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.
47344583
Double rulings for information brokerage in sensor networks
We study the problem of information brokerage in sensor networks, where information consumers (sinks, users) search for data acquired by information producers (sources). In-network storage such as geographical hash table (GHT) has been proposed to store data at rendezvous nodes for consumers to retrieve. In this paper, we propose a double rulings scheme that stores data replicas on a curve instead of one or multiple isolated sensors. The consumer travels along another curve that is guaranteed to intersect the producer curve. The double rulings is a natural extension of the flat hashing scheme such as GHTs. It has improved query locality--i.e., consumers close to producers find the data quickly--and structured aggregate queries, i.e., a consumer following a curve is able to retrieve all the data. Furthermore, by the flexibility of retrieval mechanisms, we have better routing robustness (as multiple retrieval paths are available) and data robustness against regional node failures. We show by simulation that the double rulings scheme provides reduced communication costs and more balanced traffic load on the sensors.
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.
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.

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.}
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.
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.
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.
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.
13640860
Parallel Multiresolution Volume Rendering of Large Data Sets with Error-Guided Load Balancing
We present a new parallel multiresolution volume rendering algorithm for visualizing large data sets. Using the wavelet transform, the raw data is first converted into a multiresolution wavelet tree. To eliminate the parent-child data dependency for reconstruction and achieve load-balanced rendering, we design a novel algorithm to partition the tree and distribute the data along a hierarchical space-filling curve with error-guided bucketization. At run time, the wavelet tree is traversed according to the user-specified error tolerance, data blocks of different resolutions are decompressed and rendered to compose the final image in parallel. Experimental results showed that our algorithm can reduce the run-time communication cost to a minimum and ensure a well-balanced workload among processors when visualizing gigabytes of data with arbitrary error tolerances.