Kernel Representation Research Articles

Text Categorization of Biomedical Data Sets Using Graph Kernels and a Controlled Vocabulary

Recently, graph representations of text have been showing improved performance over conventional bag-of-words representations in text categorization applications. In this paper, we present a graph-based representation for biomedical articles and use graph kernels to classify those articles into high-level categories. In our representation, common biomedical concepts and semantic relationships are identified with the help of an existing ontology and are used to build a rich graph structure that provides a consistent feature set and preserves additional semantic information that could improve a classifier's performance. We attempt to classify the graphs using both a set-based graph kernel that is capable of dealing with the disconnected nature of the graphs and a simple linear kernel. Finally, we report the results comparing the classification performance of the kernel classifiers to common text-based classifiers.

Kernels of representations of Drinfeld doubles of finite groups

Abstract A description of the commutator of a normal subcategory of the fusion category of representation Rep A of a semisimple Hopf algebra A is given. Formulae for the kernels of representations of Drinfeld doubles D(G) of finite groups G are presented. It is shown that all these kernels are normal Hopf subalgebras.

Realization and elimination in rational representations of behaviors

This article deals with the relationship between rational representations of linear differential systems and their state representations. In particular we study the relationship between rational representations on the one hand, and output nulling and driving variable representations on the other. In the input–output framework it is well-known that every controllable and observable realization of the transfer matrix of the system yields a minimal input/state/output representation. If a proper rational matrix is used for a rational kernel or image representation of the system, then the question arises under what conditions realizations of this rational matrix give rise to state representations. We will establish conditions under which realizations of the proper rational matrix appearing in a rational image representation yield minimal driving variable representations of the system. Likewise, we find conditions under which realization leads from rational kernel representations to minimal output nulling representations. We also study the converse problem, namely state elimination from driving variable and output nulling representations. We will establish closed form expressions for kernel and image representations of the external behaviors associated with these particular state representations.

Robust kernel representation with statistical local features for face recognition.

Factors such as misalignment, pose variation, and occlusion make robust face recognition a difficult problem. It is known that statistical features such as local binary pattern are effective for local feature extraction, whereas the recently proposed sparse or collaborative representation-based classification has shown interesting results in robust face recognition. In this paper, we propose a novel robust kernel representation model with statistical local features (SLF) for robust face recognition. Initially, multipartition max pooling is used to enhance the invariance of SLF to image registration error. Then, a kernel-based representation model is proposed to fully exploit the discrimination information embedded in the SLF, and robust regression is adopted to effectively handle the occlusion in face images. Extensive experiments are conducted on benchmark face databases, including extended Yale B, AR (A. Martinez and R. Benavente), multiple pose, illumination, and expression (multi-PIE), facial recognition technology (FERET), face recognition grand challenge (FRGC), and labeled faces in the wild (LFW), which have different variations of lighting, expression, pose, and occlusions, demonstrating the promising performance of the proposed method.

Robust Visual Tracking via Fuzzy Kernel Representation

A r obust v isual k ernel t racking approach is presented for solving the problem of existing background pixels in object model. At first, after definition of fuzzy set on image is given, a fuzzy factor is embedded into object model to form the fuzzy kernel representation. Secondly, a fuzzy membership functions are generated by center-surround approach and log likelihood ratio of feature distributions. Thirdly, details about fuzzy kernel tracking algorithm is provided. After that, methods of parameter selection and performance evaluation for tracking algorithm are proposed. At last, a mass of experimental results are done to show our method can reduce the influence of the incomplete representation of object model via integrat ing both color features and background features.

Robust Visual Tracking via Fuzzy Kernel Representation

A r obust v isual k ernel t racking approach is presented for solving the problem of existing background pixels in object model. At first, after definition of fuzzy set on image is given, a fuzzy factor is embedded into object model to form the fuzzy kernel representation. Secondly, a fuzzy membership functions are generated by center-surround approach and log likelihood ratio of feature distributions. Thirdly, details about fuzzy kernel tracking algorithm is provided. After that, methods of parameter selection and performance evaluation for tracking algorithm are proposed. At last, a mass of experimental results are done to show our method can reduce the influence of the incomplete representation of object model via integrat ing both color features and background features.

Robust Stability Analysis for Feedback Interconnections of Time-Varying Linear Systems

Feedback interconnections of causal linear systems are studied in a continuous-time setting. The developments include a linear time-varying (LTV) generalization of Vinnicombe's nu-gap metric and an integral-quadratic-constraint-based robust L2-stability theorem for uncertain feedback interconnections of potentially open-loop unstable systems. These main results are established in terms of Toeplitz--Wiener--Hopf and Hankel operators, and the Fredholm index, for a class of causal linear systems with the following attributes: (i) a system graph (i.e., subspace of L2 input-output pairs) admits normalized strong right (i.e., image) and left (i.e., kernel) representations, and (ii) the corresponding Hankel operators are compact. These properties are first verified for stabilizable and detectable LTV state-space models to initially motivate the abstract formulation, and subsequently verified for frequency-domain multiplication by constantly proper Callier--Desoer transfer functions in analysis that confirms consistency of the developments with the time-invariant theory. To conclude, the aforementioned robust stability theorem is applied in an illustrative example concerning the feedback interconnection of distributed-parameter systems over a network with time-varying gains. (Less)

Online Coregularization for Multiview Semisupervised Learning

We propose a novel online coregularization framework for multiview semisupervised learning based on the notion of duality in constrained optimization. Using the weak duality theorem, we reduce the online coregularization to the task of increasing the dual function. We demonstrate that the existing online coregularization algorithms in previous work can be viewed as an approximation of our dual ascending process using gradient ascent. New algorithms are derived based on the idea of ascending the dual function more aggressively. For practical purpose, we also propose two sparse approximation approaches for kernel representation to reduce the computational complexity. Experiments show that our derived online coregularization algorithms achieve risk and accuracy comparable to offline algorithms while consuming less time and memory. Specially, our online coregularization algorithms are able to deal with concept drift and maintain a much smaller error rate. This paper paves a way to the design and analysis of online coregularization algorithms.

Non-parametric Fisher’s discriminant analysis with kernels for data classification

Kernel mapping has attracted a great deal of attention from researchers in the field of pattern recognition and statistical machine learning. Kernel-based approaches are the better choice whenever a non-linear classification model is needed. This paper proposes a nonlinear classification approach based on the non-parametric version of Fisher’s discriminant analysis. This technique can efficiently find a nonparametric kernel representation where linear discriminants perform better. Data classification is achieved by integrating the linear version of the nonparametric Fisher’s discriminant analysis with the kernel mapping. Based on the kernel trick, we provide a new formulation for Fisher’s criterion, defined solely in terms of the inner dot-product of the original input data. The obtained experimental results have demonstrated the competitiveness of our approach compared to major state of the art approaches.

Planar Beurling Transform and Bergman Type Spaces

In this paper we describe the actions of the operator \(S_\mathbb{D }\) or its adjoint \(S_\mathbb{D }^*\) on the poly-Bergman spaces of the unit disk \(\mathbb{D }.\) Let \(k\) and \(j\) be positive integers. We prove that \((S_\mathbb{D })^{j}\) is an isometric isomorphism between the true poly-Bergman subspace \(\mathcal{A }_{(k)}^2(\mathbb{D })\ominus N_{(k),j}\) onto the true poly-Bergman space \(\mathcal{A }_{(j+k)}^2(\mathbb{D }),\) where the linear space \(N_{(k),j}\) have finite dimension \(j.\) The action of \((S_\mathbb{D })^{j-1}\) on the canonical Hilbert base for the Bergman subspace \(\mathcal{A }^2(\mathbb{D })\ominus \mathcal{P }_{j-1},\) gives a Hilbert base \(\{ \phi _{ j , k } \}_{ k }\) for \(\mathcal{A }_{(j)}^2(\mathbb{D }).\) It is shown that \(\{ \phi _{ j , k } \}_{ j, k }\) is a Hilbert base for \(L^2(\mathbb{D },d A)\) such that whenever \(j\) and \(k\) remain constant we obtain a Hilbert base for the true poly-Bergman space \(\mathcal{A }_{(j)}^2(\mathbb{D })\) and \(\mathcal{A }_{(-k)}^2(\mathbb{D }),\) respectively. The functions \(\phi _{ j , k }\) are polynomials in \(z\) and \(\overline{z}\) and are explicitly given in terms of the \((2,1)\)-hypergeometric polynomials. We prove explicit representations for the true poly-Bergman kernels and the Koshelev representation for the poly-Bergman kernels of \(\mathbb{D }.\) The action of \(S_\Pi \) on the true poly-Bergman spaces of the upper half-plane \(\Pi \) allows one to introduce Hilbert bases for the true poly-Bergman spaces, and to give explicit representations of the true poly-Bergman and poly-Bergman kernels.

A new frequency domain representation and analysis for subharmonic oscillation

For a weakly nonlinear oscillator, the frequency domain Volterra kernels, often called the generalized frequency response functions, can provide accurate analysis of the response in terms of amplitudes and frequencies, in a transparent algebraic way. However, a Volterra series representation based analysis will become void for nonlinear oscillators that exhibit subharmonics, and the problem of finding a solution in this situation has mainly been treated by traditional analytical approximation methods. In this paper, a novel method is developed, by introducing a frequency domain subharmonic kernel representation for subharmonic systems subject to a single tone excitation frequency, to allow the advantages and the benefits associated with the traditional frequency domain representations to be applied to severely nonlinear systems that exhibit subharmonic behavior.

A Top-Down Account of Linear Canonical Transforms

We contend that what are called Linear Canonical Transforms (LCTs) should be seen as a part of the theory of unitary irreducible representations of the '2+1' Lorentz group. The integral kernel representation found by Collins, Moshinsky and Quesne, and the radial and hyperbolic LCTs introduced thereafter, belong to the discrete and continuous representation series of the Lorentz group in its parabolic subgroup reduction. The reduction by the elliptic and hyperbolic subgroups can also be considered to yield LCTs that act on functions, discrete or continuous in other Hilbert spaces. We gather the summation and integration kernels reported by Basu and Wolf when studiying all discrete, continuous, and mixed representations of the linear group of $2\times 2$ real matrices. We add some comments on why all should be considered canonical.

Kernels of linear representations of Lie groups, locally compact groups, and pro-Lie Groups

Abstract. For a topological group the intersection of all kernels of ordinary representations is studied. We show that is contained in the center of if is a connected pro-Lie group. The class is determined explicitly if is the class of connected Lie groups or the class of almost-connected Lie groups: in both cases, it consists of all compactly-generated abelian Lie groups. Every compact abelian group and every connected abelian pro-Lie group occurs as for some connected pro-Lie group . However, the dimension of is bounded by the cardinality of the continuum if is locally compact and connected. Examples are given to show that becomes complicated if contains groups with infinitely many connected components.

Kernel representations for evolving continuous functions

To parameterize continuous functions for evolutionary learning, we use kernel expansions in nested sequences of function spaces of growing complexity. This approach is particularly powerful when dealing with non-convex constraints and discontinuous objective functions. Kernel methods offer a number of beneficial properties for parameterizing continuous functions, such as smoothness and locality, which make them attractive as a basis for mutation operators. Beyond such practical considerations, kernel methods make heavy use of inner products in function space and offer a well established regularization framework. We show how evolutionary computation can profit from these properties. Searching function spaces of iteratively increasing complexity allows the solution to evolve from a simple first guess to a complex and highly refined function. At transition points where the evolution strategy is confronted with the next level of functional complexity, the kernel framework can be used to project the search distribution into the extended search space. The feasibility of the method is demonstrated on challenging trajectory planning problems where redundant robots have to avoid obstacles.

M-Idempotent and Self-Dual Morphological Filters

In this paper, we present a comprehensive analysis of self-dual and m-idempotent operators. We refer to an operator as m-idempotent if it converges after m iterations. We focus on an important special case of the general theory of lattice morphology: spatially variant morphology, which captures the geometrical interpretation of spatially variant structuring elements. We demonstrate that every increasing self-dual morphological operator can be viewed as a morphological center. Necessary and sufficient conditions for the idempotence of morphological operators are characterized in terms of their kernel representation. We further extend our results to the representation of the kernel of m-idempotent morphological operators. We then rely on the conditions on the kernel representation derived and establish methods for the construction of m-idempotent and self-dual morphological operators. Finally, we illustrate the importance of the self-duality and m-idempotence properties by an application to speckle noise removal in radar images.

The structure of homomorphisms of connected locally compact groups into compact groups

We obtain consequences of the theorem concerning the automatic continuity of locally bounded finite-dimensional representations of connected Lie groups on the commutator subgroup of the group and also of an analogue of Lie's theorem for (not necessarily continuous) finite-dimensional representations of soluble Lie groups. In particular, we prove that an almost connected locally compact group admitting a (not necessarily continuous) injective homomorphism into a compact group also admits a continuous injective homomorphism into a compact group, and thus the given group is a finite extension of the direct product of a compact group and a vector group. We solve the related problem of describing the images of (not necessarily continuous) homomorphisms of connected locally compact groups into compact groups. Moreover, we refine the description of the von Neumann kernel of a connected locally compact group and describe the intersection of the kernels of all (not necessarily continuous) finite-dimensional unitary representations of a given connected locally compact group. Some applications are mentioned. We also show that every almost connected locally compact group admitting a (not necessarily continuous) locally bounded injective homomorphism into an amenable almost connected locally compact group is amenable.

Kernels of linear representations of Lie groups, locally compact groups, and pro-Lie Groups

Kernels of linear representations of Lie groups, locally compact groups, and pro-Lie Groups

Kernel Eigenvoices (Revisited) for Large-Vocabulary Speech Recognition

Kernelized eigenvoice methods, which apply a nonlinear transform in speaker space, have previously been proposed for rapid adaptation. This paper examines, and addresses, a number of limitations and issues with the current schemes. First, the requirements for valid probability functions using kernel representations are discussed. Second, rapid speaker adaptation using these forms of representations is analyzed and the general update formulae for kernelized eigenvoice adaptation derived. The existing kernelized eigenvoice methods are then described within this formulation. This allows an EM-based, rather than gradient-descent-based, parameter estimation. To enable these approaches to be applied to large-vocabulary speech recognition tasks, eigenbases using transformations of an underlying canonical model are described and related to existing adaptation methods. Preliminary experiments on a large-vocabulary conversational telephone speech task are finally detailed.

L-two-optimal identification of errors-in-variables models: a frequency-domain approach

This paper proposes an L-two-optimal identification approach to cope with errors-in-variables model (EIVM) identification. With normalized coprime factor model (NCFM) representations, L-two-optimal approximate models are derived from the framework of an EIVM according to the kernel and image representations of related signals. Based on the optimal approximate models, the v-gap metric is employed as a minimization criterion to optimize the parameters of a system model, and thus the resulting optimization problem can be solved by linear matrix inequalities (LMIs). In terms of the optimized system model, the noise model (NM) can be readily obtained by right multiplication of an inner. Compared with other EIVM identification methods, the proposed one has a wider scope of applications because the statistical properties of disturbing noises are not demanded. It is also capable of giving identifiability. Finally, a numerical simulation is used to verify the effectiveness of the proposed method.

The Behavioral Approach to Linear Parameter-Varying Systems

Linear parameter-varying (LPV) systems are usually described in either state-space or input-output form. When analyzing system equivalence between different representations it appears that the time-shifted versions of the scheduling signal (dynamic dependence) need to be taken into account. Therefore, representations used previously to define and specify LPV systems are not equal in terms of dynamics. In order to construct a parametrization-free description of LPV systems that overcomes these difficulties, a behavioral approach is introduced that serves as a basis for specifying system theoretic properties. LPV systems are defined as the collection of trajectories of system variables (like inputs and outputs) and scheduling variables. LPV kernel, input-output, and state-space system representations are introduced with appropriate equivalence transformations.