35227272
Well-Separated Pair Decomposition for the Unit-Disk Graph Metric and Its Applications
We extend the classic notion of well-separated pair decomposition [P. B. Callahan and S. R. Kosaraju, J. ACM, 42 (1975), pp. 67--90] to the unit-disk graph metric: the shortest path distance metric induced by the intersection graph of unit disks. We show that for the unit-disk graph metric of n points in the plane and for any constant $c\geq 1$, there exists a c-well-separated pair decomposition with O(n log n) pairs, and the decomposition can be computed in O(n log n) time. We also show that for the unit-ball graph metric in k dimensions where $k\geq 3$, there exists a c-well-separated pair decomposition with O(n2-2/k) pairs, and the bound is tight in the worst case. We present the application of the well-separated pair decomposition in obtaining efficient algorithms for approximating the diameter, closest pair, nearest neighbor, center, median, and stretch factor, all under the unit-disk graph metric.
1839876
Discrete mobile centers
\emph{We propose a new randomized algorithm for maintaining a set of c lusters among moving nodes in the plane. Given a specified cluster radius, our algorithm selects and maintains a variable subset of the nodes as cluster centers. This subset has the property that (1) balls of the given radius centered at the chosen nodes cover all the others and (2) the number of centers selected is a constant-factor approximation of the minimum possible. As the nodes move, an event-based kinetic data structure updates the clustering as necessary. This kinetic data structure is shown to be responsive, efficient, local, and compact. The produced cover is also smooth, in the sense that wholesale cluster re-arrangements are avoided. The algorithm can be implemented without exact knowledge of the node positions, if each node is able to sense its distance to other nodes up to the cluster radius. Such a kinetic clustering can be used in numerous applications where mobile devices must be interconnected into an ad-hoc network to collaboratively perform some task.}
207794
Trade-Offs between Stretch Factor and Load-Balancing Ratio in Routing on Growth-Restricted Graphs
An unweighted graph has density rho and growth rate k if the number of nodes in every ball with radius r is bounded by rhork. The communication graphs of wireless networks and peer-to-peer networks often have constant bounded density and small growth rate. In this paper, we study the trade-off between two quality measures for routing in growth-restricted graphs. The two measures we consider are the stretch factor, which measures the lengths of the routing paths, and the load-balancing ratio, which measures the evenness of the traffic distribution. We show that if the routing algorithm is required to use paths with stretch factor c, then its load-balancing ratio is bounded by O(rho1/k(n/c)1-1/k), and the bound is tight in the worst case. We show the application and extension of the trade-off to the wireless network routing and VLSI layout design. We also present a load-balanced routing algorithm with the stretch factor constraint in an online setting, in which the routing requests come one by one.
10628567
Shape Segmentation and Applications in Sensor Networks
Many sensor network protocols in the literature implicitly assume that sensor nodes are deployed uniformly inside a simple geometric region. When the real deployment deviates from that, we often observe degraded performance. It is desirable to have a generic approach to handle a sensor field with complex shape. In this paper, we propose a segmentation algorithm that partitions an irregular sensor field into nicely shaped pieces such that algorithms and protocols that assume a nice sensor field can be applied inside each piece. Across the segments, problem dependent structures specify how the segments and data collected in these segments are integrated. This unified topology-adaptive spatial partitioning would benefit many settings that currently assume a nicely shaped sensor field. Our segmentation algorithm does not require sensor locations and only uses network connectivity information. Each node is given a 'flow direction' that directs away from the network boundary. A node with no flow direction becomes a sink, and attracts other nodes in the same segment. We evaluate the performance improvements by integrating shape segmentation with applications such as distributed indices and random sampling.
5160
Well-separated pair decomposition for the unit-disk graph metric and its applications
We extend the classic notion of well-separated pair decomposition [10] to the (weighted) unit-disk graph metric: the shortest path distance metric induced by the intersection graph of unit disks. We show that for the unit-disk graph metric of n points in the plane and for any constant c≥1, there exists a c-well-separated pair decomposition with O(n log n) pairs, and the decomposition can be computed in O(n log n) time. We also show that for the unit-ball graph metric in k dimensions where k≥3, there exists a c-well-separated pair decomposition with O(n2-2/k) pairs, and the bound is tight in the worst case. We present the application of the well-separated pair decomposition in obtaining efficient algorithms for approximating the diameter, closest pair, nearest neighbor, center, median, and stretch factor, all under the unit-disk graph metric.
2954526
Analysis of Incomplete Data and an Intrinsic-Dimension Helly Theorem
The analysis of incomplete data is a long-standing challenge in practical statistics. When, as is typical, data objects are represented by points in ℝd, incomplete data objects correspond to affine subspaces (lines or Δ-flats). With this motivation we study the problem of finding the minimum intersection radiusr(ℒ) of a set of lines or Δ-flats ℒ: the least r such that there is a ball of radius r intersecting every flat in ℒ. Known algorithms for finding the minimum enclosing ball for a point set (or clustering by several balls) do not easily extend to higher-dimensional flats, primarily because “distances” between flats do not satisfy the triangle inequality. In this paper we show how to restore geometry (i.e., a substitute for the triangle inequality) to the problem, through a new analog of Helly’s theorem. This “intrinsic-dimension” Helly theorem states: for any family ℒ of Δ-dimensional convex sets in a Hilbert space, there exist Δ+2 sets ℒ′⊆ℒ such that r(ℒ)≤2r(ℒ′). Based upon this we present an algorithm that computes a (1+ε)-core set ℒ′⊆ℒ, |ℒ′|=O(Δ4/ε), such that the ball centered at a point c with radius (1+ε)r(ℒ′) intersects every element of ℒ. The running time of the algorithm is O(nΔ+1dpoly (Δ/ε)). For the case of lines or line segments (Δ=1), the (expected) running time of the algorithm can be improved to O(ndpoly (1/ε)). We note that the size of the core set depends only on the dimension of the input objects and is independent of the input size n and the dimension d of the ambient space.
13948777
Steganalysis Based on Multiple Features Formed by Statistical Moments of Wavelet Characteristic Functions
In this paper, a steganalysis scheme based on multiple features formed by statistical moments of wavelet characteristic functions is proposed. Our theoretical analysis has pointed out that the defined n-th statistical moment of a wavelet characteristic function is related to the n-th derivative of the corresponding wavelet histogram, and hence is sensitive to data embedding. The selection of the first three moments of the characteristic functions of wavelet subbands of the three-level Haar wavelet decomposition as well as the test image has resulted in total 39 features for steganalysis. The effectiveness of the proposed system has been demonstrated by extensive experimental investigation. The detection rate for Cox et al.'s non-blind spread spectrum (SS) data hiding method, Piva et al.'s blind SS method, Huang and Shi's 8×8 block SS method, a generic LSB method (as embedding capacity being 0.3 bpp), and a generic QIM method (as embedding capacity being 0.1 bpp) are all above 90% over all of the 1096 images in the CorelDraw image database using the Bayes classifier. Furthermore, when these five typical data hiding methods are jointly considered for steganalysis, i.e., when the proposed steganalysis scheme is first trained sequentially for each of these five methods, and is then tested blindly for stego-images generated by all of these methods, the success classification rate is 86%, thus pointing out a new promising approach to general blind steganalysis. The detection results of steganalysis on Jsteg, Outguess and F5 have further demonstrated the effectiveness of the proposed steganalysis scheme.
2658593
A Probabilistic Framework for SVM Regression and Error Bar Estimation
In this paper, we elaborate on the well-known relationship between Gaussian Processes (GP) and Support Vector Machines (SVM) under some convex assumptions for the loss functions. This paper concentrates on the derivation of the evidence and error bar approximation for regression problems. An error bar formula is derived based on the ∈-insensitive loss function.
3016958
Multiple frame motion inference using belief propagation
We present an algorithm for automatic inference of human upper body motion. A graph model is proposed for inferring human motion, and motion inference is posed as a mapping problem between state nodes in the graph model and features in image patches. Belief propagation is utilized for Bayesian inference in this graph. A multiple-frame inference model/algorithm is proposed to combine both structural and temporal constraints in human motion. We also present a method for capturing constraints of human body configuration under different view angles. The algorithm is applied in a prototype system that can automatically label upper body motion from videos, without manual initialization of body parts.
461312
Dependence language model for information retrieval
This paper presents a new dependence language modeling approach to information retrieval. The approach extends the basic language modeling approach based on unigram by relaxing the independence assumption. We integrate the linkage of a query as a hidden variable, which expresses the term dependencies within the query as an acyclic, planar, undirected graph. We then assume that a query is generated from a document in two stages: the linkage is generated first, and then each term is generated in turn depending on other related terms according to the linkage. We also present a smoothing method for model parameter estimation and an approach to learning the linkage of a sentence in an unsupervised manner. The new approach is compared to the classical probabilistic retrieval model and the previously proposed language models with and without taking into account term dependencies. Results show that our model achieves substantial and significant improvements on TREC collections.
11423197
Unsupervised Learning of Dependency Structure for Language Modeling
This paper presents a dependency language model (DLM) that captures linguistic constraints via a dependency structure, i.e., a set of probabilistic dependencies that express the relations between headwords of each phrase in a sentence by an acyclic, planar, undirected graph. Our contributions are three-fold. First, we incorporate the dependency structure into an n-gram language model to capture long distance word dependency. Second, we present an unsupervised learning method that discovers the dependency structure of a sentence using a bootstrapping procedure. Finally, we evaluate the proposed models on a realistic application (Japanese Kana-Kanji conversion). Experiments show that the best DLM achieves an 11.3% error rate reduction over the word trigram model.