Results 1  10
of
105
A multilinear singular value decomposition
 SIAM J. Matrix Anal. Appl
, 2000
"... Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are ..."
Abstract

Cited by 472 (22 self)
 Add to MetaCart
(Show Context)
Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pairwise symmetric tensors.
Histograms of oriented optical flow and binetcauchy kernels on nonlinear dynamical systems for the recognition of human actions
 in In IEEE Conference on Computer Vision and Pattern Recognition (CVPR
, 2009
"... System theoretic approaches to action recognition model the dynamics of a scene with linear dynamical systems (LDSs) and perform classification using metrics on the space of LDSs, e.g. BinetCauchy kernels. However, such approaches are only applicable to time series data living in a Euclidean space, ..."
Abstract

Cited by 107 (6 self)
 Add to MetaCart
(Show Context)
System theoretic approaches to action recognition model the dynamics of a scene with linear dynamical systems (LDSs) and perform classification using metrics on the space of LDSs, e.g. BinetCauchy kernels. However, such approaches are only applicable to time series data living in a Euclidean space, e.g. joint trajectories extracted from motion capture data or feature point trajectories extracted from video. Much of the success of recent object recognition techniques relies on the use of more complex feature descriptors, such as SIFT descriptors or HOG descriptors, which are essentially histograms. Since histograms live in a nonEuclidean space, we can no longer model their temporal evolution with LDSs, nor can we classify them using a metric for LDSs. In this paper, we propose to represent each frame of a video using a histogram of oriented optical flow (HOOF) and to recognize human actions by classifying HOOF timeseries. For this purpose, we propose a generalization of the BinetCauchy kernels to nonlinear dynamical systems (NLDS) whose output lives in a nonEuclidean space, e.g. the space of histograms. This can be achieved by using kernels defined on the original nonEuclidean space, leading to a welldefined metric for NLDSs. We use these kernels for the classification of actions in video sequences using (HOOF) as the output of the NLDS. We evaluate our approach to recognition of human actions in several scenarios and achieve encouraging results. 1.
Proactive Detection of Distributed Denial of Service Attacks using MIB Traffic Variables  A Feasibility Study
, 2001
"... In this paper we propose a methodology for utilizing Network Management Systems for the early detection of Distributed Denial of Service (DDoS) Attacks. Although there are quite a large number of events that are prior to an attack (e.g. suspicious logons, start of processes, addition of new files, s ..."
Abstract

Cited by 50 (3 self)
 Add to MetaCart
In this paper we propose a methodology for utilizing Network Management Systems for the early detection of Distributed Denial of Service (DDoS) Attacks. Although there are quite a large number of events that are prior to an attack (e.g. suspicious logons, start of processes, addition of new files, sudden shifts in traffic, etc.), in this work we depend solely on information from MIB (Management Information Base) Traffic Variables collected from the systems participating in the Attack. Three types of DDoS attacks were effected on a Research Test Bed, and MIB variables were recorded. Using these datasets, we show how there are indeed MIBbased precursors of DDoS attacks This work was supported by the Air Force Research Laboratory (Rome, NY  USA) under contract F3060200C0126 to Scientific Systems Company, and by Aprisma's University Fellowship Program 1999/2000. 1 that render it possible to detect them before the Target is shut down. Most importantly, we describe how the relevant MI...
Robust maximumlikelihood estimation of multivariable dynamic systems
 Automatica
, 2005
"... This paper examines the problem of estimating linear timeinvariant statespace system models. In particular it addresses the parametrization and numerical robustness concerns that arise in the multivariable case. These difficulties are well recognised in the literature, resulting (for example) in e ..."
Abstract

Cited by 38 (14 self)
 Add to MetaCart
(Show Context)
This paper examines the problem of estimating linear timeinvariant statespace system models. In particular it addresses the parametrization and numerical robustness concerns that arise in the multivariable case. These difficulties are well recognised in the literature, resulting (for example) in extensive study of subspace based techniques, as well as recent interest in “data driven” local coordinate approaches to gradient search solutions. The paper here proposes a different strategy that employs the Expectation Maximisation (EM) technique. The consequence is an algorithm that is iterative, and locally convergent to stationary points of the (Gaussian) Likelihood function. Furthermore, theoretical and empirical evidence presented here establishes additional attractive properties such as numerical robustness, avoidance of difficult parametrization choices, the ability to estimate unstable systems, the ability to naturally and easily estimate nonzero initial conditions, and moderate computational cost. Moreover, since the methods here are MaximumLikelihood based, they have associated known and asymptotically optimal statistical properties. 1
Hankel matrix rank minimization with applications to system identification and realization
, 2011
"... In this paper, we introduce a flexible optimization framework for nuclear norm minimization of matrices with linear structure, including Hankel, Toeplitz and moment structures, and catalog applications from diverse fields under this framework. We discuss various firstorder methods for solving the ..."
Abstract

Cited by 37 (4 self)
 Add to MetaCart
In this paper, we introduce a flexible optimization framework for nuclear norm minimization of matrices with linear structure, including Hankel, Toeplitz and moment structures, and catalog applications from diverse fields under this framework. We discuss various firstorder methods for solving the resulting optimization problem, including alternating direction methods, proximal point algorithm and gradient projection methods. We perform computational experiments to compare these methods on system identification problem and system realization problem. For the system identification problem, the gradient projection method (accelerated by Nesterov’s extrapolation techniques) usually outperforms other firstorder methods in terms of CPU time on both real and simulated data; while for the system realization problem, the alternating direction method, as applied to a certain primal reformulation, usually outperforms other firstorder methods in terms of CPU time.
BlockToeplitz/Hankel Structured Total Least Squares
, 2003
"... Abstract. A structured total least squares problem is considered in which the extended data matrix is partitioned into blocks and each of the blocks is blockToeplitz/Hankel structured, unstructured, or exact. An equivalent optimization problem is derived and its properties are established. The spe ..."
Abstract

Cited by 24 (17 self)
 Add to MetaCart
(Show Context)
Abstract. A structured total least squares problem is considered in which the extended data matrix is partitioned into blocks and each of the blocks is blockToeplitz/Hankel structured, unstructured, or exact. An equivalent optimization problem is derived and its properties are established. The special structure of the equivalent problem enables us to improve the computational efficiency of the numerical solution methods. By exploiting the structure, the computational complexity of the algorithms (local optimization methods) per iteration is linear in the sample size. Application of the method for system identification and for model reduction is illustrated by simulation examples.
Nonstationary consistency of subspace methods
, 2006
"... In this paper we study “nonstationary consistency” of subspace methods for eigenstructure identification, i.e., the ability of subspace algorithms to converge to the true eigenstructure despite nonstationarities in the excitation and measurement noises. Note that such nonstationarities may result i ..."
Abstract

Cited by 13 (7 self)
 Add to MetaCart
(Show Context)
In this paper we study “nonstationary consistency” of subspace methods for eigenstructure identification, i.e., the ability of subspace algorithms to converge to the true eigenstructure despite nonstationarities in the excitation and measurement noises. Note that such nonstationarities may result in having timevarying zeros for the underlying system, so the problem is nontrivial. In particular, likelihood and prediction error related methods do not ensure consistency under such situation, because estimation of poles and estimation of zeros are tightly coupled. We show in turn that subspace methods ensure such consistency. Our study carefully separates statistical from nonstatistical arguments, therefore enlightening the role of statistical assumptions in this story.
Cooperative Behavior Acquisition by Learning and Evolution in a MultiAgent Environment for Mobile Robots
, 1999
"... The objective of my research described in this dissertation is to realize learning and evolutionary methods for multiagent systems. This dissertation mainly consists of four parts. We propose a method that acquires the purposive behaviors based on the estimation of the state vectors in Chapter 3. In ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
(Show Context)
The objective of my research described in this dissertation is to realize learning and evolutionary methods for multiagent systems. This dissertation mainly consists of four parts. We propose a method that acquires the purposive behaviors based on the estimation of the state vectors in Chapter 3. In order to acquire the cooperative behaviors in multiagent environments, each learning robot estimates the Local Prediction Model (hereafter LPM) between the learner and the other objects separately. The LPM estimate the local interaction while reinforcement learning copes with the global interaction between multiple LPMs and the given tasks. Based on the LPMs which satisfies the Markovian environment assumption as possible, robots learn the desired behaviors using reinforcement learning. We also propose a learning schedule in order to make learning stable especially in the early stage of multiagent systems. Chapter 4 discusses how an agent can develop its behavior according to the complexity of the interactions with its environment. A method for controlling the complexity is
Asymptotic variance of subspace estimates
 Journal of Econometrics
"... We give new simple general expressions for the asymptotic covariance of the estimated system parameters (A, B, C, D) in subspace identification. The formulas can be applied to a whole class of subspace methods including N4SID, MOESP, CVA etc. The asymptotic expressions highlight how the conditioning ..."
Abstract

Cited by 10 (4 self)
 Add to MetaCart
We give new simple general expressions for the asymptotic covariance of the estimated system parameters (A, B, C, D) in subspace identification. The formulas can be applied to a whole class of subspace methods including N4SID, MOESP, CVA etc. The asymptotic expressions highlight how the conditioning of the estimation problem influences the accuracy of the estimates.