Dandan Li, C. P. Kwong · 2008
The Basic Vector Space Model (BVSM) is well known in information retrieval. Unfortunately, it can not retrieve all relevant documents since it is based on literal term matching. The Generalized Vector Space Model (GVSM) and Latent Semantic Indexing (LSI) are two famous semantic retrieval methods, for which we assume there is some underlying latent semantic structure in a dataset. However, their assumptions about where the semantic structure locates are a bit strong. In this paper, we present a new understanding on the latent semantic space of a dataset from the dual perspective, which relaxes the above assumed conditions and leads naturally a unified kernel function for a class of vector space models and then makes its geometrical meanings clear. New semantic analysis methods based on the unified kernel function are developed, which combine the advantages of LSI and GVSM. We also present a mathematical theorem that the new methods possess the stable property of the rank choice. The experimental results of our methods are promising on the standard test sets.
Cited by 0
Asoke K. Nandi, Hosameldin Ahmed · 2019
Various techniques have been proposed to learn subspace features from a large number of vibration signals in rotating machine fault diagnosis. These include linear subspace learning (LSL), nonlinear subspace learning, and feature-selection techniques. LSL has been extensively used in several areas of information processing, such as data mining, dimensionality reduction, and pattern recognition. The basic idea of LSL is to map a high-dimensional feature space to a lower-dimensional feature space through linear projection. This chapter presents LSL techniques that can be used to learn features from a large amount of vibration signals. The techniques include: principal component analysis (PCA), independent component analysis (ICA), linear discriminant analysis (LDA), canonical correlation analysis (CCA), and partial least squares (PLS). Of these techniques, PCA, ICA, and LDA are amongst the most commonly used in machine fault diagnosis. CCA and PLS have been considered in many application of fault detection including machine fault detection.
Cited by 0
Douglas W Oldenburg, Yaoguo Li · 1994
Abslract. This paper presents a robust, flexible and efficient algorithm to solve large scale linear inverse problems. The method is iterative and at each iteration a perturbation in a q-dimensional subspace of an M-dimensional model space is sought. The basis vectors for the subspace are primarily steepest descent vectors obtained from segmenting the data misfit and model objective functions. The efficiency of the algorithm is realized because only a y x y matrix needs to be inverted at each iteration instead of a matrix of order M. As M becomes large the number of computations per iteration is of order y N M where N is the number of data. An important feature of our algorithm is that positivity can easily be incorporated into the solution. We do this by introducing n two-segment mapping which transforms positive parameters to parameters defined on the rea1 line. The nonlinear mapping requires that a line s e m h involving forward modclling is implemented so that at each iteration we obtain a model which misfits the data to a predetermined level. This obviates the need to carry out additional inversions with trial and error selection of a Lagrange multiplier. In this paper we present the details of the subspace algorithm and explore the effect on convergence of using different suategies for selecting basis vectors and altering adjustable panmeters which control the rate of decrease in the misfit and rate of increase i n the model norm as a function of iteration number. 1.
Cited by 0
Yanfang Li, Jing Lei · Statistics · 2018
We study high dimensional multigroup classification from a sparse subspace estimation perspective, unifying the linear discriminant analysis (LDA) with other recent developments in high dimensional multivariate analysis using similar tools, such as penalization method. We develop two two-stage sparse LDA models, where in the first stage, convex relaxation is used to convert two classical formulations of LDA to semidefinite programs, and furthermore subspace perspective allows for straightforward regularization and estimation. After the initial convex relaxation, we use a refinement stage to improve the accuracy. For the first model, a penalized quadratic program with group lasso penalty is used for refinement, whereas a sparse version of the power method is used for the second model. We carefully examine the theoretical properties of both methods, alongside with simulations and real data analysis.
Cited by 3
Salah Herzi, Habib Marzougui · Indian Journal of Pure and Applied Mathematics · 2023
Cited by 0
Jwo-Yuh Wu, Liang-Chi Huang, Wen-Hsian Li et al. · IEEE RESOURCE CENTERS · 2024
Cited by 0Open access
Yang Wen-qi · 2001
By giving the maxmin subspace of linear space and obtaining the follow some results:(1)Subspace M be maxmin subspace if and only if M be complemented subspace of one dimension subspace;(2)Every subspace in linear space can be written as intersection of some maxmin subspaces;(3)In the linear space with descending chain condition of subspaces,every subspace can be written as finite intersection of maxmin subspaces.
Cited by 0
Yilun Shang · Forum Mathematicum · 2016
Abstract In this note, we introduce the asymptotic subspace confinement problem, generalizing the usual concept of convergence in discrete-time linear systems. Instead of precise convergence, subspace confinement only requires the convergence of states to a certain subspace of the state space, offering useful flexibility and applicability. We establish a criterion for deciding the asymptotic subspace confinement, drawing upon a general finiteness result for the infinite product of matrices. Our results indicate that the asymptotic subspace confinement problem is algorithmically decidable when an invariant subspace for the set of matrices and some polytope norms are given.
Cited by 15
Tomohiro Sogabe · Springer series in computational mathematics · 2022
Cited by 11Open access
Xudong Jiang · IEEE Signal Processing Magazine · 2011
The ultimate goal of pattern recognition is to discriminate the class membership of the observed novel objects with the minimum misclassification rate. An observed object is often represented by a high dimensional real-valued vector after some preprocessing while its class membership can be represented by a much lower dimensional binary vector. Thus, in the discriminating process, a pattern recognition system intrinsically reduces the dimensionality of the input data into the number of classes.
Cited by 161
Hunn, David Robert Joseph · ScholarsArchive (Brigham Young University) · 2024
We introduce a new method for the study of linear codes, termed subspace decomposition, which provides new insights into code structure and performance. Briefly, subspace decomposition comprises the evaluation of complex properties of a linear code by evaluating simple properties of its constituent subspaces. We find that this technique has application to a number of problems in coding theory. When applied to the problem of evaluating the performance of secrecy codes, subspace decomposition provides an efficient method for computing the equivocation of coset codes over the binary erasure wiretap channel. It is also especially efficient in computing the chi squared divergence, a metric which relates to an eavesdropper's maximum likelihood decoding performance. We use subspace decomposition to prove theoretical results about certain classes of codes, including a new code construction termed subspace exclusion codes, which are optimal in a number of situations. We also employ subspace decomposition to the problem of finding good coset codes of any size via gradient descent. As part of this effort, we develop specialized methods to produce a discrete code from a continuous code definition vector. These methods result in secrecy codes superior to those produced by other known methods. The results of these efforts also indicate remarkably poor performance for secrecy codes based on duals of low-density parity check codes. We also present a method for efficiently determining whether different codes are equivalent based on the properties of their subspaces. A wide variety of applications for subspace decomposition are also identified for future research.
Cited by 0
Vincent Verdult, et al. · 2004
Subspace identification can be used to obtain models of piecewise linear state-space systems for which the switching is known. The models should not switch faster than the block size of the Hankel matrices used. The nonconsecutive parts of the input and output data that correspond to one of the local linear systems can be used to obtain the system matrices of that system up to a linear state transformation. The linear systems obtained in this way cannot be combined directly, because the state transformation is different for each of the local linear systems. The transitions between the local linear systems can be used to transform the models to the same state space basis. We show that the necessary transformations can be obtained from the data, if the data contains a sufficiently large number of transitions for which the states at the transition are linearly independent. An algorithm to determine the transformations is presented, and the sensitivity with respect to noise is investigated using a Monte-Carlo simulation.
Cited by 0
Shusen Wang, Bojun Tu, Congfu Xu et al. · Proceedings of the AAAI Conference on Artificial Intelligence · 2014
Subspace clustering is an important unsupervised learning problem with wide applications in computer vision and data analysis. However, the state-of-the-art methods for this problem suffer from high time complexity---quadratic or cubic in $n$ (the number of data instances). In this paper we exploit a data selection algorithm to speedup computation and the robust principal component analysis to strengthen robustness. Accordingly, we devise a scalable and robust subspace clustering method which costs time only linear in $n$. We prove theoretically that under certain mild assumptions our method solves the subspace clustering problem exactly even for grossly corrupted data. Our algorithm is based on very simple ideas, yet it is the only linear time algorithm with noiseless or noisy recovery guarantee. Finally, empirical results verify our theoretical analysis.
Cited by 26Open access
Vincent Verdult, Michel Verhaegen · 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) · 2004
Subspace identification can be used to obtain models of piecewise linear state-space systems for which the switching is known. The models should not switch faster than the block size of the Hankel matrices used. The nonconsecutive parts of the input and output data that correspond to one of the local linear systems can be used to obtain the system matrices of that system up to a linear state transformation. The linear systems obtained in this way cannot be combined directly, because the state transformation is different for each of the local linear systems. The transitions between the local linear systems can be used to transform the models to the same state space basis. We show that the necessary transformations can be obtained from the data, if the data contains a sufficiently large number of transitions for which the states at the transition are linearly independent. An algorithm to determine the transformations is presented, and the sensitivity with respect to noise is investigated using a Monte-Carlo simulation.
Cited by 79
M. Heymann, M. Pachter, R. J. Stern · Kobe University Repository Kernel (Kobe University) · 1977
Cited by 0Open access
Bulletin of Miscellaneous Information (Royal Gardens Kew)
Cited by 0
Hieu V. Nguyen · Nottingham ePrints (University of Nottingham) · 2011
Despite over 30 years of research, face recognition is still one of the most difficult problems in the field of Computer Vision. The challenge comes from many factors affecting the performance of a face recognition system: noisy input, training data collection, speed-accuracy trade-off, variations in expression, illumination, pose, or ageing. Although relatively successful attempts have been made for special cases, such as frontal faces, no satisfactory methods exist that work under completely unconstrained conditions. This thesis proposes solutions to three important problems: lack of training data, speed-accuracy requirement, and unconstrained environments. \n\nThe problem of lacking training data has been solved in the worst case: single sample per person. Whitened Principal Component Analysis is proposed as a simple but effective solution. Whitened PCA performs consistently well on multiple face datasets.\n\nSpeed-accuracy trade-off problem is the second focus of this thesis. Two solutions are proposed to tackle this problem. The first solution is a new feature extraction method called Compact Binary Patterns which is about three times faster than Local Binary Patterns. The second solution is a multi-patch classifier which performs much better than a single classifier without compromising speed.\n\nTwo metric learning methods are introduced to solve the problem of unconstrained face recognition. The first method called Indirect Neighourhood Component Analysis combines the best ideas from Neighourhood Component Analysis and One-shot learning. The second method, Cosine Similarity Metric Learning, uses Cosine Similarity instead of the more popular Euclidean distance to form the objective function in the learning process. This Cosine Similarity Metric Learning method produces the best result in the literature on the state-of-the-art face dataset: the Labelled Faces in the Wild dataset.\n\nFinally, a full face verification system based on our real experience taking part in ICPR 2010 Face Verification contest is described. Many practical points are discussed.
Cited by 8Open access
Mahak, Maheshanand Bhaintwal · Finite Fields and Their Applications · 2025
Cited by 0
Bulletin of Miscellaneous Information (Royal Gardens Kew)
Cited by 0
Daniel Schmidthäusler, Markus Clemens, Sebastian Schöps · 2013
Cited by 0