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Effectiveness of landmark analysis for establishing locality in p2p networks
Locality to other nodes on a peer-to-peer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multi-dimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality
preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and non-linear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis
have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model
with a typical power-law distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required
A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps
The Self-OrganizingMap (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topologypreservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topologypreservation, particularly using Kohonen's model. In this work, two methods for measuring the topologypreservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving ma
A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation
Intrinsic isometric shape matching has become the standard approach for pose
invariant correspondence estimation among deformable shapes. Most existing
approaches assume global consistency, i.e., the metric structure of the whole
manifold must not change significantly. While global isometric matching is well
understood, only a few heuristic solutions are known for partial matching.
Partial matching is particularly important for robustness to topological noise
(incomplete data and contacts), which is a common problem in real-world 3D
scanner data. In this paper, we introduce a new approach to partial, intrinsic
isometric matching. Our method is based on the observation that isometries are
fully determined by purely local information: a map of a single point and its
tangent space fixes an isometry for both global and the partial maps. From this
idea, we develop a new representation for partial isometric maps based on
equivalence classes of correspondences between pairs of points and their
tangent spaces. From this, we derive a local propagation algorithm that find
such mappings efficiently. In contrast to previous heuristics based on RANSAC
or expectation maximization, our method is based on a simple and sound
theoretical model and fully deterministic. We apply our approach to register
partial point clouds and compare it to the state-of-the-art methods, where we
obtain significant improvements over global methods for real-world data and
stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure
Analyzing Energy-efficiency and Route-selection of Multi-level Hierarchal Routing Protocols in WSNs
The advent and development in the field of Wireless Sensor Networks (WSNs) in
recent years has seen the growth of extremely small and low-cost sensors that
possess sensing, signal processing and wireless communication capabilities.
These sensors can be expended at a much lower cost and are capable of detecting
conditions such as temperature, sound, security or any other system. A good
protocol design should be able to scale well both in energy heterogeneous and
homogeneous environment, meet the demands of different application scenarios
and guarantee reliability. On this basis, we have compared six different
protocols of different scenarios which are presenting their own schemes of
energy minimizing, clustering and route selection in order to have more
effective communication. This research is motivated to have an insight that
which of the under consideration protocols suit well in which application and
can be a guide-line for the design of a more robust and efficient protocol.
MATLAB simulations are performed to analyze and compare the performance of
LEACH, multi-level hierarchal LEACH and multihop LEACH.Comment: NGWMN with 7th IEEE Inter- national Conference on Broadband and
Wireless Computing, Communication and Applications (BWCCA 2012), Victoria,
Canada, 201
Making Laplacians commute
In this paper, we construct multimodal spectral geometry by finding a pair of
closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are
jointly diagonalizable and hence have the same eigenbasis. Our construction
naturally extends classical data analysis tools based on spectral geometry,
such as diffusion maps and spectral clustering. We provide several synthetic
and real examples of applications in dimensionality reduction, shape analysis,
and clustering, demonstrating that our method better captures the inherent
structure of multi-modal data
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