target detection based on a dynamic subspace for hyperspectral target detection it is usually the case that only part of the targets pixels can be used as target signatures so can we use them to construct the most proper background subspace for detecting all the probable targets in this paper a dynamic subspace detection dsd method which establishes a multiple detection framework is proposed in each detection procedure blocks of pixels are calculated by the random selection and the succeeding detection performance distribution analysis manifold analysis is further used to eliminate the probable anomalous pixels and purify the subspace datasets and the remaining pixels construct the subspace for each detection procedure the final detection results are then enhanced by the fusion of target occurrence frequencies in all the detection procedures experiments with both synthetic and real hyperspectral images hsi evaluate the validation of our proposed dsd method by using several different state of the art methods as the basic detectors with several other single detectors and multiple detection methods as comparable methods improved receiver operating characteristic curves and better separability between targets and backgrounds by the dsd methods are illustrated the dsd methods also perform well with the covariance based detectors showing their efficiency in selecting covariance information for detection the dynamic subspace detection theory is a useful background statistics estimation our method can find the most suitable pixels to construct detectors targets can be further distinguished by a fusion of all the detection procedures

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

dimensionality reduction for hyperspectral data based on class aware tensor neighborhood graph and patch alignment to take full advantage of hyperspectral information to avoid data redundancy and to address the curse of dimensionality concern dimensionality reduction dr becomes particularly important to analyze hyperspectral data exploring the tensor characteristic of hyperspectral data a dr algorithm based on class aware tensor neighborhood graph and patch alignment is proposed here first hyperspectral data are represented in the tensor form through a window field to keep the spatial information of each pixel second using a tensor distance criterion a class aware tensor neighborhood graph containing discriminating information is obtained in the third step employing the patch alignment framework extended to the tensor space we can obtain global optimal spectral spatial information finally the solution of the tensor subspace is calculated using an iterative method and low dimensional projection matrixes for hyperspectral data are obtained accordingly the proposed method effectively explores the spectral and spatial information in hyperspectral data simultaneously experimental results on 3 real hyperspectral datasets show that compared with some popular vector and tensor based dr algorithms the proposed method can yield better performance with less tensor training samples required

a fast separability based feature selection method for high dimensional remotely sensed image classification because of the difficulty of obtaining an analytic expression for bayes error a wide variety of separability measures has been proposed for feature selection in this paper we show that there is a general framework based on the criterion of mutual information mi that can provide a realistic solution to the problem of feature selection for high dimensional data we give a theoretical argument showing that the mi of multi dimensional data can be broken down into several one dimensional components which makes numerical evaluation much easier and more accurate it also reveals that selection based on the simple criterion of only retaining features with high associated mi values may be problematic when the features are highly correlated although there is a direct way of selecting features by jointly maximising mi this suffers from combinatorial explosion hence we propose a fast feature selection scheme based on a greedy optimisation strategy to confirm the effectiveness of this scheme simulations are carried out on 16 land cover classes using the 92av3c data set collected from the 220 dimensional aviris hyperspectral sensor we replicate our earlier positive results which used an essentially heuristic method for mi based band selection but with much reduced computational cost and a much sounder theoretical basis

on absolute cm periods ii for a cm fieldk shimura defined the period symbolpk by factorizing periods of abelian varieties with complex multiplication we define the absolute period symbolgk using division values of the multiple gamma function and conjecture that pk coincides with gk up to the multiplication by algebraic numbers taking the action of gal q q into account we present a refined version of this conjecture we show that these conjectures are consistently formulated and discuss various numerical examples which support our conjectures strongly in our previous paper y2 we formulated a conjecture which gives an expres sion of the derivatives of artin l functions at s 0 by cm periods however we could not express cm periods themselves by such a conjecture this point will be shown explicitly by an example in 7 see also the discussion in the beginning of y2 2 in the present paper we shall give a conjecture which expresses cm periods by the values of the multiple gamma function at division points and present various numerical examples which support it let us explain our ideas and the contents of this paper more precisely let k be a cm field jk be the set of all isomorphisms of k into c and ik be the free abelian group generated by jk for every ik shimura defined s2 s3 the cm period pk c which is uniquely determined mod q t he fundamental properties of the period symbol pk will be reviewed in 1 for a b c let us write a b if b 0a nda b q u singpk we can write the chowla selberg formula as

unsupervised feature selection based on maximum information and minimum redundancy for hyperspectral images unsupervised feature selection plays an important role in hyperspectral image processing it is a very challenge issue to select an effective feature subset with the unavailability of class labels to select the features maximally preserving the information of original features a maximum joint mutual information mjmi criterion is defined since the high order distribution involved in mjmi is hard to calculate a maximum information and minimum redundancy mimr criterion is derived as the low order approximation of mjmi from information theory many classical unsupervised feature selection criteria can also be considered as the low order approximations of mjmi compared with them mimr requires more relaxed approximation condition moreover a new clonal selection algorithm csa in artificial immune system is devised to optimize the selected features with the guidance of mimr experimental results on several hyperspectral datasets demonstrate that the proposed method obtains better feature subsets compared with classical unsupervised feature selection methods a new mimr criterion is proposed for unsupervised feature selection mimr can select more informative and distinctive features many classical criteria and mimr can be unified into the same framework the theoretical advantage of mimr over many classical criteria is given feature selection problem is solved by combinatorial optimization with a new csa

feature selection based on high dimensional model representation for hyperspectral images in hyperspectral image analysis the classification task has generally been addressed jointly with dimensionality reduction due to both the high correlation between the spectral features and the noise present in spectral bands which might significantly degrade classification performance in supervised classification limited training instances in proportion with the number of spectral features have negative impacts on the classification accuracy which is known as hughes effects or curse of dimensionality in the literature in this paper we focus on dimensionality reduction problem and propose a novel feature selection algorithm which is based on the method called high dimensional model representation the proposed algorithm is tested on some toy examples and hyperspectral datasets in comparison with conventional feature selection algorithms in terms of classification accuracy stability of the selected features and computational time the results show that the proposed approach provides both high classification accuracy and robust features with a satisfactory computational time

a path integral approach to asset liability management functional integrals constitute a powerful tool in the investigation of financial models in the recent econophysics literature this technique was successfully used for the pricing of a number of derivative securities in the present contribution we introduce this approach to the field of asset liability management we work with a representation of cash flows by means of a two dimensional delta function perturbation in the case of a brownian model and a geometric brownian model we derive closed form solutions for a finite horizon alm policy the results are numerically and graphically illustrated

discovering diverse subset for unsupervised hyperspectral band selection band selection as a special case of the feature selection problem tries to remove redundant bands and select a few important bands to represent the whole image cube this has attracted much attention since the selected bands provide discriminative information for further applications and reduce the computational burden though hyperspectral band selection has gained rapid development in recent years it is still a challenging task because of the following requirements 1 an effective model can capture the underlying relations between different high dimensional spectral bands 2 a fast and robust measure function can adapt to general hyperspectral tasks and 3 an efficient search strategy can find the desired selected bands in reasonable computational time to satisfy these requirements a multigraph determinantal point process mdpp model is proposed to capture the full structure between different bands and efficiently find the optimal band subset in extensive hyperspectral applications there are three main contributions 1 graphical model is naturally transferred to address band selection problem by the proposed mdpp 2 multiple graphs are designed to capture the intrinsic relationships between hyperspectral bands and 3 mixture dpp is proposed to model the multiple dependencies in the proposed multiple graphs and offers an efficient search strategy to select the optimal bands to verify the superiority of the proposed method experiments have been conducted on three hyperspectral applications such as hyperspectral classification anomaly detection and target detection the reliability of the proposed method in generic hyperspectral tasks is experimentally proved on four real world hyperspectral data sets

exploring the boundary region of tolerance rough sets for feature selection of all of the challenges which face the effective application of computational intelligence technologies for pattern recognition dataset dimensionality is undoubtedly one of the primary impediments in order for pattern classifiers to be efficient a dimensionality reduction stage is usually performed prior to classification much use has been made of rough set theory for this purpose as it is completely data driven and no other information is required most other methods require some additional knowledge however traditional rough set based methods in the literature are restricted to the requirement that all data must be discrete it is therefore not possible to consider real valued or noisy data this is usually addressed by employing a discretisation method which can result in information loss this paper proposes a new approach based on the tolerance rough set model which has the ability to deal with real valued data whilst simultaneously retaining dataset semantics more significantly this paper describes the underlying mechanism for this new approach to utilise the information contained within the boundary region or region of uncertainty the use of this information can result in the discovery of more compact feature subsets and improved classification accuracy these results are supported by an experimental evaluation which compares the proposed approach with a number of existing feature selection techniques

explicit time dependent schrodinger propagators the authors compute explicitly the time dependent schrodinger and heat propagator for the potentials lambda 2m m 1 cosh2 lambda x a delta function potential several cases of periodic delta function potentials and a delta function potential in a square well they also discuss the semiclassical approximation for the delta function potential

on p adic absolute cm periods i the second author defined the absolute cm period symbol using the multiple gamma function this symbol is conjectured to give the same value as shimura s period symbol up to multiplication by algebraic numbers in this paper we define a p adic analogue of the absolute cm period symbol using the p adic multiple gamma function studied by the first author in the completely split case we present a conjecture which predicts the exact value of this symbol as well as supporting evidences

multiview matrix completion for multilabel image classification there is growing interest in multilabel image classification due to its critical role in web based image analytics based applications such as large scale image retrieval and browsing matrix completion mc has recently been introduced as a method for transductive semisupervised multilabel classification and has several distinct advantages including robustness to missing data and background noise in both feature and label space however it is limited by only considering data represented by a single view feature which cannot precisely characterize images containing several semantic concepts to utilize multiple features taken from different views we have to concatenate the different features as a long vector however this concatenation is prone to over fitting and often leads to very high time complexity in mc based image classification therefore we propose to weightedly combine the mc outputs of different views and present the multiview mc mvmc framework for transductive multilabel image classification to learn the view combination weights effectively we apply a cross validation strategy on the labeled set in particular mvmc splits the labeled set into two parts and predicts the labels of one part using the known labels of the other part the predicted labels are then used to learn the view combination coefficients in the learning process we adopt the average precision ap loss which is particular suitable for multilabel image classification since the ranking based criteria are critical for evaluating a multilabel classification system a least squares loss formulation is also presented for the sake of efficiency and the robustness of the algorithm based on the ap loss compared with the other losses is investigated experimental evaluation on two real world data sets pascal voc 07 and mir flickr demonstrate the effectiveness of mvmc for transductive semisupervised multilabel image classification and show that mvmc can exploit complementary properties of different features and output consistent labels for improved multilabel image classification

applications of δ function perturbation to the pricing of derivative securities in the recent econophysics literature the use of functional integrals is widespread for the calculation of option prices in this paper we extend this approach in several directions by means of function perturbations first we show that results about infinitely repulsive function are applicable to the pricing of barrier options we also introduce functional integrals over skew paths that give rise to a new european option formula when combined with function potential we propose accurate closed form approximations based on the theory of comonotonic risks in case the functional integrals are not analytically computable

unsupervised feature selection using feature similarity in this article we describe an unsupervised feature selection algorithm suitable for data sets large in both dimension and size the method is based on measuring similarity between features whereby redundancy therein is removed this does not need any search and therefore is fast a new feature similarity measure called maximum information compression index is introduced the algorithm is generic in nature and has the capability of multiscale representation of data sets the superiority of the algorithm in terms of speed and performance is established extensively over various real life data sets of different sizes and dimensions it is also demonstrated how redundancy and information loss in feature selection can be quantified with an entropy measure

boundary conditions in path integrals from point interactions for the path integral of the one dimensional dirac particle a proposal is given of how to implement point interactions and boundary conditions in the path integral the starting point is a path integral formulation of a dirac particle in one dimension the implementation of a point interaction yields by means of a perturbation expansion the corresponding green function for a relativistic particle in the non relativistic limit several cases can be distinguished depending on which of the four possibilities of the point interaction has been chosen by a proper combination of the various possibilities of implementing the point interaction the whole range of the four parameter family of boundary conditions for point interactions can be exploited in the relativistic case as well as in the non relativistic limit in addition making the strength of the point interaction infinitely repulsive yields boundary conditions at finite points on the real line in particular dirichlet and neumann boundary conditions emerge the method is illustrated with some examples

the functional integral for a free particle on a half plane a free nonrelativistic particle moving in two dimensions on a half plane can be described by self adjoint hamiltonians characterized by boundary conditions imposed on the systems the most general boundary condition is parameterized in terms of the elements of an infinite dimensional matrix we construct the brownian functional integral for each of these self adjoint hamiltonians nonlocal boundary conditions are implemented by allowing the paths striking the boundary to jump to other locations on the boundary analytic continuation in time results in the green s functions of the schrodinger equation satisfying the boundary condition characterizing the self adjoint hamiltonian