we classify all extremal and s extremal binary self dual codes of length 38 there are exactly 2744 extremal self dual codes two s extremal codes and 1730 s extremal codes we obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self dual codes of length 36 and from a generalization of this recursive algorithm for the shadow the classification of extremal codes permits to achieve the classification of all extremal codes with

efficient two dimensional pattern matching in the presence of errors abstract we give an algorithm for two dimensional pattern matching in the presence of errors we find that the complexity of our algorithm is o kn 1 n 2 log n 2 n 1 2 n 2 kn 1 m 1 m 2 where the pattern is an n 1 n 2 array the text is an m 1 m 2 array and k is the number of mismatches allowed

on extremal self dual quaternary codes of lengths 18 to 28 ii a general decomposition theorem is given for self dual codes over finite fields that have a permutation automorphism of a given form such a code can be decomposed as a direct sum of subcodes that may be viewed as shorter length codes over extension fields where the dual of each direct summand is also a direct summand situations in which it is easy to distinguish such codes are also presented these results are used to enumerate some of the extremal quaternary self dual codes of lengths 18 20 22 26 and 28

characterization of quaternary extremal codes of lengths 18 and 20 we prove that up to equivalence there is a unique extremal quaternary hermitian self dual code of length 18 and that there are two inequivalent extremal quaternary hermitian self dual codes of length 20

optimal quaternary linear rate 1 2 codes of length spl les 18 we classify all optimal linear n n 2 d codes over f sub 4 up to length 18 in particular we show that there is a unique optimal 12 6 6 code and three optimal 16 8 7 codes up to equivalence

a constrained edit distance algorithm between semi ordered trees in this paper we propose a formal definition of a new class of trees called semi ordered trees and a polynomial dynamic programming algorithm to compute a constrained edit distance between such trees the core of the method relies on a similar approach to compare unordered kaizhong zhang a constrained edit distance between unordered labeled trees algorithmica 15 1996 205 222 and ordered trees kaizhong zhang algorithms for the constrained editing distance between ordered labeled trees and related problems pattern recognition 28 3 1995 463 474 the method is currently applied to evaluate the similarity between architectures of apple trees vincent segura aida ouangraoua pascal ferraro evelyne costes comparison of tree architecture using tree edit distances application to two year old apple tree euphytica 161 2007 155 164

on extremal self dual ternary codes of lengths 28 to 40 the extremal self dual ternary codes of lengths 28 32 and 36 with monomial automorphisms of prime order r or 5 and of length 40 with monomial automorphisms of prime order r 5 are enumerated for each length and prime considered all inequivalent extremal codes with an automorphism of that order are found

complete large margin linear discriminant analysis using mathematical programming approach in this paper we develop a novel dimensionality reduction dr framework coined complete large margin linear discriminant analysis clmlda inspired by several recently proposed dr methods clmlda constructs two mathematical programming models by maximizing the minimum distance between each class center and the total class center respectively in the null space of within class scatter matrix and its orthogonal complementary space in this way clmlda not only makes full use of the discriminative information contained in the whole feature space but also overcome the weakness of linear discriminant analysis lda in dealing with the class separation problem the solutions of clmlda follow from solving two nonconvex optimization problems each of which is transformed to a series of convex quadratic programming problems by using the constrained concave convex procedure first and then solved by off the shelf optimization toolbox experiments on both toy and several publicly available databases demonstrate its feasibility and effectiveness

a new lda based face recognition system which can solve the small sample size problem a new lda based face recognition system is presented in this paper linear discriminant analysis lda is one of the most popular linear projection techniques for feature extraction the major drawback of applying lda is that it may encounter the small sample size problem in this paper we propose a new lda based technique which can solve the small sample size problem we also prove that the most expressive vectors derived in the null space of the within class scatter matrix using principal component analysis pca are equal to the optimal discriminant vectors derived in the original space using lda the experimental results show that the new lda process improves the performance of a face recognition system signi cantly 2000 pattern recognition society published by elsevier science ltd all rights reserved

maximum agreement subtree in a set of evolutionary trees metrics and efficient algorithms the maximum agreement subtree approach is one method of reconciling different evolutionary trees for the same set of species an agreement subtree enables choosing a subset of the species for whom the restricted subtree is equivalent under a suitable definition in all given evolutionary trees recently dynamic programming ideas were used to provide polynomial time algorithms for finding a maximum homeomorphic agreement subtree of two trees generalizing these methods to sets of more than two trees yields algorithms that are exponential in the number of trees unfortunately it turns out that in reality one is usually presented with more than two trees sometimes as many as thousands of trees in this paper we prove that the maximum homeomorphic agreement subtree problem is cal np complete for three trees with unbounded degrees we then show an approximation algorithm of time o kn5 for choosing the species that are not in a maximum agreement subtree of a set of k trees our approximation is guaranteed to provide a set that is no more than 4 times the optimum solution while the set of evolutionary trees may be large in practice the trees usually have very small degrees typically no larger than three we develop a new method for finding a maximum agreement subtree of k trees of which one has degree bounded by d this new method enables us to find a maximum agreement subtree in time o knd 1 n2d

a comparison of generalized linear discriminant analysis algorithms linear discriminant analysis lda is a dimension reduction method which finds an optimal linear transformation that maximizes the class separability however in undersampled problems where the number of data samples is smaller than the dimension of data space it is difficult to apply lda due to the singularity of scatter matrices caused by high dimensionality in order to make lda applicable several generalizations of lda have been proposed recently in this paper we present theoretical and algorithmic relationships among several generalized lda algorithms and compare their computational complexities and performances in text classification and face recognition towards a practical dimension reduction method for high dimensional data an efficient algorithm is proposed which reduces the computational complexity greatly while achieving competitive prediction accuracies we also present nonlinear extensions of these lda algorithms based on kernel methods it is shown that a generalized eigenvalue problem can be formulated in the kernel based feature space and generalized lda algorithms are applied to solve the generalized eigenvalue problem resulting in nonlinear discriminant analysis performances of these linear and nonlinear discriminant analysis algorithms are compared extensively

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

optimal double circulant self dual codes over f sub 4 optimal double circulant self dual codes over f sub 4 have been found for each length n spl les 40 for lengths n spl les 14 20 22 24 28 and 30 these codes are optimal self dual codes for length 26 the code attains the highest known minimum weight for n spl ges 32 the codes presented provide the highest known minimum weights the 36 18 12 self dual code improves the lower bound on the highest minimum weight for a 36 18 linear code

fast algorithms for finding nearest common ancestors we consider the following problem given a collection of rooted trees answer on line queries of the form what is the nearest common ancester of vertices x and y we show that any pointer machine that solves this problem requires omega log log n time per query in the worst case where n is the total number of vertices in the trees on the other hand we present an algorithm for a random access machine with uniform cost measure and a bound of omega log n on the number of bits per word that requires o 1 time per query and o n preprocessing time assuming that the collection of trees is static for a version of the problem in which the trees can change between queries we obtain an almost linear time and linear space algorithm

regularized max min linear discriminant analysis several dimensionality reduction methods based on the max min idea have been proposed in recent years and can obtain good classification performance in this paper inspired by the idea we develop max min linear discriminant analysis mmlda which maximizes the minimum ratio of each two class scatter measure to the within class scatter measure however the method ignores equal emphasis on the distances between class centers and there may be room to improve the classification performance we then propose regularized max min linear discriminant analysis rmmlda which introduces the shannon entropy and the corresponding distance difference regularization terms based on mmlda the changing trends of distances between class centers can be precisely controlled in optimization and the separation between classes can be emphasized approximately equally as a result rmmlda may obtain better classification performance experiments on synthetic data sets and three publicly available data sets demonstrate its effectiveness highlightswe propose max min linear discriminant analysis we present regularized max min linear discriminant analysis using shannon entropy the improved form can obtain better classification results for high dimensional data

a survey on tree edit distance and related problems we survey the problem of comparing labeled trees based on simple local operations of deleting inserting and relabeling nodes these operations lead to the tree edit distance alignment distance and inclusion problem for each problem we review the results available and present in detail one or more of the central algorithms for solving the problem

simple fast algorithms for the editing distance between trees and related problems ordered labeled trees are trees in which the left to right order among siblings is significant the distance between two ordered trees is considered to be the weighted number of edit operations insert delete and modify to transform one tree to another the problem of approximate tree matching is also considered specifically algorithms are designed to answer the following kinds of questions 1 what is the distance between two trees 2 what is the minimum distance between t 1 and t 2 when zero or more subtrees can be removed from t 2 3 let the pruning of a tree at node n mean removing all the descendants of node n the analogous question for prunings as for subtrees is answered a dynamic programming algorithm is presented to solve the three questions in sequential time o t 1 times t 2 times min textit depth t 1 textit leaves t 1 times min textit depth t 2 textit leaves t 2 and space o t 1 times t 2 compared with o t 1 times t 2 t

new self dual codes over gf 4 with the highest known minimum weights the purpose of this correspondence is to construct new hermitian self dual codes over gf 4 of lengths 22 24 26 32 and 34 which have the highest known minimum weights in particular for length 22 we construct eight new extremal self dual 22 11 8 codes over gf 4 which do not have a nontrivial automorphism of odd order the existence of such codes has been left open since 1991 by huffman

the existence of certain extremal 54 27 10 self dual codes some new extremal binary 54 27 10 self dual codes are constructed using automorphisms of order 7

a 72 36 16 doubly even code does not have an automorphism of order 11 corresp we prove that there does not exist a 72 36 16 doubly even code with an automorphism of order 11 if such a code exists it can be decomposed as a direct sum of two codes one can be viewed as a self dual 12 6 4 binary code and the other a self dual 6 3 4 code over f 1024 this is shown to be impossible

algorithms for the constrained editing distance between ordered labeled trees and related problems abstract this paper considers the problem of computing a constrained editing distance between ordered labeled trees this distance metric can be applied to pattern recognition syntactic tree comparison classification tree comparison and other applications the problem of approximate ordered tree matching is also considered we present optimal algorithms for solving these problems in sequential time o t1 t2

generalized lcs the longest common subsequence lcs is a well studied problem having a wide range of implementations its motivation is in comparing strings it has long been of interest to devise a similar measure for comparing higher dimensional objects and more complex structures in this paper we study the longest common substructure of two matrices and show that this problem is np hard we also study the longest common subforest problem for multiple trees including a constrained version as well we show np hardness for k 2 unordered trees in the constrained lcs we also give polynomial time algorithms for ordered trees and prove a lower bound for any decomposition strategy for k trees

automorphisms of codes with applications to extremal doubly even codes of length 48 general results on automorphisms of self dual binary codes are given these results are applied to the study of extremal self dual doubly even binary codes of length 48 the main theorem proved is that an extremal self dual doubly even code of length 48 with a nontrivial automorphism of odd order is equivalent to the extended quadratic residue code interesting constructions of the binary extended golay code as well as a conjecture about a possible connection between an extremal self dual doubly even code of length 72 and an extremal quaternary code of length 24 arc yielded by techniques used in the proof

class incremental generalized discriminant analysis generalized discriminant analysis gda is the nonlinear extension of the classical linear discriminant analysis lda via the kernel trick mathematically gda aims to solve a generalized eigenequation problem which is always implemented by the use of singular value decomposition svd in the previously proposed gda algorithms a major drawback of svd however is the difficulty of designing an incremental solution for the eigenvalue problem moreover there are still numerical problems of computing the eigenvalue problem of large matrices in this article we propose another algorithm for solving gda as for the case of small sample size problem which applies qr decomposition rather than svd a major contribution of the proposed algorithm is that it can incrementally update the discriminant vectors when new classes are inserted into the training set the other major contribution of this article is the presentation of the modified kernel gram schmidt mkgs orthogonalization algorithm for implementing the qr decomposition in the feature space which is more numerically stable than the kernel gram schmidt kgs algorithm we conduct experiments on both simulated and real data to demonstrate the better performance of the proposed methods

rapid and brief communication generalized null space uncorrelated fisher discriminant analysis for linear dimensionality reduction we propose a generalized null space uncorrelated fisher discriminant analysis gnufda technique integrating the uncorrelated discriminant analysis and weighted pairwise fisher criterion the gnufda can effectively deal with the small sample size problem and perform satisfactorily when the dimensionality of the null space decreases with increase in the number of training samples per class and or classes c the proposed gnufda can extract at most c 1 optimal uncorrelated discriminative vectors without being influenced by the null space dimensionality

identifying approximately common substructures in trees based on a restricted edit distance in this paper we present a dynamic programming algorithm for identifying the largest approximately common substructures lacss of two ordered labeled trees we consider a substructure of a tree t to be a connected subgraph of t given two trees t1 t2 and an integer d the lacs problem is to find a substructure u1 of t1 and a substructure u2 of t2 such that u1 is within distance d of u2 and where there does not exist any other substructure v1 of t1 and v2 of t2 such that v1 and v2 satisfy the distance restriction and the sum of the sizes of v1 and v2 is greater than the sum of the sizes of u1 and u2 the distance measure considered in the paper is a restricted edit distance originated from selkow the lacs problem is motivated by the studies of program and document comparison the proposed algorithm solves the problem in time o d2 t1 t2 which is as fast as the best known algorithm for calculating selkow s distance of two trees when the distance allowed in the common substructures is a constant independent of the input trees

homeomorphic alignment of weighted trees motion capture a currently active research area needs estimation of the pose of the subject for this purpose we match the tree representation of the skeleton of the 3d shape to a pre specified tree model unfortunately the tree representation can contain vertices that split limbs in multiple parts which do not allow a good match by usual methods to solve this problem we propose a new alignment taking into account the homeomorphism between trees rather than the isomorphism as in prior works then we develop several computationally efficient algorithms for reaching real time motion capture

waveform correlation by tree matching a waveform correlation scheme is presented the scheme consists of four parts 1 the representation of waveforms by trees 2 the definition of basic operations on tree nodes and tree distance 3 a tree matching algorithm and 4 a backtracking procedure to find the best node to node correlation this correlation scheme has been implemented results show that the scheme has the capability of handling distortions that result from stretching or shrinking of intervals or from missing intervals

fast parallel and serial multidimensional approximate array matching abstract consider the multidimensional array matching problem where differences between characters of the pattern and characters of the text are permitted a difference may be due to a mismatch between a text and pattern character superfluous text character or superfluous pattern character given a d dimensional array of size nd text and a d dimensional array of size md pattern we present the following algorithms for a given k find all occurrences of the pattern in the text with at most k differences our serial algorithm runs in time o nd dk k2 and the parallel algorithm runs in time o d dlog n k k2 using nd processors if superfluous characters are not allowed and the only permitted errors are mismatches we solve the problem serially in time o nddk and in parallel in time o d dlogn k using nd processors we present an alternate algorithm for the mismatches problem which runs serially in time o 2dndlog2 m and in parallel in time o d log n using nd processors this algorithm is more efficient for large k we also give an efficient solution to the close match problem here a mismatch weight function f 0 1 is assigned the weight function gives weight to the mismatches some mismatches being worse than others we present a serial algorithm for finding all appearances of the pattern in the text with a bounded total error in time o 2dnd log2 m our parallel algorithm is again of time complexity o d log n using nd processors

feature extraction using two dimensional local graph embedding based on maximum margin criterion in this paper we propose a novel method for image feature extraction namely the two dimensional local graph embedding which is based on maximum margin criterion and thus not necessary to convert the image matrix into high dimensional image vector and directly avoid computing the inverse matrix in the discriminant criterion this method directly learns the optimal projective vectors from 2d image matrices by simultaneously considering local graph embedding and maximum margin criterion the proposed method avoids huge feature matrix problem in eigenfaces fisherfaces laplacianfaces maximum margin criterion mmc and inverse matrix in 2d fisherfaces 2d laplacianfaces and 2d local graph embedding discriminant analysis 2dlgeda so that computational time would be saved for feature extraction experimental results on the yale and the usps databases show the effectiveness of the proposed method under various experimental conditions

a new upper bound on the minimal distance of self dual codes it is shown that the minimal distance d of a binary self dual code of length n or 74 is at most 2 n 6 10 this bound is a consequence of some new conditions on the weight enumerator of a self dual code obtained by considering a particular translate of the code called its shadow these conditions also enable one to find the highest possible minimal distance of a self dual code for all n or 60 to show that self dual codes with d or 22 with d or 8 exist precisely for n 24 32 and n or 26 and with d or 10 exist precisely for n or 46 and to show that there are exactly eight self dual codes of length 32 with d 8 several of the self dual codes of length 34 have trivial group this appears to be the smallest length where this can happen