2,568 research outputs found
Positive Semidefinite Metric Learning Using Boosting-like Algorithms
The success of many machine learning and pattern recognition methods relies
heavily upon the identification of an appropriate distance metric on the input
data. It is often beneficial to learn such a metric from the input training
data, instead of using a default one such as the Euclidean distance. In this
work, we propose a boosting-based technique, termed BoostMetric, for learning a
quadratic Mahalanobis distance metric. Learning a valid Mahalanobis distance
metric requires enforcing the constraint that the matrix parameter to the
metric remains positive definite. Semidefinite programming is often used to
enforce this constraint, but does not scale well and easy to implement.
BoostMetric is instead based on the observation that any positive semidefinite
matrix can be decomposed into a linear combination of trace-one rank-one
matrices. BoostMetric thus uses rank-one positive semidefinite matrices as weak
learners within an efficient and scalable boosting-based learning process. The
resulting methods are easy to implement, efficient, and can accommodate various
types of constraints. We extend traditional boosting algorithms in that its
weak learner is a positive semidefinite matrix with trace and rank being one
rather than a classifier or regressor. Experiments on various datasets
demonstrate that the proposed algorithms compare favorably to those
state-of-the-art methods in terms of classification accuracy and running time.Comment: 30 pages, appearing in Journal of Machine Learning Researc
High-dimensional Sparse Inverse Covariance Estimation using Greedy Methods
In this paper we consider the task of estimating the non-zero pattern of the
sparse inverse covariance matrix of a zero-mean Gaussian random vector from a
set of iid samples. Note that this is also equivalent to recovering the
underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We
present two novel greedy approaches to solving this problem. The first
estimates the non-zero covariates of the overall inverse covariance matrix
using a series of global forward and backward greedy steps. The second
estimates the neighborhood of each node in the graph separately, again using
greedy forward and backward steps, and combines the intermediate neighborhoods
to form an overall estimate. The principal contribution of this paper is a
rigorous analysis of the sparsistency, or consistency in recovering the
sparsity pattern of the inverse covariance matrix. Surprisingly, we show that
both the local and global greedy methods learn the full structure of the model
with high probability given just samples, which is a
\emph{significant} improvement over state of the art -regularized
Gaussian MLE (Graphical Lasso) that requires samples. Moreover,
the restricted eigenvalue and smoothness conditions imposed by our greedy
methods are much weaker than the strong irrepresentable conditions required by
the -regularization based methods. We corroborate our results with
extensive simulations and examples, comparing our local and global greedy
methods to the -regularized Gaussian MLE as well as the Neighborhood
Greedy method to that of nodewise -regularized linear regression
(Neighborhood Lasso).Comment: Accepted to AI STAT 2012 for Oral Presentatio
MAP: Medial Axis Based Geometric Routing in Sensor Networks
One of the challenging tasks in the deployment of dense wireless networks (like sensor networks) is in devising a routing scheme for node to node communication. Important consideration includes scalability, routing complexity, the length of the communication paths and the load sharing of the routes. In this paper, we show that a compact and expressive abstraction of network connectivity by the medial axis enables efficient and localized routing. We propose MAP, a Medial Axis based naming and routing Protocol that does not require locations, makes routing decisions locally, and achieves good load balancing. In its preprocessing phase, MAP constructs the medial axis of the sensor field, defined as the set of nodes with at least two closest boundary nodes. The medial axis of the network captures both the complex geometry and non-trivial topology of the sensor field. It can be represented compactly by a graph whose size is comparable with the complexity of the geometric features (e.g., the number of holes). Each node is then given a name related to its position with respect to the medial axis. The routing scheme is derived through local decisions based on the names of the source and destination nodes and guarantees delivery with reasonable and natural routes. We show by both theoretical analysis and simulations that our medial axis based geometric routing scheme is scalable, produces short routes, achieves excellent load balancing, and is very robust to variations in the network model
Trajectory Design of Laser-Powered Multi-Drone Enabled Data Collection System for Smart Cities
This paper considers a multi-drone enabled data collection system for smart cities, where there are two kinds of drones, i.e., Low Altitude Platforms (LAPs) and a High Altitude Platform (HAP). In the proposed system, the LAPs perform data collection tasks for smart cities and the solar-powered HAP provides energy to the LAPs using wireless laser beams. We aim to minimize the total laser charging energy of the HAP, by jointly optimizing the LAPs’ trajectory and the laser charging duration for each LAP, subject to the energy capacity constraints of the LAPs. This problem is formulated as a mixed-integer and non-convex Drones Traveling Problem (DTP), which is a combinatorial optimization problem and NP-hard. We propose an efficient and novel search algorithm named DronesTraveling Algorithm (DTA) to obtain a near-optimal solution. Simulation results show that DTA can deal with the large scale DTP (i.e., more than 400 data collection points) efficiently. Moreover, the DTA only uses 5 iterations to obtain the nearoptimal solution whereas the normal Genetic Algorithm needs nearly 10000 iterations and still fails to obtain an acceptable solution
Hamming Compressed Sensing
Compressed sensing (CS) and 1-bit CS cannot directly recover quantized
signals and require time consuming recovery. In this paper, we introduce
\textit{Hamming compressed sensing} (HCS) that directly recovers a k-bit
quantized signal of dimensional from its 1-bit measurements via invoking
times of Kullback-Leibler divergence based nearest neighbor search.
Compared with CS and 1-bit CS, HCS allows the signal to be dense, takes
considerably less (linear) recovery time and requires substantially less
measurements (). Moreover, HCS recovery can accelerate the
subsequent 1-bit CS dequantizer. We study a quantized recovery error bound of
HCS for general signals and "HCS+dequantizer" recovery error bound for sparse
signals. Extensive numerical simulations verify the appealing accuracy,
robustness, efficiency and consistency of HCS.Comment: 33 pages, 8 figure
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