6,178 research outputs found
Outlier Mining Methods Based on Graph Structure Analysis
Outlier detection in high-dimensional datasets is a fundamental and challenging problem across disciplines that has also practical implications, as removing outliers from the training set improves the performance of machine learning algorithms. While many outlier mining algorithms have been proposed in the literature, they tend to be valid or efficient for specific types of datasets (time series, images, videos, etc.). Here we propose two methods that can be applied to generic datasets, as long as there is a meaningful measure of distance between pairs of elements of the dataset. Both methods start by defining a graph, where the nodes are the elements of the dataset, and the links have associated weights that are the distances between the nodes. Then, the first method assigns an outlier score based on the percolation (i.e., the fragmentation) of the graph. The second method uses the popular IsoMap non-linear dimensionality reduction algorithm, and assigns an outlier score by comparing the geodesic distances with the distances in the reduced space. We test these algorithms on real and synthetic datasets and show that they either outperform, or perform on par with other popular outlier detection methods. A main advantage of the percolation method is that is parameter free and therefore, it does not require any training; on the other hand, the IsoMap method has two integer number parameters, and when they are appropriately selected, the method performs similar to or better than all the other methods tested.Peer ReviewedPostprint (published version
Emergent Chiral Symmetry: Parity and Time Reversal Doubles
There are numerous examples of approximately degenerate states of opposite
parity in molecular physics. Theory indicates that these doubles can occur in
molecules that are reflection-asymmetric. Such parity doubles occur in nuclear
physics as well, among nuclei with odd A 219-229. We have also suggested
elsewhere that such doubles occur in particle physics for baryons made up of
`cbu' and `cbd' quarks. In this article, we discuss the theoretical foundations
of these doubles in detail, demonstrating their emergence as a surprisingly
subtle consequence of the Born-Oppenheimer approximation, and emphasizing their
bundle-theoretic and topological underpinnings. Starting with certain ``low
energy'' effective theories in which classical symmetries like parity and time
reversal are anomalously broken on quantization, we show how these symmetries
can be restored by judicious inclusion of ``high-energy'' degrees of freedom.
This mechanism of restoring the symmetry naturally leads to the aforementioned
doublet structure. A novel by-product of this mechanism is the emergence of an
approximate symmetry (corresponding to the approximate degeneracy of the
doubles) at low energies which is not evident in the full Hamiltonian. We also
discuss the implications of this mechanism for Skyrmion physics, monopoles,
anomalies and quantum gravity.Comment: 32 pages, latex. minor changes in presentation and reference
Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian
The extraction of clusters from a dataset which includes multiple clusters
and a significant background component is a non-trivial task of practical
importance. In image analysis this manifests for example in anomaly detection
and target detection. The traditional spectral clustering algorithm, which
relies on the leading eigenvectors to detect clusters, fails in such
cases. In this paper we propose the {\it spectral embedding norm} which sums
the squared values of the first normalized eigenvectors, where can be
significantly larger than . We prove that this quantity can be used to
separate clusters from the background in unbalanced settings, including extreme
cases such as outlier detection. The performance of the algorithm is not
sensitive to the choice of , and we demonstrate its application on synthetic
and real-world remote sensing and neuroimaging datasets
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