Locality

About: Locality is a research topic. Over the lifetime, 3943 publications have been published within this topic receiving 96688 citations.

Locality Preserving Projections

Abstract: Many problems in information processing involve some form of dimensionality reduction. In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis (PCA) – a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold. As a result, LPP shares many of the data representation properties of nonlinear techniques such as Laplacian Eigenmaps or Locally Linear Embedding. Yet LPP is linear and more crucially is defined everywhere in ambient space rather than just on the training data points. This is borne out by illustrative examples on some high dimensional data sets.

The SPLASH-2 programs: characterization and methodological considerations

Abstract: The SPLASH-2 suite of parallel applications has recently been released to facilitate the study of centralized and distributed shared-address-space multiprocessors. In this context, this paper has two goals. One is to quantitatively characterize the SPLASH-2 programs in terms of fundamental properties and architectural interactions that are important to understand them well. The properties we study include the computational load balance, communication to computation ratio and traffic needs, important working set sizes, and issues related to spatial locality, as well as how these properties scale with problem size and the number of processors. The other, related goal is methodological: to assist people who will use the programs in architectural evaluations to prune the space of application and machine parameters in an informed and meaningful way. For example, by characterizing the working sets of the applications, we describe which operating points in terms of cache size and problem size are representative of realistic situations, which are not, and which re redundant. Using SPLASH-2 as an example, we hope to convey the importance of understanding the interplay of problem size, number of processors, and working sets in designing experiments and interpreting their results.

A data locality optimizing algorithm

Abstract: This paper proposes an algorithm that improves the locality of a loop nest by transforming the code via interchange, reversal, skewing and tiling. The loop transformation algorithm is based on two concepts: a mathematical formulation of reuse and locality, and a loop transformation theory that unifies the various transforms as unimodular matrix transformations.The algorithm has been implemented in the SUIF (Stanford University Intermediate Format) compiler, and is successful in optimizing codes such as matrix multiplication, successive over-relaxation (SOR), LU decomposition without pivoting, and Givens QR factorization. Performance evaluation indicates that locality optimization is especially crucial for scaling up the performance of parallel code.