Specific Subspaces Research Articles

Vehicle re-identification based on dimensional decoupling strategy and non-local relations.

Vehicle re-identification (Re-ID) is a challenging task that aims to recognize the same vehicle across different non-overlapping cameras. Existing attention mechanism-based methods for vehicle Re-ID often suffer from significant intra-class variation and inter-class variation due to various factors such as illumination, occlusion, viewpoint, etc. In this paper, we propose a novel network architecture for vehicle Re-ID, named Dimensional Decoupling Strategy and Non-local Relationship Network (DMNR-Net), which uses three modules to extract complementary features: global feature extraction module, non-local relationship capture module(NRCM), and dimensional decoupling module (DDS). The global feature extraction module captures complete and coarse-grained features from the whole image; the NRCM module extracts saliency information from feature maps in both spatial and channel dimensions; and the DDS decouples spatial and channel features into two branches to extract fine-grained features and focus on specific subspaces. We conduct extensive experiments on two popular publicly datasets, VeRi-776 and VehicleID, to evaluate the effectiveness of our method. The experimental results show that our DMNR-Net outperforms state-of-the-art methods by a large margin on both datasets.

Duality of averaging of quantum states over arbitrary symmetry groups revealing Schur–Weyl duality

It is a well-established fact in quantum information theory, that uniform averaging over the collective action of a unitary group on a multipartite quantum state projects the state to a form equivalent to a permutation operator of the subsystems. Hence states equivalent to permutation operators are untouched by collective unitary noise. A trivial observation shows that uniform averaging over permutation operators projects the state into a form with block-diagonal structure equivalent to the one of the collective action of the unitary group. We introduce a name for this property: duality of averaging. The mathematical reason behind this duality is the fact that the collective action of the unitary group on the tensor product state space of a multipartite quantum system and the action of the permutation operations are mutual commutants when treated as matrix algebras. Such pairs of matrix algebras are known as dual reductive pairs. In this work we show, that in the case of finite dimensional quantum systems such duality of averaging holds for any pairs of symmetry groups being dual reductive pairs, regardless of whether they are compact or not, as long as the averaging operation is defined via iterated integral over the Cartan decomposition of the group action. Although our result is very general, we focus much attention on the concrete example of a dual reductive pair consisting of collective action of special linear matrices and permutation operations, which physically corresponds to averaging multipartite quantum states over non-unitary SLOCC-type (Stochastic Local Operations and Classical Communication) operations. In this context we show, that noiseless subsystems known from collective unitary averaging persist in the case of SLOCC averaging in a conditional way: upon postselection to specific invariant subspaces.

Multiple color representation and fusion for diabetes mellitus diagnosis based on back tongue images

Tongue images have been proved to be effective in diabetes mellitus (DM) diagnosis. Without requirement of collecting blood sample, tongue image based diagnosis approach is non-invasive and convenient for the patients. Meanwhile, the colors of tongues play an important in aiding accurate diagnosis. However, the tongues’ colors fall on a small color gamut that makes it difficult for the existing color descripts to identify and distinguish the tiny difference of the tongues. To tackle this problem, we introduce a novel color descriptor by representing the colors with the clustering centers, namely color centroid points, of the color points sampled from tongue images. In order to boost the capacity of the descriptor, we extend it into three color spaces, i.e., RGB, HSV and LAB to mine a rich set of color information and exploit the complementary information among the three spaces. Since there exist correlation and complementarity among the features extracted from the three color spaces, we propose a novel multiple color features fusion method for DM diagnosis. Particularly, two projections are learned to project the multiple features to their corresponding shared and specific subspaces, in which their similarity and diversity are firstly measured by the Euclidean Distance and Hilbert Schmidt Independence Criterion (HSIC), respectively. To fully exploit the similar and complementary information, the two components are jointly transformed to their label vector, efficiently embedding the discriminant prior into the model, leading to significant improvement in the diagnosis outcomes. Experimental results on clinical tongue dataset substantiated the effectiveness of our proposed clustering-based color descriptor and the proposed multiple colors fusion approach. Overall, the proposed pipeline for the diagnosis of DM using back tongue images, achieved an average accuracy of up to 93.38%, indicating its potential toward realization of a clinical diagnostic tool for DM. Without loss generality, we also assessed the performance of the novel multiple features fusion method on two public datasets. The experiments prove the superiority of our multiple features learning model on general real-life application.

Revised Tunable Q-Factor Wavelet Transform for EEG-Based Epileptic Seizure Detection.

Electroencephalogram (EEG) signals are an essential tool for the detection of epilepsy. Because of the complex time series and frequency features of EEG signals, traditional feature extraction methods have difficulty meeting the requirements of recognition performance. The tunable Q-factor wavelet transform (TQWT), which is a constant-Q transform that is easily invertible and modestly oversampled, has been successfully used for feature extraction of EEG signals. Because the constant-Q is set in advance and cannot be optimized, further applications of the TQWT are restricted. To solve this problem, the revised tunable Q-factor wavelet transform (RTQWT) is proposed in this paper. RTQWT is based on the weighted normalized entropy and overcomes the problems of a nontunable Q-factor and the lack of an optimized tunable criterion. In contrast to the continuous wavelet transform and the raw tunable Q-factor wavelet transform, the wavelet transform corresponding to the revised Q-factor, i.e., RTQWT, is sufficiently better adapted to the nonstationary nature of EEG signals. Therefore, the precise and specific characteristic subspaces obtained can improve the classification accuracy of EEG signals. The classification of the extracted features was performed using the decision tree, linear discriminant, naive Bayes, SVM and KNN classifiers. The performance of the new approach was tested by evaluating the accuracies of five time-frequency distributions: FT, EMD, DWT, CWT and TQWT. The experiments showed that the RTQWT proposed in this paper can be used to extract detailed features more effectively and improve the classification accuracy of EEG signals.

SC-GAN: Subspace Clustering based GAN for Automatic Expression Manipulation

In recent years, the topics of facial attribute manipulation and decomposition have gained great popularity in computer vision and human computer interaction. Even though such methods have been preliminarily employed in some photo beautification applications, it still remains challenging due to the highly-versatile facial attributes and their drastic appearance changes subject to variation of deformation, illumination, pose, etc. The prevailing problems are especially severe when we are faced with group photos involving many faces. To overcome such critical limitations and discover more meaningful visual attributes and their possible decompositions, we develop a subspace clustering based generative adversarial network (SC-GAN) in this paper. Our SC-GAN can simultaneously decompose multiple subspaces and generate diverse samples correspondingly, thus the training of the generative models could be more effectively guided by facial attribute and its decomposition and manipulation in a natural and meaningful fashion. Our SC-GAN incorporates the SIFT K-means cluster, which could split the holistic semantic facial space into different subspaces without supervision, and help the new GAN generate more convincing results within specific subspaces. Extensive experiments and comprehensive evaluations confirm that, our method can greatly reduce the unexpected influences caused by portrait diversities and outperform the state-of-the-art facial attribute manipulation approaches.11https://github.com/buaaswf/SC-GAN/

Real time surveillance for low resolution and limited data scenarios: An image set classification approach

This paper proposes a novel image set classification technique based on the concept of linear regression. Unlike most other approaches, the proposed technique does not require any training. We represent the gallery image sets as subspaces in a high dimensional space. Class specific gallery subspaces are used to estimate regression models for each image in the test image set. Images of the test set are then projected onto the gallery subspaces. The residuals, calculated using the Euclidean distance between the original and the projected test images, are used as the distance metric. Three different strategies are devised to decide on the final class of the test image set. We extensively evaluated the proposed technique using both low resolution and noisy images and with less gallery data to assess the suitability of our technique for the tasks of surveillance and video-based face recognition. The experiments show that the proposed technique achieves superior classification accuracy and has a faster execution time compared with existing techniques, especially under the challenging conditions of low resolution and a limited amount of gallery and test data.

Approximate Canonical Correlation Analysis for common/specific subspace decompositions

The objective of this paper is to present a new technique for jointly decomposing two sets of signals. The proposed method is a modified version of Canonical Correlation Analysis (CCA), which automatically identifies from the two (a priori noisy) data-sets, having the same number of samples but potentially different number of variables (measurements), an approximate bisector common subspace and its complementary specific subspaces. Within these subspaces, common and specific parts of the signals can be reconstructed and analysed separately. The method we propose here can also be seen as an extension of other joint decomposition methods based on “stacking” the analysed data sets, but, unlike these methods, we propose a “stacked basis” approach and we show its relationship with the CCA. The proposed method is validated with convincing results on simulated data and applied successfully on (stereo-)electroencephalographic signals, either for artefact cancelling or for identifying common and specific activities for two different physiological conditions (sleep – wake).

Multiple discriminant analysis for collaborative representation-based classification

Collaborative Representation-based Classifier (CRC) has shown its advantages and impressive results in face recognition. To further imporve the performance of CRC, we propose a novel dimensionality reduction method termed Multiple Discriminant Analysis for Collaborative Representation-based Classification (MDA-CRC). Considering the labeling criterion of CRC is class-specific, MDA-CRC solves a group of binary classification problems where specific feature subspaces are learned for each class. In each binary classification problem, an orthogonal discriminant analysis method based on collaborative representation is adopted. Hence, MDA-CRC can improve the discriminant ability of collaborative representation and be consistent with the labeling criterion of CRC simultaneously. Further, the convergence of MDA-CRC is proven. Extensive experiments on several benchmark datasets demonstrate the effectiveness of MDA-CRC.

Median Sets of Isometries in CAT(0) Cube Complexes and Some Applications

In this paper, we associate with isometries of CAT(0) cube complexes specific subspaces, referred to as median sets, which play a similar role as minimizing sets of semisimple isometries in CAT(0) spaces. Various applications are deduced, including a cubulation of centralizers, a splitting theorem, a proof that Dehn twists in mapping class groups must be elliptic for every action on a CAT(0) cube complex, a cubical version of the flat torus theorem, and a structural theorem about polycyclic groups acting on CAT(0) cube complexes.

Exploring inequalities in India through housing overcrowding

The influence of economic development on the resorption of inequality levels in India is an open debate. Inequality shapes both the Indian society as a whole and, spatially, the different regions of this subcontinent-wide country. In this article, emphasis is given to the conception and to the spatial analysis of an indicator named “Non-Crowded Housing” (abbr. NCH). The latter uses official census data, is easily computed and focuses on the absence of housing overcrowding. This indicator offers a good alternative to explore the standard of living gap in India in terms of housing usage and unveil specific sub-spaces and trajectories within the 2001–2011 period. Census data are complemented with field studies in order to shed new light on the geography and nature of housing and spatial inequalities linked to rapid urbanization. The case studies reveal the strengths and weaknesses of the NCH index, which is able to provide a comprehensive overview of the human well-being, focusing on housing conditions only, though being scale-dependent and sensitive to urbanization levels.

Hybrid self-organizing feature map (SOM) for anomaly detection in cloud infrastructures using granular clustering based upon value-difference metrics

We have witnessed an increase in the availability of data from diverse sources over the past few years. Cloud computing, big data and Internet-of-Things (IoT) are distinctive cases of such an increase which demand novel approaches for data analytics in order to process and analyze huge volumes of data for security and business use. Cloud computing has been becoming popular for critical structure IT mainly due to cost savings and dynamic scalability. Current offerings, however, are not mature enough with respect to stringent security and resilience requirements. Mechanisms such as anomaly detection hybrid systems are required in order to protect against various challenges that include network based attacks, performance issues and operational anomalies. Such hybrid AI systems include Neural Networks, blackboard systems, belief (Bayesian) networks, case-based reasoning and rule-based systems and can be implemented in a variety of ways. Traffic in the cloud comes from multiple heterogeneous domains and changes rapidly due to the variety of operational characteristics of the tenants using the cloud and the elasticity of the provided services. The underlying detection mechanisms rely upon measurements drawn from multiple sources. However, the characteristics of the distribution of measurements within specific subspaces might be unknown. We argue in this paper that there is a need to cluster the observed data during normal network operation into multiple subspaces each one of them featuring specific local attributes, i.e. granules of information. Clustering is implemented by the inference engine of a model hybrid NN system. Several variations of the so-called value-difference metric (VDM) are investigated like local histograms and the Canberra distance for scalar attributes, the Jaccard distance for binary word attributes, rough sets as well as local histograms over an aggregate ordering distance and the Canberra measure for vectorial attributes. Low-dimensional subspace representations of each group of points (measurements) in the context of anomaly detection in critical cloud implementations is based upon VD metrics and can be either parametric or non-parametric. A novel application of a Self-Organizing-Feature Map (SOFM) of reduced/aggregate ordered sets of objects featuring VD metrics (as obtained from distributed network measurements) is proposed. Each node of the SOFM stands for a structured local distribution of such objects within the input space. The so-called Neighborhood-based Outlier Factor (NOOF) is defined for such reduced/aggregate ordered sets of objects as a value-difference metric of histogrammes. Measurements that do not belong to local distributions are detected as anomalies, i.e. outliers of the trained SOFM. Several methods of subspace clustering using Expectation-Maximization Gaussian Mixture Models (a parametric approach) as well as local data densities (a non-parametric approach) are outlined and compared against the proposed method using data that are obtained from our cloud testbed in emulated anomalous traffic conditions. The results—which are obtained from a model NN system—indicate that the proposed method performs well in comparison with conventional techniques.

Research on a full envelop controller for an unmanned ducted-fan helicopter based on switching control theory

Rotor and ducted-fan structured unmanned helicopters have shown energy efficiency in low flight speed and hovering, due to the novel ducted-fan structure. However, its aerodynamic characteristics may change dramatically when flight at higher speed, resulting in a wide flight envelope when compared with conventional structured helicopters. Hence, the flight controller is required to schedule itself based on the flight states and guarantees the overall performances of the helicopter on the entire flight envelop. This paper presents a switching system theory based approach to design the optimal controllers over a wide region of flight envelop. In the proposed method, a family of robust controller are designed based on typical operational conditions and the controller is adjusted to guarantee the stability when the switching event is trigged. A hysteresis switching logic is utilized to ensure smooth transient between specific operational subspaces. The stability of the proposed control method was analyzed through Lyapunov theory. Nonlinear simulations based flight dynamics of the prototype helicopter have demonstrated the flexibility and efficiency of the proposed work.

Influence of bounded states in the Neumann Laplacian in a thin waveguide

Let $-\Delta _\Omega ^N$ be the Neumann Laplacian operator restricted to a twisted waveguide $\Omega $. Our first goal is to find the effective operator when $\Omega $ is ``squeezed.'' However, since, in this process, there are divergent eigenvalues, we consider $-\Delta _\Omega ^N$ acting in specific subspaces of the initial Hilbert space. The strategy is interesting since we find different effective operators in each situation. In the case where $\Omega $ is periodic and sufficiently thin, we also obtain information regarding the absolutely continuous spectrum of $-\Delta _\Omega ^N$ (restricted to such subspaces) and the existence and location of band gaps in its structure.

Isolating incipient sensor fault based on recursive transformed component statistical analysis

This paper considers the isolation problem of incipient sensor fault. Based on recursive transformed component statistical analysis (RTCSA), two different isolation methods are proposed. The first method is called subspace reconstruction, where elements in specific subspaces are eliminated, and then reconstructed by minimizing the reconstructed detection index. The faulty variable is determined by the least scaled reconstructed detection index. The second method is called subblock detection, which has less online computational complexity. The subblocks of the measurement matrix are sequentially selected in each sliding window to calculate the subblock detection indices, and the faulty variable is determined by the largest subblock detection margin. Compared with the existing isolation methods such as reconstruction-based contribution (RBC) and its variant termed as average residual-difference reconstruction contribution plot (ARdR-CP), the superior isolation performances of the proposed methods are illustrated by a numerical example as well as a simulation on a continuous stirred tank reactor.

Landau Damping to Partially Locked States in the Kuramoto Model

AbstractIn the Kuramoto model of globally coupled oscillators, partially locked states (PLS) are stationary solutions that capture the emergence of partial synchrony when the interaction strength increases. While PLS have long been considered, existing results on their stability are limited to neutral stability of the linearized dynamics in strong topology or to specific invariant subspaces (obtained via the so‐called Ott‐Antonsen (OA) ansatz) with specific frequency distributions for the oscillators. In the mean‐field limit, the Kuramoto model shows various ingredients of the Landau damping mechanism in the Vlasov equation. This analogy has been a source of inspiration for stability proofs of regular Kuramoto equilibria. In addition, the major mathematical issue with PLS asymptotic stability is that these states consist of heterogeneous and singular measures. Here we establish an explicit criterion for their spectral stability and prove their local asymptotic stability in weak topology for a large class of analytic frequency marginals. The proof strongly relies on a suitable functional space that contains (Fourier transforms of) singular measures, and for which the linearized dynamics is well under control. For illustration, the stability criterion is evaluated in some standard examples. We confirm in particular that no loss of generality results in assuming the OA ansatz. To the best of our knowledge, our result provides the first proof of Landau damping to heterogeneous and irregular equilibria in the absence of dissipation. © 2018 Wiley Periodicals, Inc.

An Improved Negative Selection Algorithm Based on Subspace Density Seeking

Negative selection algorithm (NSA) is an important method for generating detectors in artificial immune systems. Traditional NSAs randomly generate detectors in the whole feature space. However, with increasing dimensions, data samples aggregate in some specific subspaces, not uniformly distributed in the whole space. The detectors randomly generated by traditional NSAs cannot exactly fall into these specific subspaces, which results in a low coverage of detectors and a poor performance in a high-dimensional space. To overcome this defect, an improved real NSA based on subspace density seeking (SDS-RNSA) is proposed in this paper. In an SDS-RNSA, a subspace density seeking algorithm is adopted to procure the dense subspace regions of samples. Then, detectors are generated in each subspace region to cover up nonself-region efficiently and improve the performance of the algorithm. During the process of detector generation, the redundancy of candidate detectors is calculated, and the redundant is eliminated to minimize the time expense of the algorithm. Experimental results demonstrate that, compared with the classic NSAs, the SDS-RNSA can significantly improve the detection rate with an approximative false alarm rate and a smaller time expense. At the best case, the detection rate of the SDS-RNSA is increased by 14.7%, while the time expense is decreased by 78.1%.

Bagged Subspaces for Unsupervised Outlier Detection

In many domains, important events are not represented as the common scenario, but as deviations from the rule. The importance and impact associated with these particular, outnumbered, deviant, and sometimes even previously unseen events is directly related to the application domain (e.g., breast cancer detection, satellite image classification, etc.). The detection of these rare events or outliers has recently been gaining popularity as evidenced by the wide variety of algorithms currently available. These algorithms are based on different assumptions about what constitutes an outlier, a characteristic pointing toward their integration in an ensemble to improve their individual detection rate. However, there are two factors that limit the use of current ensemble outlier detection approaches: first, in most cases, outliers are not detectable in full dimensionality, but instead are located in specific subspaces of data; and second, despite the expected improvement on detection rate achieved using an ensemble of detectors, the computational efficiency of the ensemble will increase linearly as the number of components increases. In this article, we propose an ensemble approach that identifies outliers based on different subsets of features and subsamples of data, providing more robust results while improving the computational efficiency of similar ensemble outlier detection approaches.

The point variety of quantum polynomial rings

We show that the reduced point variety of a quantum polynomial algebra is the union of specific linear subspaces in Pn; we describe its irreducible components and give a combinatorial description of the possible configurations in small dimensions.

Learning Discriminative Subspaces on Random Contrasts for Image Saliency Analysis.

In visual saliency estimation, one of the most challenging tasks is to distinguish targets and distractors that share certain visual attributes. With the observation that such targets and distractors can sometimes be easily separated when projected to specific subspaces, we propose to estimate image saliency by learning a set of discriminative subspaces that perform the best in popping out targets and suppressing distractors. Toward this end, we first conduct principal component analysis on massive randomly selected image patches. The principal components, which correspond to the largest eigenvalues, are selected to construct candidate subspaces since they often demonstrate impressive abilities to separate targets and distractors. By projecting images onto various subspaces, we further characterize each image patch by its contrasts against randomly selected neighboring and peripheral regions. In this manner, the probable targets often have the highest responses, while the responses at background regions become very low. Based on such random contrasts, an optimization framework with pairwise binary terms is adopted to learn the saliency model that best separates salient targets and distractors by optimally integrating the cues from various subspaces. Experimental results on two public benchmarks show that the proposed approach outperforms 16 state-of-the-art methods in human fixation prediction.

Integrability spaces for the Fourier transform of a function of bounded variation

New relations between the Fourier transform of a function of bounded variation and the Hilbert transform of its derivative are revealed. After various preceding works of the last 25 years where the behavior of the Fourier transform has been considered on specific subspaces of the space of functions of bounded variation, in this paper such problems are considered on the whole space of functions of bounded variation. The widest subspaces of the space of functions of bounded variation are studied for which the cosine and sine Fourier transforms are integrable. The main result of the paper is an asymptotic formula for the sine Fourier transform of an arbitrary locally absolutely continuous function of bounded variation. Interrelations of various function spaces are studied, in particular, the sharpness of Hardy's inequality is established and the inequality itself is strengthened in certain cases. A way to extend the obtained results to the radial case is shown.