3104769
Deformable spanners and applications
For a set S of points in ℝ3, an s-spanner is a graph on S such that any pair of points is connected via some path in the spanner whose total length is at most s times the Euclidean distance between the points. In this paper we propose a new sparse (1+ε)-spanner with O(n/εd) edges, where ε is a specified parameter. The key property of this spanner is that it can be efficiently maintained under dynamic insertion or deletion ofpoints, as well as under continuous motion of the points in both the kinetic data structures setting and in the more realistic blackbox displacement model we introduce. Our deformable spanner succinctly encodes all proximity information in a deforming point cloud, giving us efficient kinetic algorithms for problems such as the closest pair, the near neighbors of all points, approximate nearest neighbor search (aka approximate Voronoi diagram), well-separated pair decomposition, and approximate k-centers.
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.
45076012
Discrete Mobile Centers 


Abstract. We propose a new randomized algorithm for maintaining a set of clusters 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. This clustering algorithm is distributed in nature and can enable numerous applications in ad hoc wireless networks, where mobile devices must be interconnected to perform various tasks collaboratively.

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.
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.
39022820
A multi-Kalman filtering approach for video tracking of human-delineated objects in cluttered environments
17256385
A flocking based algorithm for document clustering analysis
Social animals or insects in nature often exhibit a form of emergent collective behavior known as flocking. In this paper, we present a novel Flocking based approach for document clustering analysis. Our Flocking clustering algorithm uses stochastic and heuristic principles discovered from observing bird flocks or fish schools. Unlike other partition clustering algorithm such as K-means, the Flocking based algorithm does not require initial partitional seeds. The algorithm generates a clustering of a given set of data through the embedding of the high-dimensional data items on a two-dimensional grid for easy clustering result retrieval and visualization. Inspired by the self-organized behavior of bird flocks, we represent each document object with a flock boid. The simple local rules followed by each flock boid result in the entire document flock generating complex global behaviors, which eventually result in a clustering of the documents. We evaluate the efficiency of our algorithm with both a synthetic dataset and a real document collection that includes 100 news articles collected from the Internet. Our results show that the Flocking clustering algorithm achieves better performance compared to the K- means and the Ant clustering algorithm for real document clustering.
14630821
A New Semi-Supervised Subspace Clustering Algorithm on Fitting Mixture Models
We propose a new subspace clustering algorithm (EPSCMIX), which is based on the feature saliency measure that is obtained by using both the Emerging Patterns algorithm and the EM algorithm, for the analysis of microarray data. For the model selection, it employs a novel agglomerative step together with MDL criterion. And, we present the result of comparative experiments between AIC, MDL and minimum message length (MML) used to determine a criterion for our algorithm. The robustness of using emerging patterns based on mixture models, as well as using the Gaussian mixture model for subspace clustering, was demonstrated on both synthetic and real data sets. In experiments, it also certified that a new agglomerative method that merges mostly correlated components with MDL consistently worked better than the one that removes weak weight components.
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.
45585785
Predictive cardiac motion modelling and correction
Abstract The quest for higher image quality and resolution for assessing cardiovascular anatomy and function requires an effective way of handing non-periodic, patient specific tissue deformation. This paper presents a new technique for predictive cardiac motion modelling and correction. It uses partial least squares regression to extract intrinsic relationships between 3D cardiac deformation due to respiration and 1D real time measurable intensity traces taken from tissue interfaces. This abstraction allows for the construction of a patient specific model for dense motion field prediction. The effectiveness of the proposed method is validated for a range of respiratory positions with data acquired from 10 asymptomatic subjects, using reconstructed image data sets.