6,150 research outputs found
Recommended from our members
Learning distance to subspace for the nearest subspace methods in high-dimensional data classification
The nearest subspace methods (NSM) are a category of classification methods widely applied to classify high-dimensional data. In this paper, we propose to improve the classification performance of NSM through learning tailored distance metrics from samples to class subspaces. The learned distance metric is termed as ‘learned distance to subspace’ (LD2S). Using LD2S in the classification rule of NSM can make the samples closer to their correct class subspaces while farther away from their wrong class subspaces. In this way, the classification task becomes easier and the classification performance of NSM can be improved. The superior classification performance of using LD2S for NSM is demonstrated on three real-world high-dimensional spectral datasets
Local Subspace-Based Outlier Detection using Global Neighbourhoods
Outlier detection in high-dimensional data is a challenging yet important
task, as it has applications in, e.g., fraud detection and quality control.
State-of-the-art density-based algorithms perform well because they 1) take the
local neighbourhoods of data points into account and 2) consider feature
subspaces. In highly complex and high-dimensional data, however, existing
methods are likely to overlook important outliers because they do not
explicitly take into account that the data is often a mixture distribution of
multiple components.
We therefore introduce GLOSS, an algorithm that performs local subspace
outlier detection using global neighbourhoods. Experiments on synthetic data
demonstrate that GLOSS more accurately detects local outliers in mixed data
than its competitors. Moreover, experiments on real-world data show that our
approach identifies relevant outliers overlooked by existing methods,
confirming that one should keep an eye on the global perspective even when
doing local outlier detection.Comment: Short version accepted at IEEE BigData 201
Programmable quantum state discriminators with simple programs
We describe a class of programmable devices that can discriminate between two
quantum states. We consider two cases. In the first, both states are unknown.
One copy of each of the unknown states is provided as input, or program, for
the two program registers, and the data state, which is guaranteed to be
prepared in one of the program states, is fed into the data register of the
device. This device will then tell us, in an optimal way, which of the
templates stored in the program registers the data state matches. In the second
case, we know one of the states while the other is unknown. One copy of the
unknown state is fed into the single program register, and the data state which
is guaranteed to be prepared in either the program state or the known state, is
fed into the data register. The device will then tell us, again optimally,
whether the data state matches the template or is the known state. We determine
two types of optimal devices. The first performs discrimination with minimum
error, the second performs optimal unambiguous discrimination. In all cases we
first treat the simpler problem of only one copy of the data state and then
generalize the treatment to n copies. In comparison to other works we find that
providing n > 1 copies of the data state yields higher success probabilities
than providing n > 1 copies of the program states.Comment: 17 pages, 5 figure
Modeling Quantum Behavior in the Framework of Permutation Groups
Quantum-mechanical concepts can be formulated in constructive finite terms
without loss of their empirical content if we replace a general unitary group
by a unitary representation of a finite group. Any linear representation of a
finite group can be realized as a subrepresentation of a permutation
representation. Thus, quantum-mechanical problems can be expressed in terms of
permutation groups. This approach allows us to clarify the meaning of a number
of physical concepts. Combining methods of computational group theory with
Monte Carlo simulation we study a model based on representations of permutation
groups.Comment: 8 pages, based on plenary lecture at Mathematical Modeling and
Computational Physics 2017, Dubna, July 3--7, 201
- …