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Classical foundations of Statistical Learning Theory rely on the assumption that the input patterns are independently and identically distributed. However, in many applications, the inputs, represented as feature vectors, are also embedded into a network of pair wise relations. Transductive approaches like graph regularization rely on the network topology without considering the feature vectors. Semi-supervised...
Recently, covariance matrices have been shown to be interesting features for signal classification and object detection. In this paper, we review and compare the existing kernels on covariance matrices and explore their use for EEG classification in Brain-Computer Interfaces (BCI). This study adresses both experimental and theoretical aspects of the problem. Beside the apparent complexity of the kernels,...
Compressive sensing allows us to recover signals that are linearly sparse in some basis from a smaller number of measurements than traditionally required. However, it has been shown that many classes of images or video can be more efficiently modeled as lying on a nonlinear manifold, and hence described as a non-linear function of a few underlying parameters. Recently, there has been growing interest...
As a large proportion of the available video media concerns humans, human action retrieval is posed as a new topic in the domain of content-based video retrieval. For retrieving complex human actions, measuring the similarity between two videos represented by local features is a critical issue. In this paper, a fast and explicit feature correspondence approach is presented to compute the match cost...
For hyperspectral image classification, manifold learning based graph Laplacian is proposed in the Laplacian support vector machine (LapSVM) classifier. The manifold regularization term in LapSVM constrains the smoothness of classification function on the data manifold. Since manifold learning approach is capable of exploring the manifold geometry of data, it is suitable for calculating the graph...
This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and the nonlinear function are unknown. The first step of the proposed method estimates...
This paper proposes a novel and efficient point cloud registration algorithm based on the kernel-induced feature map. Point clouds are mapped to a high-dimensional (Hilbert) feature space, where they are modeled with Gaussian distributions. A rigid transformation is first computed in feature space by elegantly computing and aligning a small number of eigenvectors with kernel PCA (KPCA) and is then...
This paper presents algorithms for biomedical video denoising using real-valued side information. In certain clinical settings, side information correlated to the underlying motion under imaging is available and can be used to infer motion and act as a global constraint for image denoising. Our methods assume the input data are noisy samples that lie on or near an image manifold parameterized by the...
For affinity propagation algorithm, traditional Euclidean distance measure cannot fully reflect the complex spatial distribution of the data sets. We propose a self-tuning kernel geodesic distance as the similarity measure which can reflect the inherent manifold structure information effectively. Meanwhile, according to the neighborhood density of the data sets, it identifies and eliminates the influence...
In this paper, inspired by the application potential of Regular Multiple Criteria Linear Programming (RMCLP), we proposed a novel Laplacian RMCLP(called Lap-RMCLP)method for semi-supervised classification problem, which can exploit the geometry information of the marginal distribution embedded in unlabeled data to construct a more reasonable classifier and is a useful extension of TSVM. Furthermore,...
This paper introduces a novel coding scheme based on the diffusion map framework. The idea is to run a t-step random walk on the data graph to capture the similarity of a data point to the codebook atoms. By doing this we exploit local similarities extracted from the data structure to obtain a global similarity which takes into account the non-linear structure of the data. Unlike the locality-based...
Several studies explored the application of Discriminant analysis on Grassmann manifolds to tackle the image sets matching. But these methods suffer from not considering the local structure of the data. In this paper, a new method of face recognition which based on a graph embedding framework and geometric distance perturbation has been proposed. By introducing similarity graphs and maximal linear...
Metric learning is a fundamental problem in computer vision. Different features and algorithms may tackle a problem from different angles, and thus often provide complementary information. In this paper, we propose a fusion algorithm which outputs enhanced metrics by combining multiple given metrics (similarity measures). Unlike traditional co-training style algorithms where multi-view features or...
In this paper, we deal with the estimation of body and head poses (i.e orientations) in surveillance videos, and we make three main contributions. First, we address this issue as a joint model adaptation problem in a semi-supervised framework. Second, we propose to leverage the adaptation on multiple information sources (external labeled datasets, weak labels provided by the motion direction, data...
Computing a faithful affinity map is essential to the clustering and segmentation tasks. In this paper, we propose a graph-based affinity (metric) learning method and show its application to image clustering and segmentation. Our method, self-diffusion (SD), performs a diffusion process by propagating the similarity mass along the intrinsic manifold of data points. Theoretical analysis is given to...
In real-world applications of visual recognition, many factors — such as pose, illumination, or image quality — can cause a significant mismatch between the source domain on which classifiers are trained and the target domain to which those classifiers are applied. As such, the classifiers often perform poorly on the target domain. Domain adaptation techniques aim to correct the mismatch. Existing...
We propose a novel discriminative learning approach to image set classification by modeling the image set with its natural second-order statistic, i.e. covariance matrix. Since nonsingular covariance matrices, a.k.a. symmetric positive definite (SPD) matrices, lie on a Riemannian manifold, classical learning algorithms cannot be directly utilized to classify points on the manifold. By exploring an...
The subspace constrained mean shift (SCMS) algorithm is an iterative method for finding an underlying manifold associated with an intrinsically low dimensional data set embedded in a high dimensional space. We investigate the application of the SCMS algorithm to the problem of noisy source vector quantization where the clean source needs to be estimated from its noisy observation before quantizing...
We propose an automated morphology reconstruction method for curvilinear network analysis. The proposed approach first projects samples to the ridge of the intensity image of the curvilinear system. Then, a manifold deviation measure is utilized to approximate the ridge with piecewise linear segments between the projected samples. A nonparametric system workflow based on the kernel interpolation and...
Mean shift (MS) and subspace constrained mean shift (SCMS) algorithms are iterative methods to find an underlying manifold associated with an intrinsically low dimensional data set embedded in a high dimensional space. Although the MS and SCMS algorithms have been used in many applications related to information and signal processing, a rigorous study of their convergence properties is still missing...
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