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21
PrivacyPreserving Multivariate Statistical Analysis: Linear Regression and Classification
 In Proceedings of the 4th SIAM International Conference on Data Mining
, 2004
"... analysis technique that has found applications in various areas. In this paper, we study some multivariate statistical analysis methods in Secure 2party Computation (S2C) framework illustrated by the following scenario: two parties, each having a secret data set, want to conduct the statistical ana ..."
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Cited by 65 (1 self)
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analysis technique that has found applications in various areas. In this paper, we study some multivariate statistical analysis methods in Secure 2party Computation (S2C) framework illustrated by the following scenario: two parties, each having a secret data set, want to conduct the statistical analysis on their joint data, but neither party is willing to disclose its private data to the other party or any third party. The current statistical analysis techniques cannot be used directly to support this kind of computation because they require all parties to send the necessary data to a central place. In this paper, We define two Secure 2party multivariate statistical analysis problems: Secure 2party Multivariate Linear Regression problem and Secure 2party Multivariate Classification problem. We have developed a practical security model, based on which we have developed a number of building blocks for solving these two problems.
Interpolation, Spectrum Analysis, ErrorControl Coding, and FaultTolerant Computing
 In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 97, volume III
, 1997
"... This paper uncovers relations between the topics mentioned in the title, relations that we believe to have gone nearly unnoticed so far. More precisely, we show that four often studied problems in signal processing, spectrum analysis, information theory, and computing are closely related or even equ ..."
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Cited by 16 (7 self)
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This paper uncovers relations between the topics mentioned in the title, relations that we believe to have gone nearly unnoticed so far. More precisely, we show that four often studied problems in signal processing, spectrum analysis, information theory, and computing are closely related or even equivalent in a certain sense (if one of them can be solved, so can any of the others, and using essentially the same algorithms). The problems are (i) a nonlinear bandlimited finitedimensional interpolation problem (ii) the problem of estimating a signal that is the superposition of a finite number of harmonics (iii) an errorcontrol coding problem in the real field, and (iv) certain techniques that occur in algorithmbased fault tolerant computing. The advantages of recognizing these problems as equivalent are obvious: the techniques commonly used in one field can be imported to the others, the duplication of research e#orts is prevented, and the overall degree of understanding of the four problems increases. New algorithms are suggested as a result of these investigations. 1. NOTATION The complex ndimensional space, with the usual inner product and norm, is denoted by C n . A signal is a ndimensional complex vector x, with components, or samples, x(0), x(1), . . . , x(n 1). The Fourier matrix F is the n n matrix whose elements F ab are given by F ab = e j n ab where j denotes the imaginary unit. The discrete Fourier transform (DFT) of x, denoted by x, is defined by x = Fx. A signal x is bandlimited if a subset of the samples of x vanish, and is lowpass if the nonzero DFT Fax +35134370545, emails vieira@inesca.pt and pjf@inesca.pt. This work was supported by JNICT.
NonConcurrent Error Detection and Correction in FaultTolerant Linear FiniteState Machines
 IEEE Transactions on Automatic Control
, 2002
"... Previous work constructed faulttolerant linear finitestate machines (LFSMs) by embedding a given LFSM into a larger, redundant LFSM that preserves the evolution and properties of the original one while enabling an external mechanism to perform concurrent error detection and correction. In this pap ..."
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Cited by 13 (5 self)
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Previous work constructed faulttolerant linear finitestate machines (LFSMs) by embedding a given LFSM into a larger, redundant LFSM that preserves the evolution and properties of the original one while enabling an external mechanism to perform concurrent error detection and correction. In this paper, we construct faulttolerant LFSMs that allow the external mechanism to perform nonconcurrent error detection and correction (i.e., to perform checking periodically, for instance, once every N time steps). This approach relaxes the requirements on the reliability of the error detecting/correcting mechanism because the mechanism can operate at a slower speed than the rest of the system. We characterize constructions for nonconcurrent detection of single errors and also present schemes which use BCH coding to allow for efficient nonconcurrent detection and correction of multiple errors.
Mathematics for Multimedia Signal Processing II: Discrete Finite Frames and Signal Reconstruction
 in Signal Processing for Multimedia
, 1999
"... . Certain signal reconstruction problems can be understood in terms of frames and redundant representations. The redundancy is useful because it leads to robust signal representations, that is, representations in which partial loss of data can be tolerated without misbehavior or adverse effects. ..."
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Cited by 10 (3 self)
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. Certain signal reconstruction problems can be understood in terms of frames and redundant representations. The redundancy is useful because it leads to robust signal representations, that is, representations in which partial loss of data can be tolerated without misbehavior or adverse effects. This chapter begins by presenting a few engineering problems in which robust data representations play a central role. It turns out that these problems, which occur in signal processing, spectrum analysis, information theory, and faulttolerant computing, are closely related or even equivalent. However, perhaps surprisingly, the connections between them have gone nearly unnoticed so far. Frames, and in particular discrete finite frames, provide one of the ways of understanding certain of these problems, including the important missing data problem. Some of the methods that can be used to recover from missing data errors are examined, emphasizing finitedimensional theory because of i...
Structured Redundancy for Fault Tolerance in LTI StateSpace Models and Petri Nets
 Kybernetika
, 1999
"... The design and implementation of dynamic systems has traditionally focused on minimal representations which require the least number of state variables. However, \structured redundancy"  redundancy that has been intentionally introduced in some systematic way  can be extremely important when ..."
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Cited by 9 (9 self)
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The design and implementation of dynamic systems has traditionally focused on minimal representations which require the least number of state variables. However, \structured redundancy"  redundancy that has been intentionally introduced in some systematic way  can be extremely important when fault tolerance is desired. The redundancy can be used to detect and correct errors or to guarantee desirable performance despite hardware or computational failures. Modular redundancy, the traditional approach to fault tolerance, is prohibitively expensive because of the overhead in replicating the hardware. This paper discusses alternative methods for systematically introducing redundancy in dynamic systems. Our approach consists of mapping the state space of the original system into a redundant space of higher dimension while preserving the properties of the original system in some encoded form within this larger space. We illustrate our approach by focusing on linear timeinvariant (LTI) dyna...
Numerically Stable Real Number Codes Based on Random Matrices
 In Proceeding of the 5th International Conference on Computational Science (ICCS2005
, 2004
"... Abstract. Error correction codes defined over realnumber field have been studied and recognized as useful in many applications. However, most realnumber codes in literature are quite suspect in their numerical stability. In this paper, we introduce a class of realnumber codes based on random gene ..."
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Cited by 5 (5 self)
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Abstract. Error correction codes defined over realnumber field have been studied and recognized as useful in many applications. However, most realnumber codes in literature are quite suspect in their numerical stability. In this paper, we introduce a class of realnumber codes based on random generator matrices over realnumber fields. Codes over complexnumber field are also discussed. Experiment results demonstrate our codes are numerically much more stable than existing codes in literature. 1
Numerically stable realnumber codes based on random matrices
 in ITW2004
"... Abstract — Error correction codes defined over realnumber and complexnumber fields have been studied and recognized as useful in many applications. However, most realnumber and complexnumber codes in literature are quite suspect in their numerical stability. In this paper, we introduce a class of ..."
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Cited by 3 (2 self)
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Abstract — Error correction codes defined over realnumber and complexnumber fields have been studied and recognized as useful in many applications. However, most realnumber and complexnumber codes in literature are quite suspect in their numerical stability. In this paper, we introduce a class of numerically stable realnumber and complexnumber codes that are based on random generator matrices over realnumber and complexnumber fields.
Fault tolerant QRDecomposition Algorithm Based on Householder
 Reflections and its Parallel Implementation, Proc.4th Int. Workshop Parallel Numerics`97
, 1997
"... Abstract. A faulttolerant algorithms based on Givens rotations and modified weighted checksum methods are proposed for matrix QRdecomposition. The purpose is to detect and correct the calculation errors occurred due to transient hardware faults during computation. The proposed algorithm enables to ..."
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Cited by 3 (1 self)
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Abstract. A faulttolerant algorithms based on Givens rotations and modified weighted checksum methods are proposed for matrix QRdecomposition. The purpose is to detect and correct the calculation errors occurred due to transient hardware faults during computation. The proposed algorithm enables to correct a single error in each row or column of an input matrix A(M,N) occurred at any among N steps of algorithm implementation. Consequently, it is possible to correct up to N 2 single transient errors during solving the whole decomposition problem. This effect is obtained by increasing the computational complexity of the original Givens method on 2,5N 2 + O(N) multiplyadd operations. Finally, the parallel version of proposed algorithm is designed, dedicated for realisation on a fixedsize linear processor array with fully local communications and low I/O requirements. 1
A Unified Approach to Sparse Signal Processing
, 2009
"... A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, ar ..."
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Cited by 2 (1 self)
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A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, component analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding in finite and real Galois fields is then related to oversampling with similar reconstruction algorithms. The methods of Prony, Pisarenko, and MUltiple SIgnal Classification (MUSIC) are next shown to be targeted at analyzing signals with sparse frequency domain representations. Specifically, the relations of the approach of Prony to an annihilating filter in rate of innovation and Error Locator Polynomials in coding are emphasized; the Pisarenko and MUSIC methods are further improvements of the Prony method. Such narrowband spectral estimation is then related to multisource location and direction of arrival estimation in array processing. The notions of sparse array beamforming and sparse sensor networks are also introduced. Sparsity in unobservable source signals is also shown to facilitate source separation in Sparse Component Analysis (SCA); the algorithms developed in this area are also widely used in compressed sensing. Finally, the nature of the multipath channel estimation problem is shown to have a sparse formulation; algorithms similar to sampling and coding are used to estimate typical multicarrier communication channels.
Optimal Real Number Codes for Fault Tolerant Matrix Operations
"... Today s long running high performance computing applications typically tolerate failstop failures by checkpointing. However, applications such as dense linear algebra computations often modify a large mount of memory between checkpoints and checkpointing usually introduces considerable overhead whe ..."
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Cited by 2 (0 self)
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Today s long running high performance computing applications typically tolerate failstop failures by checkpointing. However, applications such as dense linear algebra computations often modify a large mount of memory between checkpoints and checkpointing usually introduces considerable overhead when the number of processors used for computation is large. It has been demonstrated in [13] that single failstop failure in ScaLAPACK matrix multiplication can be tolerated without checkpointing at a decreasing overhead rate of 1 / √ p, where p is the number of processors used for computation. Multiple simultaneous processor failures can be tolerated without checkpointing by encoding matrices using a realnumber erasure correction code. However, the floatingpoint representation of a real number in today’s high performance computers introduces round off errors which can be enlarged and cause the loss of precision of possibly all digits during recovery when the number of processors in the system is large. In this paper, we present a class of ReedSolomon style realnumber erasure correcting codes which is numerically optimal during recovery. We analytically construct the numerically best erasure correcting codes for 2 erasures and develop an approximation method to computationally construct numerically good codes for 3 or more erasures. We prove that it is impossible even for the numerically best minimum redundancy erasure correcting codes to correct all erasure patterns when the total number of processors is large. We give the conditions that guarantee to correct all two erasures. Experimental results demonstrate that the proposed codes are numerically much more stable than existing codes. 1.