117,736 research outputs found
Parameterized Construction of Program Representations for Sparse Dataflow Analyses
Data-flow analyses usually associate information with control flow regions.
Informally, if these regions are too small, like a point between two
consecutive statements, we call the analysis dense. On the other hand, if these
regions include many such points, then we call it sparse. This paper presents a
systematic method to build program representations that support sparse
analyses. To pave the way to this framework we clarify the bibliography about
well-known intermediate program representations. We show that our approach, up
to parameter choice, subsumes many of these representations, such as the SSA,
SSI and e-SSA forms. In particular, our algorithms are faster, simpler and more
frugal than the previous techniques used to construct SSI - Static Single
Information - form programs. We produce intermediate representations isomorphic
to Choi et al.'s Sparse Evaluation Graphs (SEG) for the family of data-flow
problems that can be partitioned per variables. However, contrary to SEGs, we
can handle - sparsely - problems that are not in this family
On the representation of functions and finite difference operators on adaptive sparse grids
In this paper we describe methods to approximate functions and differential operators on adaptive sparse grids. We distinguish between several representations of a function on the sparse grid, and we describe how finite difference (FD) operators can be applied to these representations. For general variable coefficient equations on sparse grids, FD operators allow a more efficient operator evaluation than finite element operators. However, the structure of the FD operators is more complex. In order to examine the possibility to construct efficient solution methods, we analyze the discrete FD (Laplace) operator and compare its hierarchical representation on sparse and on full grids. The analysis gives a motivation for a MG solution algorithm
Comparative Evaluation of Action Recognition Methods via Riemannian Manifolds, Fisher Vectors and GMMs: Ideal and Challenging Conditions
We present a comparative evaluation of various techniques for action
recognition while keeping as many variables as possible controlled. We employ
two categories of Riemannian manifolds: symmetric positive definite matrices
and linear subspaces. For both categories we use their corresponding nearest
neighbour classifiers, kernels, and recent kernelised sparse representations.
We compare against traditional action recognition techniques based on Gaussian
mixture models and Fisher vectors (FVs). We evaluate these action recognition
techniques under ideal conditions, as well as their sensitivity in more
challenging conditions (variations in scale and translation). Despite recent
advancements for handling manifolds, manifold based techniques obtain the
lowest performance and their kernel representations are more unstable in the
presence of challenging conditions. The FV approach obtains the highest
accuracy under ideal conditions. Moreover, FV best deals with moderate scale
and translation changes
On the representation of functions and finite difference operators on adaptive dyadic grids
In this paper we describe methods to approximate functions and differential operators on adaptive sparse (dyadic) grids. We distinguish between several representations of a function on the sparse grid and we describe how finite difference (FD) operators can be applied to these representations. For general variable coefficient equations on sparse grids, genuine finite element (FE) discretizations are not feasible and FD operators allow an easier operator evaluation than the adapted FE operators. However, the structure of the FD operators is complex. With the aim to construct an efficient multigrid procedure, we analyze the structure of the discrete Laplacian in its hierarchical representation and show the relation between the full and the sparse grid case. The rather complex relations, that are expressed by scaling matrices for each separate coordinate direction, make us doubt about the possibility of constructing efficient preconditioners that show spectral equivalence. Hence, we question the possibility of constructing a natural multigrid algorithm with optimal O(N) efficiency. We conjecture that for the efficient solution of a general class of adaptive grid problems it is better to accept an additional condition for the dyadic grids (condition L) and to apply adaptive hp-discretization
Multi-dimensional sparse structured signal approximation using split bregman iterations
International audienceThe paper focuses on the sparse approximation of signals using overcomplete representations, such that it preserves the (prior) structure of multi-dimensional signals. The underlying optimization problem is tackled using a multi-dimensional extension of the split Bregman optimization approach. An extensive empirical evaluation shows how the proposed approach compares to the state of the art depending on the signal features
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