This letter proposes a numerical method for approximating the location of and dynamics on a class of chaotic saddles. In contrast to the conventional strategy of maximizing the escape time, our proposal is to impose a zero-expansion condition along transversely repelling directions of chaotic saddles. This strategy exploits the existence of skeleton-forming unstable periodic orbits embedded in chaotic saddles, and thus can be conveniently implemented as a variant of subspace Newton-type methods. The algorithm is examined through an illustrative and another standard example.

We propose a kernel-based quadratic classification method based on kernel principal component analysis (KPCA). Subspace methods have been widely used for multiclass classification problems, and they have been extended by the kernel trick. However, there are large computational complexities for the subspace methods that use the kernel trick because the problems are defined in the space spanned by all of the training samples. To reduce the computational complexity of the subspace methods for multiclass classification problems, we extend Oja's averaged learning subspace method and apply a subset approximation of KPCA. We also propose an efficient method for selecting the basis vectors for this. Due to these extensions, for many problems, our classification method exhibits a higher classification accuracy with fewer basis vectors than does the support vector machine (SVM) or conventional subspace methods.

The alternating direction implicit (ADI) method is proposed for low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. The low-rank solution is expressed by Cholesky factor that is similar to that of Cholesky factorization for linear system of equations. The Cholesky factor is represented in a real form so that it is useful for balanced truncation of sparsely connected RLC networks. Moreover, we show how to determine the shift parameters which are required for the ADI iterations, where Krylov subspace method is used for finding the shift parameters that reduce the residual error quickly. In the illustrative examples, we confirm that the real Cholesky factor certainly provides low-rank solution of projected generalized continuous-time algebraic Lyapunov equations. Effectiveness of the shift parameters determined by Krylov subspace method is also demonstrated.

This paper proposes a method for recognizing hand-shapes by using multi-viewpoint image sets. The recognition of a hand-shape is a difficult problem, as appearance of the hand changes largely depending on viewpoint, illumination conditions and individual characteristics. To overcome this problem, we apply the Kernel Orthogonal Mutual Subspace Method (KOMSM) to shift-invariance features obtained from multi-viewpoint images of a hand. When applying KOMSM to hand recognition with a lot of learning images from each class, it is necessary to consider how to run the KOMSM with heavy computational cost due to the kernel trick technique. We propose a new method that can drastically reduce the computational cost of KOMSM by adopting centroids and the number of images belonging to the centroids, which are obtained by using k-means clustering. The validity of the proposed method is demonstrated through evaluation experiments using multi-viewpoint image sets of 30 classes of hand-shapes.

In this paper, the performance of the induced dimension reduction (IDR) method implemented along with the method of moments (MoM) is described. The MoM is based on a combined field integral equation for solving large-scale electromagnetic scattering problems involving conducting objects. The IDR method is one of Krylov subspace methods. This method was initially developed by Peter Sonneveld in 1979; it was subsequently generalized to the IDR(s) method. The method has recently attracted considerable attention in the field of computational physics. However, the performance of the IDR(s) has hardly been studied or practiced for electromagnetic wave problems. In this study, the performance of the IDR(s) is investigated and clarified by comparing the convergence property and memory requirement of the IDR(s) with those of other representative Krylov solvers such as biconjugate gradient (BiCG) methods and generalized minimal residual algorithm (GMRES). Numerical experiments reveal that the characteristics of the IDR(s) against the parameter s strongly depend on the geometry of the problem; in a problem with a complex geometry, s should be set to an adequately small value in order to avoid the "spurious convergence" which is a problem that the IDR(s) inherently holds. As for the convergence behavior, we observe that the IDR(s) has a better convergence ability than GPBiCG and GMRES(m) in a variety of problems with different complexities. Furthermore, we also confirm the IDR(s)'s inherent advantage in terms of the memory requirements over GMRES(m).

This paper presents flexible inner-outer Krylov subspace methods, which are implemented using the fast multipole method (FMM) for solving scattering problems with mixed dielectric and conducting object. The flexible Krylov subspace methods refer to a class of methods that accept variable preconditioning. To obtain the maximum efficiency of the inner-outer methods, it is desirable to compute the inner iterations with the least possible effort. Hence, generally, inaccurate matrix-vector multiplication (MVM) is performed in the inner solver within a short computation time. This is realized by using a particular feature of the multipole techniques. The accuracy and computational cost of the FMM can be controlled by appropriately selecting the truncation number, which indicates the number of multipoles used to express far-field interactions. On the basis of the abovementioned fact, we construct a less-accurate but much cheaper version of the FMM by intentionally setting the truncation number to a sufficiently low value, and then use it for the computation of inaccurate MVM in the inner solver. However, there exists no definite rule for determining the suitable level of accuracy for the FMM within the inner solver. The main focus of this study is to clarify the relationship between the overall efficiency of the flexible inner-outer Krylov solver and the accuracy of the FMM within the inner solver. Numerical experiments reveal that there exits an optimal accuracy level for the FMM within the inner solver, and that a moderately accurate FMM operator serves as the optimal preconditioner.

The passive and sparse reduced-order modeling of a RLC network is presented, where eigenvalues and eigenvectors of the original network are used, and thus the obtained macromodel is more accurate than that provided by the Krylov subspace methods or TBR procedures for a class of circuits. Furthermore, the proposed method is applied to low pass filtering of a reduced-order model produced by these methods without breaking the passivity condition. Therefore, the proposed eigenspace method is not only a reduced-order macromodeling method, but also is embedded in other methods enhancing their performances.

We propose a method of face identification under various illumination conditions. Because we use image based method for identification, the accurate position of the face is required. First, face features are detected, and the face region is determined using the features. Then, by registering the face region to the average face, the horizontal position of the face is adjusted. Finally, the size of the face region is adjusted based on the distance of two eyes determined from all input frames. If the sizes of images for all faces are normalized into one size, the face length feature is lost in the normalized face image. The face is classified into three categories according to the face length, and the subspace is generated in each category so that the face length feature is preserved. We demonstrate the effectiveness of the proposed method by experiments.

We have proposed in [5] a practical blind channel identification algorithm for the white observation noise. In this paper, we examine the effectiveness of the algorithm given in [5] for the colored observation noise. The proposed algorithm utilizes Gram-Schmidt orthogonalization procedure and estimates (1) the channel order, (2) the noise variance and then (3) the channel impulse response with less computational complexity compared to the conventional algorithms using eigenvalue decomposition. It can be shown through numerical examples that the algorithm proposed in [5] is quite effective in the colored noise case.

We have proposed a recognition method for pulmonary nodules based on experimentally selected feature values (such as contrast, circularity, etc.) of pathologic candidate regions detected by our Variable N-Quoit (VNQ) filter. In this paper, we propose a new recognition method for pulmonary nodules by use of not experimentally selected feature values, but each CT value itself in a region of interest (ROI) as a feature value. The proposed method has 2 phases: learning and recognition. In the learning phase, first, the pathologic candidate regions are classified into several clusters based on a principal component score. This score is calculated from a set of CT values in the ROI that are regarded as a feature vector, and then eigen vectors and eigen values are calculated for each cluster by application of principal component analysis to the cluster. The eigen vectors (we call them "eigen-images") corresponding to the S-th largest eigen values are utilized as base vectors for subspaces of the clusters in a feature space. In the recognition phase, correlations are measured between the feature vector derived from testing data and the subspace which is spanned by the eigen-images. If the correlation with the nodule subspace is large, the pathologic candidate region is determined to be a nodule, otherwise, it is determined to be a normal organ. In the experiment, first, we decide on the optimal number of subspace dimensions. Then, we demonstrated the robustness of our algorithm by using simulated nodule images.

We propose a practical blind channel identification algorithm based on the principal component analysis. The algorithm estimates (1) the channel order, (2) the noise variance, and then identifies (3) the channel impulse response, from the autocorrelation of the channel output signal without using the eigenvalue and singular-value decomposition. The special features of the proposed algorithm are (1) practical method to find the channel order and (2) reduction of computational complexity. Numerical examples show the effectiveness of the proposed algorithm.

The processing of noise-corrupted signals is a common problem in signal processing applications. In most of the cases, it is assumed that the additive noise is white Gaussian and that the constant noise variance is either available or can be easily measured. However, this may not be the case in practical situations. We present a new approach to additive white Gaussian noise variance estimation. The observations are assumed to be from an autoregressive process. The method presented here is iterative, and uses low-order Yule-Walker equations (LOYWEs). The noise variance is obtained by minimizing the difference in the second norms of the noisy Yule-Walker solution and the estimated noise-free Yule-Walker solution. The noise-free solution is constrained to match the observed autocorrelation sequence. In the iterative noise variance estimation method, a variable step-size update scheme for the noise variance parameter is utilized. Simulation results are given to confirm the effectiveness of the proposed method.

The propagator method (PM) belongs to a class of subspace based methods for direction-of-arrival estimation which only requires linear operations but does not involve any eigendecomposition or singular value decomposition as in common subspace techniques. In this paper, we apply the PM for estimating the frequencies of multiple real sinusoids in noise and a computationally simple as well as high resolution multiple frequency estimation algorithm is developed. The estimation accuracy of the proposed method is contrasted with the conventional MUSIC and Cramer-Rao lower bound under different noise conditions.

In this paper, a novel confidence scoring method that is applied to N-best hypotheses (word candidates) output from an HMM-based classifier is proposed. In the first pass of the proposed method, the HMM-based classifier with monophone models outputs N-best hypotheses and boundaries of all monophones in the hypotheses. In the second pass, an SM (Subspace Method)-based verifier tests the hypotheses by comparing confidence scores. To test the hypotheses, at first, the SM-based verifier calculates the similarity between phone vectors and an eigen vector set of monophones, then this similarity score is converted into a likelihood score with normalization of acoustic quality, and finally, an HMM-based likelihood of word level and an SM-based likelihood of monophone level are combined to formulate the confidence measure. Two kinds of experiments were performed to evaluate this confidence measure on speaker-independent word recognition. The results showed that the proposed confidence scoring method significantly reduced the word error rate from 4.7% obtained by the standard HMM classifier to 2.0%, and in an unknown word rejection, it reduced the equal error rate from 9.0% to 6.5%.

This paper aims to provide a robust multiuser detection structure that adaptively tracks signature waveform distortion for CDMA multipath signals. In practical wireless environment, multipath fading leads to signature waveform distortion that severely degrades the performance of the linear multiuser detectors (LMDs) designed by exploiting the original signature waveform. In what follows, an iterative algorithm is proposed to track the signature waveform perturbation. The rationale of adaptive processing is based on the subspace method and the Minimum Variance Distortionless Response (MVDR) beamforming concept. Performance evaluation reveals that the proposed adaptive multiuser detection structure reduces the impact of signature waveform perturbation on the performance of the LMDs to a great extent. Moreover, the proposed iterative algorithm is near-far resistant since both the subspace method and the MVDR beamforming technique are energy independent to the interferers.

An algorithm for blind identification of multichannel (single-input and multiple-output) FIR systems is proposed. The proposed algorithm is based on subspace approach to blind identification, which requires so-called noise space spanned by some eigenvectors of correlation matrices of observations. It is shown that a subspace of the noise space can be obtained by one-step scalar-valued linear prediction and then the subspace is sufficient for blind identification. To acquire the subspace, the proposed algorithm utilizes one-step scalar-valued linear prediction in place of a singular- (or eigen-) value decomposition and hence it is computationally efficient. Computer simulations are presented to compare the proposed algorithm with the original one.

As a preprocessor of the automatic speech recognizer in a noisy environment, a microphone array system has been investigated to reduce the environmental noise. In usual microphone array design, a plane wave is assumed for the sake of simplicity (far-field assumption). However, this far-field assumption does not always hold, resulting in distortion in the array output. In this report, the subspace method, which is one of the high resolution spectrum estimator, is applied to the near-field source localization problem. A high resolution method is necessary especially for the near-field source localization with a small-sized array. By combining the source localization technique with a spatial inverse filter, the signal coming from the multiple sources in the near-field range can be separated. The modified minimum variance beamformer is used to design the spatial inverse filter. As a result of the experiment in a real environment with two sound sources in the near-field range, 60-70% of word recognition rate was achieved.

In general cases of pattern recognition, a pattern to be recognized is first represented by a set of features and the measured values of the features are then classified. Finding features relevant to recognition is thus an important issue in recognizer design. As a fundamental design framework taht systematically enables one to realize such useful features, the Subspace Method (SM) has been extensively used in various recognition tasks. However, this promising methodological framework is still inadequate. The discriminative power of early versions was not very high. The training behavior of a recent discriminative version called the Learning Subspace Method has not been fully clarified due to its empirical definition, though its discriminative power has been improved. To alleviate this insufficiency, we propose in this paper a new discriminative SM algorithm based on the Minimum Classification Error/Generalized Probabilistic Descent method and show that the proposed algorithm achieves an optimal accurate recognition result, i.e., the (at least locally) minimum recognition error situation, in the probabilistic descent sense.

A method for recovering the LPC spectrum from a microphone array input signal corrupted by less directional ambient noise is proposed. This method is based on the subspace method, in which directional signal and non-directional noise is classified in the subspace domain using eigenvalue analysis of the spatial correlation matrix. In this paper, the coherent subspace (CSS) method, a broadband extension of the subspace method, is employed. The advantage of this method is that is requires a much smaller number of averages in the time domain for estimating subspace, suitable feature for frame processing such as speech recognition. To enhance the performance of noise reduction, elimination of noise-dominant subspace using projection is further proposed, which is effective when the SNR is low and classification of noise and signals using eigenvalue analysis is difficult.

We present theoretical results on the convergence of iterative methods for the solution of linear differential-algebraic equations arising form circuit simulation. The iterative methods considered include the continuous-time and discretetime waveform relaxation methods and the Krylov subspace methods in function space. The waveform generalized minimal residual method for solving linear differential-algebraic equations in function space is developed, which is one of the waveform Krylov subspace methods. Some new criteria for convergence of these iterative methods are derived. Examples are given to verify the convergence conditions.