2,274 research outputs found
Innovation Pursuit: A New Approach to Subspace Clustering
In subspace clustering, a group of data points belonging to a union of
subspaces are assigned membership to their respective subspaces. This paper
presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of
subspace clustering using a new geometrical idea whereby subspaces are
identified based on their relative novelties. We present two frameworks in
which the idea of innovation pursuit is used to distinguish the subspaces.
Underlying the first framework is an iterative method that finds the subspaces
consecutively by solving a series of simple linear optimization problems, each
searching for a direction of innovation in the span of the data potentially
orthogonal to all subspaces except for the one to be identified in one step of
the algorithm. A detailed mathematical analysis is provided establishing
sufficient conditions for iPursuit to correctly cluster the data. The proposed
approach can provably yield exact clustering even when the subspaces have
significant intersections. It is shown that the complexity of the iterative
approach scales only linearly in the number of data points and subspaces, and
quadratically in the dimension of the subspaces. The second framework
integrates iPursuit with spectral clustering to yield a new variant of
spectral-clustering-based algorithms. The numerical simulations with both real
and synthetic data demonstrate that iPursuit can often outperform the
state-of-the-art subspace clustering algorithms, more so for subspaces with
significant intersections, and that it significantly improves the
state-of-the-art result for subspace-segmentation-based face clustering
Data Dropout in Arbitrary Basis for Deep Network Regularization
An important problem in training deep networks with high capacity is to
ensure that the trained network works well when presented with new inputs
outside the training dataset. Dropout is an effective regularization technique
to boost the network generalization in which a random subset of the elements of
the given data and the extracted features are set to zero during the training
process. In this paper, a new randomized regularization technique in which we
withhold a random part of the data without necessarily turning off the
neurons/data-elements is proposed. In the proposed method, of which the
conventional dropout is shown to be a special case, random data dropout is
performed in an arbitrary basis, hence the designation Generalized Dropout. We
also present a framework whereby the proposed technique can be applied
efficiently to convolutional neural networks. The presented numerical
experiments demonstrate that the proposed technique yields notable performance
gain. Generalized Dropout provides new insight into the idea of dropout, shows
that we can achieve different performance gains by using different bases
matrices, and opens up a new research question as of how to choose optimal
bases matrices that achieve maximal performance gain
Interaction With Tilting Gestures In Ubiquitous Environments
In this paper, we introduce a tilting interface that controls direction based
applications in ubiquitous environments. A tilt interface is useful for
situations that require remote and quick interactions or that are executed in
public spaces. We explored the proposed tilting interface with different
application types and classified the tilting interaction techniques. Augmenting
objects with sensors can potentially address the problem of the lack of
intuitive and natural input devices in ubiquitous environments. We have
conducted an experiment to test the usability of the proposed tilting interface
to compare it with conventional input devices and hand gestures. The experiment
results showed greater improvement of the tilt gestures in comparison with hand
gestures in terms of speed, accuracy, and user satisfaction.Comment: 13 pages, 10 figure
High Dimensional Low Rank plus Sparse Matrix Decomposition
This paper is concerned with the problem of low rank plus sparse matrix
decomposition for big data. Conventional algorithms for matrix decomposition
use the entire data to extract the low-rank and sparse components, and are
based on optimization problems with complexity that scales with the dimension
of the data, which limits their scalability. Furthermore, existing randomized
approaches mostly rely on uniform random sampling, which is quite inefficient
for many real world data matrices that exhibit additional structures (e.g.
clustering). In this paper, a scalable subspace-pursuit approach that
transforms the decomposition problem to a subspace learning problem is
proposed. The decomposition is carried out using a small data sketch formed
from sampled columns/rows. Even when the data is sampled uniformly at random,
it is shown that the sufficient number of sampled columns/rows is roughly
O(r\mu), where \mu is the coherency parameter and r the rank of the low rank
component. In addition, adaptive sampling algorithms are proposed to address
the problem of column/row sampling from structured data. We provide an analysis
of the proposed method with adaptive sampling and show that adaptive sampling
makes the required number of sampled columns/rows invariant to the distribution
of the data. The proposed approach is amenable to online implementation and an
online scheme is proposed.Comment: IEEE Transactions on Signal Processin
Spatial Random Sampling: A Structure-Preserving Data Sketching Tool
Random column sampling is not guaranteed to yield data sketches that preserve
the underlying structures of the data and may not sample sufficiently from
less-populated data clusters. Also, adaptive sampling can often provide
accurate low rank approximations, yet may fall short of producing descriptive
data sketches, especially when the cluster centers are linearly dependent.
Motivated by that, this paper introduces a novel randomized column sampling
tool dubbed Spatial Random Sampling (SRS), in which data points are sampled
based on their proximity to randomly sampled points on the unit sphere. The
most compelling feature of SRS is that the corresponding probability of
sampling from a given data cluster is proportional to the surface area the
cluster occupies on the unit sphere, independently from the size of the cluster
population. Although it is fully randomized, SRS is shown to provide
descriptive and balanced data representations. The proposed idea addresses a
pressing need in data science and holds potential to inspire many novel
approaches for analysis of big data
Stuck in Traffic (SiT) Attacks: A Framework for Identifying Stealthy Attacks that Cause Traffic Congestion
Recent advances in wireless technologies have enabled many new applications
in Intelligent Transportation Systems (ITS) such as collision avoidance,
cooperative driving, congestion avoidance, and traffic optimization. Due to the
vulnerable nature of wireless communication against interference and
intentional jamming, ITS face new challenges to ensure the reliability and the
safety of the overall system. In this paper, we expose a class of stealthy
attacks -- Stuck in Traffic (SiT) attacks -- that aim to cause congestion by
exploiting how drivers make decisions based on smart traffic signs. An attacker
mounting a SiT attack solves a Markov Decision Process problem to find
optimal/suboptimal attack policies in which he/she interferes with a
well-chosen subset of signals that are based on the state of the system. We
apply Approximate Policy Iteration (API) algorithms to derive potent attack
policies. We evaluate their performance on a number of systems and compare them
to other attack policies including random, myopic and DoS attack policies. The
generated policies, albeit suboptimal, are shown to significantly outperform
other attack policies as they maximize the expected cumulative reward from the
standpoint of the attacker
A new methodology for designing PID controllers
It is known that it is impossible to select fixed gains for a PD controller that will critically damp the response to disturbances for all configurations of a given robot system. Because of this the potential for overshoot is always present and cannot be avoided unless the system is severely overdamped. This is not necessarily a practical solution and can be an economically unacceptable approach. On the other hand, however, if overshoot is permissible to some degree for some systems in the case of conventional Serial robots it is still prohibited in the case of Parallel robots as it may easily bring the robot to one of its possible singular configurations, causing damage to the system. This paper introduces a new algorithm for the design of PD controllers that ensures uniform and fast dynamic responses, which are free from overshoots for all robot configurations. The technique also satisfies general stability requirements for the system
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