118 research outputs found
Deformable Prototypes for Encoding Shape Categories in Image Databases
We describe a method for shape-based image database search that uses deformable prototypes to represent categories. Rather than directly comparing a candidate shape with all shape entries in the database, shapes are compared in terms of the types of nonrigid deformations (differences) that relate them to a small subset of representative prototypes. To solve the shape correspondence and alignment problem, we employ the technique of modal matching, an information-preserving shape decomposition for matching, describing, and comparing shapes despite sensor variations and nonrigid deformations. In modal matching, shape is decomposed into an ordered basis of orthogonal principal components. We demonstrate the utility of this approach for shape comparison in 2-D image databases.Office of Naval Research (Young Investigator Award N00014-06-1-0661
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices
We propose a Preconditioned Locally Harmonic Residual (PLHR) method for
computing several interior eigenpairs of a generalized Hermitian eigenvalue
problem, without traditional spectral transformations, matrix factorizations,
or inversions. PLHR is based on a short-term recurrence, easily extended to a
block form, computing eigenpairs simultaneously. PLHR can take advantage of
Hermitian positive definite preconditioning, e.g., based on an approximate
inverse of an absolute value of a shifted matrix, introduced in [SISC, 35
(2013), pp. A696-A718]. Our numerical experiments demonstrate that PLHR is
efficient and robust for certain classes of large-scale interior eigenvalue
problems, involving Laplacian and Hamiltonian operators, especially if memory
requirements are tight
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Ultra-wideband systems exploiting orthonormal waveforms
textElectrical and Computer Engineerin
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Optimally efficient neural systems for processing spoken language.
Cognitive models claim that spoken words are recognized by an optimally efficient sequential analysis process. Evidence for this is the finding that nonwords are recognized as soon as they deviate from all real words (Marslen-Wilson 1984), reflecting continuous evaluation of speech inputs against lexical representations. Here, we investigate the brain mechanisms supporting this core aspect of word recognition and examine the processes of competition and selection among multiple word candidates. Based on new behavioral support for optimal efficiency in lexical access from speech, a functional magnetic resonance imaging study showed that words with later nonword points generated increased activation in the left superior and middle temporal gyrus (Brodmann area [BA] 21/22), implicating these regions in dynamic sound-meaning mapping. We investigated competition and selection by manipulating the number of initially activated word candidates (competition) and their later drop-out rate (selection). Increased lexical competition enhanced activity in bilateral ventral inferior frontal gyrus (BA 47/45), while increased lexical selection demands activated bilateral dorsal inferior frontal gyrus (BA 44/45). These findings indicate functional differentiation of the fronto-temporal systems for processing spoken language, with left middle temporal gyrus (MTG) and superior temporal gyrus (STG) involved in mapping sounds to meaning, bilateral ventral inferior frontal gyrus (IFG) engaged in less constrained early competition processing, and bilateral dorsal IFG engaged in later, more fine-grained selection processes
Combinations of Deformable Shape Prototypes
We propose to investigate a model-based technique for encoding non-rigid object classes in terms of object prototypes. Objects from the same class can be parameterized by identifying shape and appearance invariants of the class to devise low-level representations. The approach presented here creates a flexible model for an object class from a set of prototypes. This model is then used to estimate the parameters of low-level representation of novel objects as combinations of the prototype parameters. Variations in the object shape are modeled as non-rigid deformations. Appearance variations are modeled as intensity variations. In the training phase, the system is presented with several example prototype images. These prototype images are registered to a reference image by a finite element-based technique called Active Blobs. The deformations of the finite element model to register a prototype image with the reference image provide the shape description or shape vector for the prototype. The shape vector for each prototype, is then used to warp the prototype image onto the reference image and obtain the corresponding texture vector. The prototype texture vectors, being warped onto the same reference image have a pixel by pixel correspondence with each other and hence are "shape normalized". Given sufficient number of prototypes that exhibit appropriate in-class variations, the shape and the texture vectors define a linear prototype subspace that spans the object class. Each prototype is a vector in this subspace. The matching phase involves the estimation of a set of combination parameters for synthesis of the novel object by combining the prototype shape and texture vectors. The strengths of this technique lie in the combined estimation of both shape and appearance parameters. This is in contrast with the previous approaches where shape and appearance parameters were estimated separately
Efficient algorithms for computing rank-revealing factorizations on a GPU
Standard rank-revealing factorizations such as the singular value
decomposition and column pivoted QR factorization are challenging to implement
efficiently on a GPU. A major difficulty in this regard is the inability of
standard algorithms to cast most operations in terms of the Level-3 BLAS. This
paper presents two alternative algorithms for computing a rank-revealing
factorization of the form , where and are orthogonal and
is triangular. Both algorithms use randomized projection techniques to cast
most of the flops in terms of matrix-matrix multiplication, which is
exceptionally efficient on the GPU. Numerical experiments illustrate that these
algorithms achieve an order of magnitude acceleration over finely tuned GPU
implementations of the SVD while providing low-rank approximation errors close
to that of the SVD
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Albany: Using Component-based Design to Develop a Flexible, Generic Multiphysics Analysis Code
Abstract:
Albany is a multiphysics code constructed by assembling a set of reusable, general components. It is an implicit, unstructured grid finite element code that hosts a set of advanced features that are readily combined within a single analysis run. Albany uses template-based generic programming methods to provide extensibility and flexibility; it employs a generic residual evaluation interface to support the easy addition and modification of physics. This interface is coupled to powerful automatic differentiation utilities that are used to implement efficient nonlinear solvers and preconditioners, and also to enable sensitivity analysis and embedded uncertainty quantification capabilities as part of the forward solve. The flexible application programming interfaces in Albany couple to two different adaptive mesh libraries; it internally employs generic integration machinery that supports tetrahedral, hexahedral, and hybrid meshes of user specified order. We present the overall design of Albany, and focus on the specifics of the integration of many of its advanced features. As Albany and the components that form it are openly available on the internet, it is our goal that the reader might find some of the design concepts useful in their own work. Albany results in a code that enables the rapid development of parallel, numerically efficient multiphysics software tools. In discussing the features and details of the integration of many of the components involved, we show the reader the wide variety of solution components that are available and what is possible when they are combined within a simulation capability.
Key Words: partial differential equations, finite element analysis, template-based generic programmin
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