140,878 research outputs found
Provable Self-Representation Based Outlier Detection in a Union of Subspaces
Many computer vision tasks involve processing large amounts of data
contaminated by outliers, which need to be detected and rejected. While outlier
detection methods based on robust statistics have existed for decades, only
recently have methods based on sparse and low-rank representation been
developed along with guarantees of correct outlier detection when the inliers
lie in one or more low-dimensional subspaces. This paper proposes a new outlier
detection method that combines tools from sparse representation with random
walks on a graph. By exploiting the property that data points can be expressed
as sparse linear combinations of each other, we obtain an asymmetric affinity
matrix among data points, which we use to construct a weighted directed graph.
By defining a suitable Markov Chain from this graph, we establish a connection
between inliers/outliers and essential/inessential states of the Markov chain,
which allows us to detect outliers by using random walks. We provide a
theoretical analysis that justifies the correctness of our method under
geometric and connectivity assumptions. Experimental results on image databases
demonstrate its superiority with respect to state-of-the-art sparse and
low-rank outlier detection methods.Comment: 16 pages. CVPR 2017 spotlight oral presentatio
Sparse Subspace Clustering: Algorithm, Theory, and Applications
In many real-world problems, we are dealing with collections of
high-dimensional data, such as images, videos, text and web documents, DNA
microarray data, and more. Often, high-dimensional data lie close to
low-dimensional structures corresponding to several classes or categories the
data belongs to. In this paper, we propose and study an algorithm, called
Sparse Subspace Clustering (SSC), to cluster data points that lie in a union of
low-dimensional subspaces. The key idea is that, among infinitely many possible
representations of a data point in terms of other points, a sparse
representation corresponds to selecting a few points from the same subspace.
This motivates solving a sparse optimization program whose solution is used in
a spectral clustering framework to infer the clustering of data into subspaces.
Since solving the sparse optimization program is in general NP-hard, we
consider a convex relaxation and show that, under appropriate conditions on the
arrangement of subspaces and the distribution of data, the proposed
minimization program succeeds in recovering the desired sparse representations.
The proposed algorithm can be solved efficiently and can handle data points
near the intersections of subspaces. Another key advantage of the proposed
algorithm with respect to the state of the art is that it can deal with data
nuisances, such as noise, sparse outlying entries, and missing entries,
directly by incorporating the model of the data into the sparse optimization
program. We demonstrate the effectiveness of the proposed algorithm through
experiments on synthetic data as well as the two real-world problems of motion
segmentation and face clustering
A real time classification algorithm for EEG-based BCI driven by self-induced emotions
Background and objective: The aim of this paper is to provide an efficient, parametric, general, and completely automatic real time classification method of electroencephalography (EEG) signals obtained from self-induced emotions. The particular characteristics of the considered low-amplitude signals (a self-induced emotion produces a signal whose amplitude is about 15% of a really experienced emotion) require exploring and adapting strategies like the Wavelet Transform, the Principal Component Analysis (PCA) and the Support Vector Machine (SVM) for signal processing, analysis and classification. Moreover, the method is thought to be used in a multi-emotions based Brain Computer Interface (BCI) and, for this reason, an ad hoc shrewdness is assumed. Method: The peculiarity of the brain activation requires ad-hoc signal processing by wavelet decomposition, and the definition of a set of features for signal characterization in order to discriminate different self-induced emotions. The proposed method is a two stages algorithm, completely parameterized, aiming at a multi-class classification and may be considered in the framework of machine learning. The first stage, the calibration, is off-line and is devoted at the signal processing, the determination of the features and at the training of a classifier. The second stage, the real-time one, is the test on new data. The PCA theory is applied to avoid redundancy in the set of features whereas the classification of the selected features, and therefore of the signals, is obtained by the SVM. Results: Some experimental tests have been conducted on EEG signals proposing a binary BCI, based on the self-induced disgust produced by remembering an unpleasant odor. Since in literature it has been shown that this emotion mainly involves the right hemisphere and in particular the T8 channel, the classification procedure is tested by using just T8, though the average accuracy is calculated and reported also for the whole set of the measured channels. Conclusions: The obtained classification results are encouraging with percentage of success that is, in the average for the whole set of the examined subjects, above 90%. An ongoing work is the application of the proposed procedure to map a large set of emotions with EEG and to establish the EEG headset with the minimal number of channels to allow the recognition of a significant range of emotions both in the field of affective computing and in the development of auxiliary communication tools for subjects affected by severe disabilities
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