discrete hessian eigenmaps method for dimensionality reduction for a given set of data points lying on a low dimensional manifold embedded in a high dimensional space the dimensionality reduction is to recover a low dimensional parametrization from the data set the recently developed hessian eigenmaps method is a mathematically rigorous method that also sets a theoretical framework for the nonlinear dimensionality reduction problem in this paper we develop a discrete version of the hessian eigenmaps method and present an analysis giving conditions under which the method works as intended as an application a procedure to modify the standard constructions of k nearest neighborhoods is presented to ensure that hessian lle can recover the original coordinates up to an affine transformation

on the subgroup structure of classical groups in this paper we establish a result on the subgroup structure of classical groups over algebraically closed elds and use this to give a new proof of a fundamental theorem of m aschbacher on subgroups of nite classical groups let v be a nite dimensional vector space over an algebraically closed eld k and let g be one of the classical algebraic groups sl v sp v or so v our result is a reduction theorem concerning the subgroups of g we de ne a certain collection c of natural proper subgroups of g and prove that any closed nite or in nite subgroup of g either lies in a member of c or is roughly speaking a simple group acting irreducibly on v aschbacher s result is an analogous reduction theorem for subgroups of nite classical groups we obtain this as a relatively easy consequence of our main result by taking xed points under the action of a frobenius morphism using a standard process involving lang s theorem the proof of the main result uses elementary linear algebra together with a few basic facts from the theory of algebraic groups various complications which arise in the nite group setting in as become much more straightforward in the algebraic group setting in particular questions involving extension elds do not occur and issues of conjugacy are easily settled when we descend to nite invent math 134 427 453 1998

data driven facial animation via semi supervised local patch alignment abstract this paper reports a novel data driven facial animation technique which drives a neutral source face to get the expressive target face using a semi supervised local patch alignment framework we define the local patch and assume that there exists a linear transformation between a patch of the target face and the intrinsic embedding of the corresponding patch of the source face based on this assumption we compute the intrinsic embeddings of source patches and align these embeddings to form the result during the course of alignment we use a set of motion data as shape regularizer to impel the result to approach the unknown target face the intrinsic embedding can be computed through both locally linear embedding and local tangent space alignment experimental results indicate that the proposed framework can obtain decent face driving results quantitative and qualitative evaluations of the proposed framework demonstrate its superiority to existing methods

manifold warp segmentation of human action human action segmentation is important for human action analysis which is a highly active research area most segmentation methods are based on clustering or numerical descriptors which are only related to data and consider no relationship between the data and physical characteristics of human actions physical characteristics of human motions are those that can be directly perceived by human beings such as speed acceleration continuity and so on which are quite helpful in detecting human motion segment points we propose a new physical based descriptor of human action by curvature sequence warp space alignment cswsa approach for sequence segmentation in this paper furthermore time series warp metric curvature segmentation method is constructed by the proposed descriptor and cswsa in our segmentation method descriptor can express the changes of human actions and cswsa is an auxiliary method to give suggestions for segmentation the experimental results show that our segmentation method is effective in both cmu human motion and video based data sets

adaptive manifold learning manifold learning algorithms seek to find a low dimensional parameterization of high dimensional data they heavily rely on the notion of what can be considered as local how accurately the manifold can be approximated locally and last but not least how the local structures can be patched together to produce the global parameterization in this paper we develop algorithms that address two key issues in manifold learning 1 the adaptive selection of the local neighborhood sizes when imposing a connectivity structure on the given set of high dimensional data points and 2 the adaptive bias reduction in the local low dimensional embedding by accounting for the variations in the curvature of the manifold as well as its interplay with the sampling density of the data set we demonstrate the effectiveness of our methods for improving the performance of manifold learning algorithms using both synthetic and real world data sets

global registration of multiple point clouds using semidefinite programming consider n points in r d and m local coordinate systems that are related through unknown rigid transforms for each point we are given possibly noisy measurements of its local coordinates in some of the coordinate systems alternatively for each coordinate system we observe the coordinates of a subset of the points the problem of estimating the global coordinates of the n points up to a rigid transform from such measurements comes up in distributed approaches to molecular conformation and sensor network localization and also in computer vision and graphics the least squares formulation of this problem although nonconvex has a well known closed form solution when m 2 based on the singular value decomposition svd however no closed form solution is known for m geq 3 in this paper we demonstrate how the least squares formulation can be relaxed into a convex program namely a semidefinite program sdp by setting up connections between the uniqueness of this sdp and results fr

learning the dynamical system behind sensory data this letter looks at the physics behind sensory data by identifying the parameters that govern the physical system and estimating them from sensory observations we extend takens s delay embedding theorem to the dynamical systems controlled by parameters an embedding of the product space of the phase and the parameter spaces of the dynamical system can be obtained by the delay embedding map provided that the parameter of the dynamical system changes slowly the reconstruction error is bounded for slowly varying parameters a manifold learning technique is applied to the embedding obtained to extract a low dimensional global coordinate system representing the product space the phase space of the deterministic dynamics can be contracted by using the adjacency relationship in time which enables recovery of only the parameter space as examples the manifolds of synthetic and real world vowels with time varying fundamental frequency f0 are analyzed and the f0 contours are extracted by an unsupervised algorithm experimental results show that the proposed method leads to robust performance under various noise conditions and rapid changes of f0 compared with the current state of the art f0 estimation algorithms

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

joint analysis of refractions with surface waves an inverse solution to the refraction traveltime problem we describe a possible solution to the inverse refraction traveltime problem irtp that reduces the range of possible solutions nonuniqueness this approach uses a reference model derived from surface wave shear wave velocity estimates as a constraint the application of the joint analysis of refractions with surface waves jars method provided a more realistic solution than the conventional refraction tomography methods which did not benefit from a reference model derived from real data this confirmed our conclusion that the proposed method is an advancement in the irtp analysis the unique basic principles of the jars method might be applicable to other inverse geophysical problems

low rank matrix approximation with manifold regularization this paper proposes a new model of low rank matrix factorization that incorporates manifold regularization to the matrix factorization superior to the graph regularized nonnegative matrix factorization this new regularization model has globally optimal and closed form solutions a direct algorithm for data with small number of points and an alternate iterative algorithm with inexact inner iteration for large scale data are proposed to solve the new model a convergence analysis establishes the global convergence of the iterative algorithm the efficiency and precision of the algorithm are demonstrated numerically through applications to six real world datasets on clustering and classification performance comparison with existing algorithms shows the effectiveness of the proposed method for low rank factorization in general

spectral properties of the alignment matrices in manifold learning local methods for manifold learning generate a collection of local parameterizations which is then aligned to produce a global parameterization of the underlying manifold the alignment procedure is carried out through the computation of a partial eigendecomposition of a so called alignment matrix in this paper we present an analysis of the eigenstructure of the alignment matrix giving both necessary and sufficient conditions under which the null space of the alignment matrix recovers the global parameterization we show that the gap in the spectrum of the alignment matrix is proportional to the square of the size the precise definition of the size is given in section sec sp of the overlap of the local parameterizations thus deriving a quantitative measure of how stably the null space can be computed numerically we also give a perturbation analysis of the null space of the alignment matrix when the computation of the local parameterizations is subject to error our analysis provides insights into the behaviors and performance of local manifold learning algorithms

proximity based frameworks for generating embeddings from multi output data this paper is about supervised and semi supervised dimensionality reduction dr by generating spectral embeddings from multi output data based on the pairwise proximity information two flexible and generic frameworks are proposed to achieve supervised dr sdr for multilabel classification one is able to extend any existing single label sdr to multilabel via sample duplication referred to as mesd the other is a multilabel design framework that tackles the sdr problem by computing weight proximity matrices based on simultaneous feature and label information referred to as mope as a generalization of many current techniques a diverse set of different schemes for label based proximity calculation as well as a mechanism for combining label based and feature based weight information by considering information importance and prioritization are proposed for mope additionally we summarize many current spectral methods for unsupervised dr udr single multilabel sdr and semi supervised dr ssdr and express them under a common template representation as a general guide to researchers in the field we also propose a general framework for achieving ssdr by combining existing sdr and udr models and also a procedure of reducing the computational cost via learning with a target set of relation features the effectiveness of our proposed methodologies is demonstrated with experiments with document collections for multilabel text categorization from the natural language processing domain

unfolding kernel embeddings of graphs in this paper we investigate the use of manifold learning techniques to enhance the separation properties of standard graph kernels the idea stems from the observation that when we perform multidimensional scaling on the distance matrices extracted from the kernels the resulting data tends to be clustered along a curve that wraps around the embedding space a behavior that suggests that long range distances are not estimated accurately resulting in an increased curvature of the embedding space hence we propose to use a number of manifold learning techniques to compute a low dimensional embedding of the graphs in an attempt to unfold the embedding manifold and increase the class separation we perform an extensive experimental evaluation on a number of standard graph datasets using the shortest path borgwardt and kriegel 2005 graphlet shervashidze et al 2009 random walk kashima et al 2003 and weisfeiler lehman shervashidze et al 2011 kernels we observe the most significant improvement in the case of the graphlet kernel which fits with the observation that neglecting the locational information of the substructures leads to a stronger curvature of the embedding manifold on the other hand the weisfeiler lehman kernel partially mitigates the locality problem by using the node labels information and thus does not clearly benefit from the manifold learning interestingly our experiments also show that the unfolding of the space seems to reduce the performance gap between the examined kernels highlightswe use manifold learning techniques to enhance the performance of graph kernels we try to increase the class separation by unfolding the embedding manifold we propose a procedure to find the optimal embedding of the data the kernels which neglect the locational information show the largest improvement the unfolding of the space helps to reduce the performance gap between the kernels

compact gravity inversion we present a new criterion for the inversion of gravity data the principle employed is to minimize the volume of the causative body which is equivalent to maximizing its compactness the anomalous density distribution is obtained using an iterative technique which is numerically stable and rapidly convergent the principle can also be adapted to include modeling of gravity anomalies by single density sources the advantage of this approach is that desirable geologic characteristics are automatically incorporated into the model with a minimum of subjective judgments on the part of the interpreter the treatment of noise in the data fits naturally into the formulation of the inversion procedure the method is illustrated by the inversion of noise free and noisy data generated from a two dimensional model consisting of a regular array of identical rectangular blocks whose densities can be individually specified in every case the algorithm successfully recovers the correct density distribution from the dat

local linear regression on manifolds and its geometric interpretation high dimensional data analysis has been an active area and the main focus areas have been variable selection and dimension reduction in practice it occurs often that the variables are located on an unknown lower dimensional nonlinear manifold under this manifold assumption one purpose of this article is regression and gradient estimation on the manifold and another is developing a new tool for manifold learning as regards the first aim we suggest directly reducing the dimensionality to the intrinsic dimension d of the manifold and performing the popular local linear regression llr on a tangent plane estimate an immediate consequence is a dramatic reduction in the computational time when the ambient space dimension p d we provide rigorous theoretical justification of the convergence of the proposed regression and gradient estimators by carefully analyzing the curvature boundary and nonuniform sampling effects we propose a bandwidth selector that can handle heteroscedastic errors with re

conditions for unique graph realizations the graph realization problem is that of computing the relative locations of a set of vertices placed in euclidean space relying only upon some set of inter vertex distance measurements this paper is concerned with the closely related problem of determining whether or not a graph has a unique realization both these problems are np hard but the proofs rely upon special combinations of edge lengths if one assumes the vertex locations are unrelated then the uniqueness question can be approached from a purely graph theoretic angle that ignores edge lengths this paper identifies three necessary graph theoretic conditions for a graph to have a unique realization in any dimension efficient sequential and nc algorithms are presented for each condition although these algorithms have very different flavors in different dimensions

riemannian manifold learning recently manifold learning has been widely exploited in pattern recognition data analysis and machine learning this paper presents a novel framework called riemannian manifold learning rml based on the assumption that the input high dimensional data lie on an intrinsically low dimensional riemannian manifold the main idea is to formulate the dimensionality reduction problem as a classical problem in riemannian geometry that is how to construct coordinate charts for a given riemannian manifold we implement the riemannian normal coordinate chart which has been the most widely used in riemannian geometry for a set of unorganized data points first two input parameters the neighborhood size k and the intrinsic dimension d are estimated based on an efficient simplicial reconstruction of the underlying manifold then the normal coordinates are computed to map the input high dimensional data into a low dimensional space experiments on synthetic data as well as real world images demonstrate that our algorithm can learn intrinsic geometric structures of the data preserve radial geodesic distances and yield regular embeddings

semantic preserving distance metric learning and applications how do we accurately browse a large set of images or efficiently annotate the images from an image library image clustering methods are invaluable tools for applications such as content based image retrieval and image annotation to perform these tasks it is critical to have proper features to describe the visual and semantic content of images and to define an accurate distance metric to measure the dissimilarity between any two images however existing methods which adopt the features of color histograms edge direction histograms and shape context lack the ability to describe semantic content to solve this problem we propose a new approach that utilizes user provided pairwise constraints to describe the semantic relationship between two images a semantic preserving distance metric learning sp dml algorithm is developed to explore the complementary characteristics of the visual features and pairwise constraints in a unified feature space in this space the learned distance metric can be used to measure the dissimilarity between two images specifically the manifold structure adopted in sp dml is revealed by the image s visual features to integrate semantic contents in distance metric learning sp dml utilizes pairwise constraints to build semantic patches and align these patches to obtain the optimal distance metric for the new feature space experimental results in image clustering demonstrate that the performance of sp dml is appealing

dimensionality estimation manifold learning and function approximation using tensor voting we address instance based learning from a perceptual organization standpoint and present methods for dimensionality estimation manifold learning and function approximation under our approach manifolds in high dimensional spaces are inferred by estimating geometric relationships among the input instances unlike conventional manifold learning we do not perform dimensionality reduction but instead perform all operations in the original input space for this purpose we employ a novel formulation of tensor voting which allows an n d implementation tensor voting is a perceptual organization framework that has mostly been applied to computer vision problems analyzing the estimated local structure at the inputs we are able to obtain reliable dimensionality estimates at each instance instead of a global estimate for the entire data set moreover these local dimensionality and structure estimates enable us to measure geodesic distances and perform nonlinear interpolation for data sets with varying density outliers perturbation and intersections that cannot be handled by state of the art methods quantitative results on the estimation of local manifold structure using ground truth data are presented in addition we compare our approach with several leading methods for manifold learning at the task of measuring geodesic distances finally we show competitive function approximation results on real data

nonlinear embedding preserving multiple local linearities locally linear embedding lle is one of the effective and efficient algorithms for nonlinear dimensionality reduction this paper discusses the stability of lle focusing on the optimal weights for extracting local linearity behind the considered manifold it is proven that there are multiple sets of weights that are approximately optimal and can be used to improve the stability of lle a new algorithm using multiple weights is then proposed together with techniques for constructing multiple weights this algorithm is called as nonlinear embedding preserving multiple local linearities neml neml improves the preservation of local linearity and is more stable than lle a short analysis for neml is also given for isometric manifolds neml is compared with the local tangent space alignment ltsa in methodology since both of them adopt multiple local constraints numerical examples are given to show the improvement and efficiency of neml

hessian eigenmaps locally linear embedding techniques for high dimensional data we describe a method for recovering the underlying parametrization of scattered data m i lying on a manifold m embedded in high dimensional euclidean space the method hessian based locally linear embedding derives from a conceptual framework of local isometry in which the manifold m viewed as a riemannian submanifold of the ambient euclidean space r n is locally isometric to an open connected subset of euclidean space r d because does not have to be convex this framework is able to handle a significantly wider class of situations than the original isomap algorithm the theoretical framework revolves around a quadratic form h f m h f m f dm defined on functions f m r here hf denotes the hessian of f and h f averages the frobenius norm of the hessian over m to define the hessian we use orthogonal coordinates on the tangent planes of m the key observation is that if m truly is locally isometric to an open connected subset of r d then h f has a d 1 dimensional null space consisting of the constant functions and a d dimensional space of functions spanned by the original isometric coordinates hence the isometric coordinates can be recovered up to a linear isometry our method may be viewed as a modification of locally linear embedding and our theoretical framework as a modification of the laplacian eigenmaps framework where we substitute a quadratic form based on the hessian in place of one based on the laplacian

restriction of irreducible modules for spin 2n 1 k to spin 2n k abstract let k be an algebraically closed field of characteristic p 0 and let y spin 2 n 1 k n 3 be a simply connected simple algebraic group of type b n over k also let x be the subgroup of type d n embedded in y in the usual way as the derived subgroup of the stabilizer of a non singular one dimensional subspace of the natural module for y in this paper we give a complete set of isomorphism classes of finite dimensional irreducible rational ky modules on which x acts with exactly two composition factors completing the work of ford in 12

incremental nonlinear dimensionality reduction by manifold learning understanding the structure of multidimensional patterns especially in unsupervised cases is of fundamental importance in data mining pattern recognition and machine learning several algorithms have been proposed to analyze the structure of high dimensional data based on the notion of manifold learning these algorithms have been used to extract the intrinsic characteristics of different types of high dimensional data by performing nonlinear dimensionality reduction most of these algorithms operate in a batch mode and cannot be efficiently applied when data are collected sequentially in this paper we describe an incremental version of isomap one of the key manifold learning algorithms our experiments on synthetic data as well as real world images demonstrate that our modified algorithm can maintain an accurate low dimensional representation of the data in an efficient manner

on irreducible subgroups of simple algebraic groups let g be a simple algebraic group over an algebraically closed field k of characteristic p geqslant 0 let h be a proper closed subgroup of g and let v be a nontrivial irreducible kg module which is p restricted tensor indecomposable and rational assume that the restriction of v to h is irreducible in this paper we study the triples g h v of this form when g is a classical group and h is positive dimensional combined with earlier work of dynkin seitz testerman and others our main theorem reduces the problem of classifying the triples g h v to the case where g is an orthogonal group v is a spin module and h normalizes an orthogonal decomposition of the natural kg module

a construction of certain maximal subgroups of the algebraic groups e6 and f4 keywords maximal closed connected subgroup exceptional algebraic groups irreducible embeddings of semisimple algebraic groups rational modules irreducible representations embeddings of parabolic subgroups reference ctg article 1989 002doi 10 1016 0021 8693 89 90218 4 record created on 2008 12 16 modified on 2017 05 12

full space local topology extraction for cross modal retrieval with the ever increasing availability of various kinds of multimedia data cross modal retrieval which enables information retrieval from various types of data given various types of query has become a research hotspot hashing based techniques have been developed to solve this problem however most previous works cannot capture the shared underlying structure of real world multimodal data which degrades their retrieval performances in this paper we propose a novel hashing method based on the extraction of the common manifold structure shared among different feature spaces to faithfully represent the common structure two kinds of local topology information are exploited in our method local angles are incorporated within the extraction of local topology of each feature space which is then used to learn a common intermediate subspace after heterogeneous features being embedded into this subspace local similarities are exploited to extract the local topology between different feature spaces and learn compact hamming embeddings to facilitate cross modal retrieval the proposed method is referred to as full space local topology extraction for hashing extensive comparisons with other state of the art methods on three benchmark multimedia data sets demonstrate the superiority of our proposed method in terms of retrieval recall and search accuracy

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

a1 type overgroups of elements of order p in semisimple algebraic groups and the associated finite groups keywords semisimple algebraic groups closed connected subgroups finite groups fixed point subgroups reference ctg article 1995 001doi 10 1006 jabr 1995 1285 record created on 2008 12 16 modified on 2017 05 12

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

multiscale adjoint waveform tomography for surface and body waves abstractwe have developed a wavelet multiscale adjoint scheme for the elastic full waveform inversion of seismic data including body waves bws and surface waves sws we start the inversion on the sw portion of the seismograms to avoid cycle skipping and reduce the dependence on the initial model of these dispersive waves we commence by minimizing an envelope based misfit function subsequently we proceed to the minimization of a waveform difference wd metric applied to the sws only after that we fit bws and sws indiscriminately using a wd misfit metric in each of these three steps we guide the iterative inversion through a sequence of nested subspace projections in a wavelet basis sw analysis preserves a wealth of near surface features that would be lost in conventional bw tomography we used a toy model to illustrate the dispersive and cycle skipping behavior of the sws and to introduce the two ways by which we combat the nonlinearity of waveform inversions involving sws the first is the

efficient simplicial reconstructions of manifolds from their samples an algorithm for manifold learning is presented given only samples of a finite dimensional differentiable manifold and no a priori knowledge of the manifold s geometry or topology except for its dimension the goal is to find a description of the manifold the learned manifold must approximate the true manifold well both geometrically and topologically when the sampling density is sufficiently high the proposed algorithm constructs a simplicial complex based on approximations to the tangent bundle of the manifold an important property of the algorithm is that its complexity depends on the dimension of the manifold rather than that of the embedding space successful examples are presented in the cases of learning curves in the plane curves in space and surfaces in space in addition a case when the algorithm fails is analyzed

occam s inversion a practical algorithm for generating smooth models from electromagnetic sounding data the inversion of electromagnetic sounding data does not yield a unique solution but inevitably a single model to interpret the observations is sought we recommend that this model be as simple or smooth as possible in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models to obtain smooth models the nonlinear forward problem is linearized about a starting model in the usual way but it is then solved explicitly for the desired model rather than for a model correction by parameterizing the model in terms of its first or second derivative with depth the minimum norm solution yields the smoothest possible model rather than fitting the experimental data as well as possible which maximizes the roughness of the model the smoothest model which fits the data to within an expected tolerance is sought a practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models resulting in a stable and rapidly convergent algorithm the inversion of both magnetotelluric and schlumberger sounding field data and a joint magnetotelluric resistivity inversion demonstrate the method and show it to have practical application

irreducible disconnected subgroups of exceptional algebraic groups this dissertation is concerned with the study of irreducible embeddings of simple algebraic groups of exceptional type it is motivated by the role of such embeddings in the study of positive dimensional closed subgroups of classical algebraic groups the classification of the maximal closed connected subgroups of simple algebraic groups was carried out by e b dynkin g m seitz and d m testerman their analysis for the classical groups was based primarily on a striking result if g is a simple algebraic group and o g sl v is a tensor indecomposable irreducible rational representation then with specified exceptions the image of g is maximal among closed connected subgroups of one of the classical groups sl v sp v or so v in the case of closed not necessarily connected subgroups of the classical groups one is interested in considering irreducible embeddings of simple algebraic groups and their automorphism groups given a simple algebraic group y defined over an algebraically closed field k one is led to study the embeddings g 0 g is a closed non connected positive dimensional subgroup of y and v is a nontrivial irreducible rational ky module such that v g is irreducible we obtain a precise description of such triples g y v

irreducible modules and parabolic subgroups summary it seems desirable from the point of view of finite group theorists to develop further the representation theory of finite chevalley groups in the characteristic of their definition say p by focusing attention on the full array of p local subgroups that is the parabolics rather than the usual single borel or cartan subgroup the following observation may be regarded as a generalization to arbitrary parabolic subgroups of the standard result 3 theorem 39 d for a borel subgroup namely that in an irreducible module the subspace fixed by a maximal unipotent subgroup is 1 dimensional and so affords an irreducible module for a levi complement which is an abelian cartan subgroup it seems natural to state the result first for algebraic groups

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

quadratic projection based feature extraction with its application to biometric recognition this paper presents a novel quadratic projection based feature extraction framework where a set of quadratic matrices is learned to distinguish each class from all other classes we formulate quadratic matrix learning qml as a standard semidefinite programming sdp problem however the conventional interior point sdp solvers do not scale well to the problem of qml for high dimensional data to solve the scalability of qml we develop an efficient algorithm termed dualqml based on the lagrange duality theory to extract nonlinear features to evaluate the feasibility and effectiveness of the proposed framework we conduct extensive experiments on biometric recognition experimental results on three representative biometric recognition tasks including face palmprint and ear recognition demonstrate the superiority of the dualqml based feature extraction algorithm compared to the current state of the art algorithms highlightsa novel quadratic projection based feature extraction framework is developed a set of quadratic matrices is learnt to distinguish each class from other classes quadratic matrix learning qml is formulated as an sdp problem an efficient algorithm is developed to solve qml based on lagrange duality theory experiments on biometric recognition show the effectiveness of our algorithm

nonlinear dimensionality reduction using a temporal coherence principle temporal coherence principle is an attractive biologically inspired learning rule to extract slowly varying features from quickly varying input data in this paper we develop a new nonlinear neighborhood preserving nnp technique by utilizing the temporal coherence principle to find an optimal low dimensional representation from the original high dimensional data nnp is based on a nonlinear expansion of the original input data such as polynomials of a given degree it can be solved by the eigenvalue problem without using gradient descent and is guaranteed to find the global optimum nnp can be viewed as a nonlinear dimensionality reduction framework which takes into consideration both time series and data sets without an obvious temporal structure according to different situations we introduce three algorithms of nnp named nnp 1 nnp 2 and nnp 3 the objective function of nnp 1 is equal to slow feature analysis sfa and it works well for time series such as image sequences nnp 2 artificially constructs time series consisting of neighboring points for data sets without a clear temporal structure such as image data nnp 3 is proposed for classification tasks which can minimize the distances of neighboring points in the embedding space and ensure that the remaining points are as far apart as possible simultaneously furthermore the kernel extension of nnp is also discussed in this paper the proposed algorithms work very well on some image sequences and image data sets compared to other methods meanwhile we perform the classification task on the mnist handwritten digit database using the supervised nnp algorithms the experimental results demonstrate that nnp is an effective technique for nonlinear dimensionality reduction tasks