90153
Staying in the Middle: Exact and Approximate Medians in R1 and R2 for Moving Points
Many divide-and-conquer based geometric algorithms and order-statistics problems ask for a point that lies "in the middle" of a given point set. We study several fun- damental problems of this type for moving points in one and two dimensions. In particular, we show how to kinetically maintain the median of a set of n points moving on the real line, and a center point of a set of n points moving in the plane, that is, a point such that any line through it has at most 2n/3 on either side of it. Since the maintenance of exact medians and center points can be quite expensive, we also show how to maintain "-approximate medians and center points and argue that the latter can be made to be much more stable under motion. These results are based on a new algorithm to maintain an "-approximation of a range space under insertions and deletions, which is of independent interest. All our approximation algorithms run in near-linear time.
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.
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.
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.

37200874
Some remarks on Kalman filters for the multisensor fusion
Abstract Multisensor data fusion has found widespread application in industry and commerce. The purpose of data fusion is to produce an improved model or estimate of a system from a set of independent data sources. There are various multisensor data fusion approaches, of which Kalman filtering is one of the most significant. Methods for Kalman filter based data fusion includes measurement fusion and state fusion. This paper gives first a simple a review of both measurement fusion and state fusion, and secondly proposes two new methods of state fusion based on fusion procedures at the prediction and update level, respectively, of the Kalman filter. The theoretical derivation for these algorithms are derived. To illustrate their application, a simple example is performed to evaluate the proposed methods and compare their performance with the conventional state fusion method and measurement fusion methods.
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.
8809724
Chinese Named Entity Identification Using Class-based Language Model
We consider here the problem of Chinese named entity (NE) identification using statistical language model(LM). In this research, word segmentation and NE identification have been integrated into a unified framework that consists of several class-based language models. We also adopt a hierarchical structure for one of the LMs so that the nested entities in organization names can be identified. The evaluation on a large test set shows consistent improvements. Our experiments further demonstrate the improvement after seamlessly integrating with linguistic heuristic information, cache-based model and NE abbreviation identification.
13951367
Interactive color image segmentation editor driven by active contour model
A new general-purpose color image segmentation editor (CISE) for the purpose of extracting a semantic object is designed, implemented and tested on a number of various natural scene images. Our editor integrates a deformable model and image statistics including intensity, color, gradient and texture. The editor starts with a coarse region segmentation which applies the Canny's operator followed by a low-complexity edge linking algorithm. This segmentation basically builds regions of smooth intensity by closing all dangling edges. Next, a topologically-based region labeling method makes full use of relationship among pixels and produces useful labeled image. Finally, to refine the extracted object of interest (O/sup 2/I), a deformable model based on energy minimization is applied by incorporating both the gradient and region criteria to the external constraint force. These processes are demonstrated through examples on natural scene color images. Experimental results suggest the efficiency and accuracy of the algorithm in its segmentation operations.
18339723
Automatic video object shape extraction and its classification with camera in motion
In this paper, we present an automatic moving object extraction and classification system. For automatic extraction of object taken by a moving camera, a novel technique is proposed, in which optical flow handles the background modeling and camera motion estimation, and frame difference information yields the exact object shape. We also use forward region boundary based change detection approach for frame difference. This approach assures change detection for uniform intensity regions. For classification, weighted likelihood discriminant based shape classifier is designed. Unlike maximum likelihood (ML) methods, our proposed method utilizes information from all classes to design the classifier. In the description phase of the classifier, curvature features are extracted from the shape and are utilized to build a hidden Markov model (HMM). The HMM provides a robust ML description of the shape. In the discrimination phase, a weighted likelihood discriminant function is introduced, which weights the likelihoods of curvature at individual points of the shape to minimize the classification error. The weights are estimated by generalized probabilistic descent (GPD) method. To demonstrate the performance of the proposed method, we present results achieved for car shapes extraction and classification.