Order statistics, i.e., quantiles, are frequentlyused in databases both at the database serveras ... more Order statistics, i.e., quantiles, are frequentlyused in databases both at the database serveras well as the application level. For example,they are useful in selectivity estimation duringquery optimization, in partitioning large relations,in estimating query result sizes whenbuilding user interfaces, and in characterizingthe data distribution of evolving datasets inthe process of data mining.
Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154), 2000
Page 1. Nonlinear vector multiresolution analysis Maya Gupta Department of Electrical Engineering... more Page 1. Nonlinear vector multiresolution analysis Maya Gupta Department of Electrical Engineering Stanford University Stanford, CA guptamaQstanford.edu Abstract ... Pmc. of the IEEE, 1990. V. Barnett. The ordering of multivariate data (with discus-sion). J R. Statist. Soc. ...
We consider a streaming data model in which n sensors observe individual streams of data, present... more We consider a streaming data model in which n sensors observe individual streams of data, presented in a turnstile model. Our goal is to analyze the singular value decomposition (SVD) of the matrix of data defined implicitly by the stream of updates. Each column i of the data matrix is given by the stream of updates seen at sensor i. Our approach is to sketch each column of the matrix, forming a "sketch matrix" Y, and then to compute the SVD of the sketch matrix. We show that the singular values and right singular vectors of Y are close to those of X, with small relative error. We also believe that this bound is of independent interest in non-streaming and non-distributed data collection settings. Assuming that the data matrix X is of size Nxn, then with m linear measurements of each column of X, we obtain a smaller matrix Y with dimensions mxn. If m = O(k \epsilon^{-2} (log(1/\epsilon) + log(1/\delta)), where k denotes the rank of X, then with probability at least 1-\delt...
This paper describes a signal recognition system that is jointly optimized from mathematical repr... more This paper describes a signal recognition system that is jointly optimized from mathematical representation, algorithm design and final implementation. The goal is to exploit signal properties to jointly optimize a computation, beginning with first principles (mathe- matical representation) and completed with implementation. We use a BestBasis algorithm to search a large collection of orthogonal transforms derived from the Walsh-Hadamard transform to find a series of trans- forms which best discriminate among signal classes.The implementation exploits the structure of these matrices to compress the matrix repre- sentation, and in the process of multiplying the signal by the transform, reuse the results of prior computation and parallelize the implementation in hardware. Through this joint optimization, this dynamic, data-driven system is able to yield much more highly optimized results than if the optimizations were performed statically and in isolation. We provide re- sults taken f...
This paper evaluates the potential of exploiting computation reuse in a signal recognition system... more This paper evaluates the potential of exploiting computation reuse in a signal recognition system that is jointly optimized from mathematical representation, algorithm design and final implementation. Walsh wavelet packets in conjunction with a BestBasis algorithm are used to derive transforms that discriminate between signals. The FPGA implementation of this computation exploits the structure of the resulting transform matrices in several ways to derive a highly optimized hardware representation of this signal recognition problem. Specifically, we observe in the transform matrices a significant amount of reuse of subrows, thus indicating redundant computation. Through analysis of this reuse, we discover the potential for a 3times reduction in the amount of computation of combining a transform matrix and signal. In this paper, we focus on how the implementation might exploit this reuse in a profitable way. By exploiting a subset of this computation reuse, the system can navigate the...
Domain-specific optimizations that exploit specific arithmetic and representation formats have be... more Domain-specific optimizations that exploit specific arithmetic and representation formats have been shown to achieve significant performance/area gains in FPGA hardware designs. In this work, we describe an approach to domain-specific optimization that goes beyond this representation level. We perform a joint optimization from a high-level mathematical abstract representation and hardware implementation point of view. We focus on a signal recognition system that distinguishes between spoken digits. We construct transform matrices from Walsh wavelet packets in conjunction with a BestBasis algorithm. The resulting transform matrices exhibit a rich algebraic structure and contain significant overlap across rows, exhibiting significant computation reuse in the dot-product operation of the transform matrix applied to the signal vector. We have developed an algorithm for identifying the computation reuse and scheduling the row computations across various computation units to significantly...
Proceeding of the ACM/SIGDA international symposium on Field programmable gate arrays - FPGA '09, 2009
Domain-specific optimizations that exploit specific arithmetic and representation formats have be... more Domain-specific optimizations that exploit specific arithmetic and representation formats have been shown to achieve significant performance/area gains in FPGA hardware designs. In this work, we describe an approach to domain-specific optimization that goes beyond this representation level. We perform a joint optimization from a high-level mathematical abstract representation and hardware implementation point of view. We focus on a signal recognition
2008 IEEE International Symposium on Parallel and Distributed Processing, 2008
... USA Portugal USA {melina,mhall}@isi.edu pedro.diniz@tagus.ist.utl.pt {annacg,yiws}@ umich.edu... more ... USA Portugal USA {melina,mhall}@isi.edu pedro.diniz@tagus.ist.utl.pt {annacg,yiws}@ umich.edu Abstract ... The optimization strategy begins with the derivation of a mathematical trans-form most appropriate for a training set of phonemes. ...
Page 1. Sublinear recovery of sparse wavelet signals R. Maleh AC Gilbert ∗ Department of Mathemat... more Page 1. Sublinear recovery of sparse wavelet signals R. Maleh AC Gilbert ∗ Department of Mathematics, University of Michigan January 8, 2008 Abstract There are two main classes of decoding algorithms for compressed sens ...
Order statistics, i.e., quantiles, are frequentlyused in databases both at the database serveras ... more Order statistics, i.e., quantiles, are frequentlyused in databases both at the database serveras well as the application level. For example,they are useful in selectivity estimation duringquery optimization, in partitioning large relations,in estimating query result sizes whenbuilding user interfaces, and in characterizingthe data distribution of evolving datasets inthe process of data mining.
Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154), 2000
Page 1. Nonlinear vector multiresolution analysis Maya Gupta Department of Electrical Engineering... more Page 1. Nonlinear vector multiresolution analysis Maya Gupta Department of Electrical Engineering Stanford University Stanford, CA guptamaQstanford.edu Abstract ... Pmc. of the IEEE, 1990. V. Barnett. The ordering of multivariate data (with discus-sion). J R. Statist. Soc. ...
We consider a streaming data model in which n sensors observe individual streams of data, present... more We consider a streaming data model in which n sensors observe individual streams of data, presented in a turnstile model. Our goal is to analyze the singular value decomposition (SVD) of the matrix of data defined implicitly by the stream of updates. Each column i of the data matrix is given by the stream of updates seen at sensor i. Our approach is to sketch each column of the matrix, forming a "sketch matrix" Y, and then to compute the SVD of the sketch matrix. We show that the singular values and right singular vectors of Y are close to those of X, with small relative error. We also believe that this bound is of independent interest in non-streaming and non-distributed data collection settings. Assuming that the data matrix X is of size Nxn, then with m linear measurements of each column of X, we obtain a smaller matrix Y with dimensions mxn. If m = O(k \epsilon^{-2} (log(1/\epsilon) + log(1/\delta)), where k denotes the rank of X, then with probability at least 1-\delt...
This paper describes a signal recognition system that is jointly optimized from mathematical repr... more This paper describes a signal recognition system that is jointly optimized from mathematical representation, algorithm design and final implementation. The goal is to exploit signal properties to jointly optimize a computation, beginning with first principles (mathe- matical representation) and completed with implementation. We use a BestBasis algorithm to search a large collection of orthogonal transforms derived from the Walsh-Hadamard transform to find a series of trans- forms which best discriminate among signal classes.The implementation exploits the structure of these matrices to compress the matrix repre- sentation, and in the process of multiplying the signal by the transform, reuse the results of prior computation and parallelize the implementation in hardware. Through this joint optimization, this dynamic, data-driven system is able to yield much more highly optimized results than if the optimizations were performed statically and in isolation. We provide re- sults taken f...
This paper evaluates the potential of exploiting computation reuse in a signal recognition system... more This paper evaluates the potential of exploiting computation reuse in a signal recognition system that is jointly optimized from mathematical representation, algorithm design and final implementation. Walsh wavelet packets in conjunction with a BestBasis algorithm are used to derive transforms that discriminate between signals. The FPGA implementation of this computation exploits the structure of the resulting transform matrices in several ways to derive a highly optimized hardware representation of this signal recognition problem. Specifically, we observe in the transform matrices a significant amount of reuse of subrows, thus indicating redundant computation. Through analysis of this reuse, we discover the potential for a 3times reduction in the amount of computation of combining a transform matrix and signal. In this paper, we focus on how the implementation might exploit this reuse in a profitable way. By exploiting a subset of this computation reuse, the system can navigate the...
Domain-specific optimizations that exploit specific arithmetic and representation formats have be... more Domain-specific optimizations that exploit specific arithmetic and representation formats have been shown to achieve significant performance/area gains in FPGA hardware designs. In this work, we describe an approach to domain-specific optimization that goes beyond this representation level. We perform a joint optimization from a high-level mathematical abstract representation and hardware implementation point of view. We focus on a signal recognition system that distinguishes between spoken digits. We construct transform matrices from Walsh wavelet packets in conjunction with a BestBasis algorithm. The resulting transform matrices exhibit a rich algebraic structure and contain significant overlap across rows, exhibiting significant computation reuse in the dot-product operation of the transform matrix applied to the signal vector. We have developed an algorithm for identifying the computation reuse and scheduling the row computations across various computation units to significantly...
Proceeding of the ACM/SIGDA international symposium on Field programmable gate arrays - FPGA '09, 2009
Domain-specific optimizations that exploit specific arithmetic and representation formats have be... more Domain-specific optimizations that exploit specific arithmetic and representation formats have been shown to achieve significant performance/area gains in FPGA hardware designs. In this work, we describe an approach to domain-specific optimization that goes beyond this representation level. We perform a joint optimization from a high-level mathematical abstract representation and hardware implementation point of view. We focus on a signal recognition
2008 IEEE International Symposium on Parallel and Distributed Processing, 2008
... USA Portugal USA {melina,mhall}@isi.edu pedro.diniz@tagus.ist.utl.pt {annacg,yiws}@ umich.edu... more ... USA Portugal USA {melina,mhall}@isi.edu pedro.diniz@tagus.ist.utl.pt {annacg,yiws}@ umich.edu Abstract ... The optimization strategy begins with the derivation of a mathematical trans-form most appropriate for a training set of phonemes. ...
Page 1. Sublinear recovery of sparse wavelet signals R. Maleh AC Gilbert ∗ Department of Mathemat... more Page 1. Sublinear recovery of sparse wavelet signals R. Maleh AC Gilbert ∗ Department of Mathematics, University of Michigan January 8, 2008 Abstract There are two main classes of decoding algorithms for compressed sens ...
Uploads