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This article introduces a spectral method for statistical subspace clustering. The method is built upon standard kernel spectral clustering techniques, however carefully tuned by theoretical understanding arising from random matrix findings. We show in particular that our method provides high clustering performance while standard kernel choices provably fail. An application to user grouping based...
Kernel independent component analysis (KICA) detects primary independent components of data by minimizing kernelized canonical correlation of random variables in a reproducing kernel Hilbert space. KICA has been widely used in many practical tasks, e.g., blind source separation and speech recognition. However, the dense kernel matrix in traditional KICA causes high computational complexity which prohibits...
The amount of data is exploding with the development of Internet and multimedia technology. Rapid retrieval of mass data is becoming more and more important. To meet the demand of the rapid retrieval, many approximate nearest neighobor methods have been proposed to accelerate the exhaustive search process. Hashing is such an example with great balance of time and accuracy. Hashing methods achieve...
Designing image operators is a hard task usually tackled by specialists in image processing. An alternative approach is to use machine learning to estimate local transformations, that characterize the image operators, from pairs of input-output images. The main challenge of this approach, called W-operator learning, is estimating operators over large windows without overfitting. Current techniques...
This paper presents a novel 3D partial shape retrieval algorithm based on time-series analysis. Given a piece of a 3D shape, the proposed method encodes the shape descriptor given by the Heat Kernel Signature (HKS) as a time-series, where the time is considered an ordered sequence of vertices provided by the Fiedler vector. Finally, a similarity metric is created using a well-known tool in time-series...
In this brief article, we prove the dominant role of the 1-twisted equilibrium point on the dynamical properties of the Kuramoto model with an interconnection topology given by a Harary graph. This is a very regular topology and helps to understand the complexity of the dynamic, associated to a very simple mathematical model.
Various internet services, including cloud providers and social networks collect large amounts of information that needs to be processed for statistical or other reasons without breaching user privacy. We present a novel approach where privacy protection can be viewed as a data transformation problem. The problem is formulated as a pair of classification tasks, (a) a privacy-insensitive and (b) a...
This paper aims to tackle the problem of brain network classification with machine learning algorithms using spectra of networks' matrices. Two approaches are discussed: first, linear and tree-based models are trained on the vectors of sorted eigenvalues of the adjacency matrix, the Laplacian matrix and the normalized Laplacian; next, SVM classifier is trained with kernels based on information divergence...
With the advance of 3-dimensional sensing devices, the in-air handwriting, as a more natural way for human and computer interaction, is being developed by the UCAS-CVMT Lab. Compared with the conventional handwritten Chinese characters generated by touching, it is more challenging to accurately recognize them due to unconstrained one-stroke writing style. This paper presents two recognizers to address...
The metric in the reproducing kernel Hilbert space (RKHS) is known to be given by the Gram matrix (which is also called the kernel matrix). It has been reported that the metric leads to a decorrelation of the kernelized input vector because its autocorrelation matrix can be approximated by the (down scaled) squared Gram matrix subject to some condition. In this paper, we derive a better metric (a...
To achieve the effective plant leaf classification using manifold learning, the local geometry structure of plant leaves is able to be preserved effectively and a discriminant manifold-based projection should be learned to capture the dominant structure features better. We firstly use Gabor filter to model the texture of plant leaf images as the samples. Then for the high-dimensional features, we...
Dimensionality reduction is an important issue in information processing and has popular applications in many fields, where locally linear embedding (LLE) is widely used due to accuracy and simple to implement. However, LLE is lack of robustness, and sensitive to local structure that can't preserve neighborhood character sometimes. Instead, Laplacian eigenmaps (LE) can overcome these weaknesses. In...
In this paper, an improved Kernel Fisher Discriminant (KFD) method is used in face recognition. A Generalized Kernel Fisher Discriminant Analysis (GKFD) is proposed to make the most of two kinds of discriminant information in “double discriminant subspaces”. It can also uniform the discriminant functions in two subspaces of DSDA. Experimental results on ORL face database show the feasibility of the...
Blind deblurring attempts to recover the latent sharp image from a blurred one. Such task is a well-known ill-posed inverse problem and is therefore usually solved as a posteriori probability estimation, incorporating prior information on natural images. In this paper, we propose a general blind noisy deblurring model based on hyper Laplacian (HL) in gradient domain and kernel spectra prior. This...
Kernel independent component analysis (KICA) has an important application in blind source separation, in which how to select the optimal kernel, including the kernel functional form and its parameters, is the key issue for obtaining the optimal performance. In practices, a single kernel is usually chosen as the kernel model of KICA in light of experience. However, selecting a suitable kernel model...
This paper studies how to sample load more realistically and efficiently for security constraint unit commitment (SCUC) problems in order to achieve a high degree of robustness of the unit commitment (UC) solution. For example, given the UC solution, 95% of load profiles can be supplied. Principal component analysis (PCA) is introduced to find a clear feature of the historical load in two-dimensional...
Often in real-world applications such as web page categorization, automatic image annotations and protein function prediction, each instance is associated with multiple labels (categories) simultaneously. In addition, due to the labeling cost one usually deals with a large amount of unlabeled data while the fraction of labeled data points will typically be small. In this paper, we propose a multi-label...
Kernel Spectral Clustering (KSC) solves a weighted kernel principal component analysis problem in a primal-dual optimization framework. It builds an unsupervised model on a small subset of data using the dual solution of the optimization problem. This allows KSC to have a powerful out-of-sample extension property leading to good cluster generalization w.r.t. unseen data points. However, in the presence...
Canonical correlation analysis(CCA) is a popular technique that works for finding the correlation between two sets of variables. However, CCA faces the problem of small sample size in dealing with high dimensional data. Several approaches have been proposed to overcome this issue, but the resulting transformation matrix fails to extract shared structures among data samples. In this paper, we propose...
The coordination of agents in an autonomous system can greatly increase its ability to perform missions in a wide array of applications including distributed computing, coordination of mobile autonomous agents, and cooperative sensing. To expand the functionality of these systems to a wider array of applications, a need exists for coordinated control algorithms driving the system of nodes or agents...
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