Showing papers on "Euclidean distance published in 2005"

Exact indexing of dynamic time warping

Abstract: The problem of indexing time series has attracted much interest. Most algorithms used to index time series utilize the Euclidean distance or some variation thereof. However, it has been forcefully shown that the Euclidean distance is a very brittle distance measure. Dynamic time warping (DTW) is a much more robust distance measure for time series, allowing similar shapes to match even if they are out of phase in the time axis. Because of this flexibility, DTW is widely used in science, medicine, industry and finance. Unfortunately, however, DTW does not obey the triangular inequality and thus has resisted attempts at exact indexing. Instead, many researchers have introduced approximate indexing techniques or abandoned the idea of indexing and concentrated on speeding up sequential searches. In this work, we introduce a novel technique for the exact indexing of DTW. We prove that our method guarantees no false dismissals and we demonstrate its vast superiority over all competing approaches in the largest and most comprehensive set of time series indexing experiments ever undertaken.

Robust and fast similarity search for moving object trajectories

Abstract: An important consideration in similarity-based retrieval of moving object trajectories is the definition of a distance function. The existing distance functions are usually sensitive to noise, shifts and scaling of data that commonly occur due to sensor failures, errors in detection techniques, disturbance signals, and different sampling rates. Cleaning data to eliminate these is not always possible. In this paper, we introduce a novel distance function, Edit Distance on Real sequence (EDR) which is robust against these data imperfections. Analysis and comparison of EDR with other popular distance functions, such as Euclidean distance, Dynamic Time Warping (DTW), Edit distance with Real Penalty (ERP), and Longest Common Subsequences (LCSS), indicate that EDR is more robust than Euclidean distance, DTW and ERP, and it is on average 50% more accurate than LCSS. We also develop three pruning techniques to improve the retrieval efficiency of EDR and show that these techniques can be combined effectively in a search, increasing the pruning power significantly. The experimental results confirm the superior efficiency of the combined methods.

On the Euclidean distance of images

Abstract: We present a new Euclidean distance for images, which we call image Euclidean distance (IMED). Unlike the traditional Euclidean distance, IMED takes into account the spatial relationships of pixels. Therefore, it is robust to small perturbation of images. We argue that IMED is the only intuitively reasonable Euclidean distance for images. IMED is then applied to image recognition. The key advantage of this distance measure is that it can be embedded in most image classification techniques such as SVM, LDA, and PCA. The embedding is rather efficient by involving a transformation referred to as standardizing transform (ST). We show that ST is a transform domain smoothing. Using the face recognition technology (FERET) database and two state-of-the-art face identification algorithms, we demonstrate a consistent performance improvement of the algorithms embedded with the new metric over their original versions.

Meridian: a lightweight network location service without virtual coordinates

Abstract: This paper introduces a lightweight, scalable and accurate framework, called Meridian, for performing node selection based on network location. The framework consists of an overlay network structured around multi-resolution rings, query routing with direct measurements, and gossip protocols for dissemination. We show how this framework can be used to address three commonly encountered problems, namely, closest node discovery, central leader election, and locating nodes that satisfy target latency constraints in large-scale distributed systems without having to compute absolute coordinates. We show analytically that the framework is scalable with logarithmic convergence when Internet latencies are modeled as a growth-constrained metric, a low-dimensional Euclidean metric, or a metric of low doubling dimension. Large scale simulations, based on latency measurements from 6.25 million node-pairs as well as an implementation deployed on PlanetLab show that the framework is accurate and effective.

Theory of semidefinite programming for sensor network localization

Abstract: We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior-point algorithm theories to prove that the SDP localizes any network or graph that has unique sensor positions to fit given distance measures. Therefore, we show, for the first time, that these networks can be localized in polynomial time. We also give a simple and efficient criterion for checking whether a given instance of the localization problem has a unique realization in R2 using graph rigidity theory. Finally, we introduce a notion called strong localizability and show that the SDP model will identify all strongly localizable subnetworks in the input network.

Offline geometric parameters for automatic signature verification using fixed-point arithmetic

Abstract: This paper presents a set of geometric signature features for offline automatic signature verification based on the description of the signature envelope and the interior stroke distribution in polar and Cartesian coordinates. The features have been calculated using 16 bits fixed-point arithmetic and tested with different classifiers, such as hidden Markov models, support vector machines, and Euclidean distance classifier. The experiments have shown promising results in the task of discriminating random and simple forgeries.

Radar HRRP target recognition based on higher order spectra

Abstract: Radar high-resolution range profile (HRRP) is very sensitive to time-shift and target-aspect variation; therefore, HRRP-based radar automatic target recognition (RATR) requires efficient time-shift invariant features and robust feature templates. Although higher order spectra are a set of well-known time-shift invariant features, direct use of them (except for power spectrum) is impractical due to their complexity. A method for calculating the Euclidean distance in higher order spectra feature space is proposed in this paper, which avoids calculating the higher order spectra, effectively reducing the computation complexity and storage requirement. Moreover, according to the widely used scattering center model, theoretical analysis and experimental results in this paper show that the feature vector extracted from the average profile in a small target-aspect sector has better generalization performance than the average feature vector in the same sector when both of them are used as feature templates in HRRP-based RATR. The proposed Euclidean distance calculation method and average profile-based template database are applied to two classification algorithms [the template matching method (TMM) and the radial basis function network (RBFN)] to evaluate the recognition performances of higher order spectra features. Experimental results for measured data show that the power spectrum has the best recognition performance among higher order spectra.

Aggregate nearest neighbor queries in road networks

Abstract: Aggregate nearest neighbor queries return the object that minimizes an aggregate distance function with respect to a set of query points. Consider, for example, several users at specific locations (query points) that want to find the restaurant (data point), which leads to the minimum sum of distances that they have to travel in order to meet. We study the processing of such queries for the case where the position and accessibility of spatial objects are constrained by spatial (e.g., road) networks. We consider alternative aggregate functions and techniques that utilize Euclidean distance bounds, spatial access methods, and/or network distance materialization structures. Our algorithms are experimentally evaluated with synthetic and real data. The results show that their relative performance depends on the problem characteristics.

Using the inner-distance for classification of articulated shapes

Abstract: We propose using the inner-distance between landmark points to build shape descriptors. The inner-distance is defined as the length of the shortest path between landmark points within the shape silhouette. We show that the inner-distance is articulation insensitive and more effective at capturing complex shapes with part structures than Euclidean distance. To demonstrate this idea, it is used to build a new shape descriptor based on shape contexts. After that, we design a dynamic programming based method for shape matching and comparison. We have tested our approach on a variety of shape databases including an articulated shape dataset, MPEG7 CE-Shape-1, Kimia silhouettes, a Swedish leaf database and a human motion silhouette dataset. In all the experiments, our method demonstrates effective performance compared with other algorithms.

Projective nonnegative matrix factorization for image compression and feature extraction

Abstract: In image compression and feature extraction, linear expansions are standardly used. It was recently pointed out by Lee and Seung that the positivity or non-negativity of a linear expansion is a very powerful constraint, that seems to lead to sparse representations for the images. Their technique, called Non-negative Matrix Factorization (NMF), was shown to be a useful technique in approximating high dimensional data where the data are comprised of non-negative components. We propose here a new variant of the NMF method for learning spatially localized, sparse, part-based subspace representations of visual patterns. The algorithm is based on positively constrained projections and is related both to NMF and to the conventional SVD or PCA decomposition. Two iterative positive projection algorithms are suggested, one based on minimizing Euclidean distance and the other on minimizing the divergence of the original data matrix and its non-negative approximation. Experimental results show that P-NMF derives bases which are somewhat better suitable for a localized representation than NMF.

Alternative Solutions for Continuous K Nearest Neighbor Queries in Spatial Network Databases

Abstract: Continuous K nearest neighbor queries (C-KNN) are defined as finding the nearest points of interest along an enitre path (e.g., finding the three nearest gas stations to a moving car on any point of a pre-specified path). The result of this type of query is a set of intervals (or split points) and their corresponding KNNs, such that the KNNs of all points within each interval are the same. The current studies on C-KNN focus on vector spaces where the distance between two objects is a function of their spatial attributes (e.g., Euclidean distance metric). These studies are not applicable to spatial network databases (SNDB) where the distance between two objects is a function of the network connectivity (e.g., shortest path between two objects). In this paper, we propose two techniques to address C-KNN queries in SNDB: Intersection Examination (IE) and Upper Bound Algorithm (UBA). With IE, we first find the KNNs of all nodes on a path and then, for those adjacent nodes whose nearest neighbors are different, we find the intermediate split points. Finally, we compute the KNNs of the split points using the KNNs of the surrounding nodes. The intuition behind UBA is that the performance of IE can be improved by determining the adjacent nodes that cannot have any split points in between, and consequently eliminating the computation of KNN queries for those nodes. Our empirical experiments show that the UBA approach outperforms IE, specially when the points of interest are sparsely distributed in the network.

A novel bit level time series representation with implication of similarity search and clustering

Abstract: Because time series are a ubiquitous and increasingly prevalent type of data, there has been much research effort devoted to time series data mining recently. As with all data mining problems, the key to effective and scalable algorithms is choosing the right representation of the data. Many high level representations of time series have been proposed for data mining. In this work, we introduce a new technique based on a bit level approximation of the data. The representation has several important advantages over existing techniques. One unique advantage is that it allows raw data to be directly compared to the reduced representation, while still guaranteeing lower bounds to Euclidean distance. This fact can be exploited to produce faster exact algorithms for similarly search. In addition, we demonstrate that our new representation allows time series clustering to scale to much larger datasets.

Determining approximate shortest paths on weighted polyhedral surfaces

Abstract: In this article, we present an approximation algorithm for solving the single source shortest paths problem on weighted polyhedral surfaces. We consider a polyhedral surface P as consisting of n triangular faces, where each face has an associated positive weight. The cost of travel through a face is the Euclidean distance traveled, multiplied by the face's weight. For a given parameter e, 0

PAPR reduction of OFDM signals using partial transmit sequence: an optimal approach using sphere decoding

Abstract: List-based algorithms for. decoding block turbo Codes (BTC) have gained popularity due to their low computational complexity. The normal way to calculate the soft outputs involves searching for a decision code word D and a competing codeword B. In addition, a scaling factor /spl alpha/ and an estimated reliability value /spl beta/ are used. In this letter, we present a new approach that does not require /spl alpha/ and /spl beta/. Soft outputs are generated based on the Euclidean distance property of decision code words. By using the new algorithm, we achieve better error performance with even less complexity-for certain BTCs.

Robust centerline extraction framework using level sets

Abstract: In this paper, we present a novel framework for computing centerlines for both 2D and 3D shape analysis. The framework works as follows: an object centerline point is selected automatically as the point of global maximum Euclidean distance from the boundary, and is considered a point source (Ps) that transmits a wave front that evolves over time and traverses the object domain. The front propagates at each object point with a speed that is proportional to its Euclidean distance from the boundary. The motion of the front is governed by a nonlinear partial differential equation whose solution is computed efficiently using level set methods. Initially, the P/sub S/ transmits a moderate speed wave to explore the object domain and extract its topological information such as merging and extreme points. Then, it transmits a new front that is much faster at centerline points than non central ones. As a consequence, centerlines intersect the propagating fronts at those points of maximum positive curvature. Centerlines are computed by tracking them, starting from each topological point until the Ps is reached, by solving an ordinary differential equation using an efficient numerical scheme. The proposed method is computationally inexpensive, handles efficiently objects with complex topology, and computes centerlines that are centered, connected, one point thick, and less sensitive to boundary noise. In addition, the extracted paths form a tree graph without additional cost. We have extensively validated the robustness of the proposed method both quantitatively and qualitatively against several 2D and 3D shapes.

A multiresolution symbolic representation of time series

Abstract: Efficiently and accurately searching for similarities among time series and discovering interesting patterns is an important and non-trivial problem. In this paper, we introduce a new representation of time series, the multiresolution vector quantized (MVQ) approximation, along with a new distance function. The novelty of MVQ is that it keeps both local and global information about the original time series in a hierarchical mechanism, processing the original time series at multiple resolutions. Moreover, the proposed representation is symbolic employing key subsequences and potentially allows the application of text-based retrieval techniques into the similarity analysis of time series. The proposed method is fast and scales linearly with the size of database and the dimensionality. Contrary to the vast majority in the literature that uses the Euclidean distance, MVQ uses a multi-resolution/hierarchical distance function. We performed experiments with real and synthetic data. The proposed distance function consistently outperforms all the major competitors (Euclidean, dynamic time warping, piecewise aggregate approximation) achieving up to 20% better precision/recall and clustering accuracy on the tested datasets.

Pareto evolutionary neural networks

Abstract: For the purposes of forecasting (or classification) tasks neural networks (NNs) are typically trained with respect to Euclidean distance minimization. This is commonly the case irrespective of any other end user preferences. In a number of situations, most notably time series forecasting, users may have other objectives in addition to Euclidean distance minimization. Recent studies in the NN domain have confronted this problem by propagating a linear sum of errors. However this approach implicitly assumes a priori knowledge of the error surface defined by the problem, which, typically, is not the case. This study constructs a novel methodology for implementing multiobjective optimization within the evolutionary neural network (ENN) domain. This methodology enables the parallel evolution of a population of ENN models which exhibit estimated Pareto optimality with respect to multiple error measures. A new method is derived from this framework, the Pareto evolutionary neural network (Pareto-ENN). The Pareto-ENN evolves a population of models that may be heterogeneous in their topologies inputs and degree of connectivity, and maintains a set of the Pareto optimal ENNs that it discovers. New generalization methods to deal with the unique properties of multiobjective error minimization that are not apparent in the uni-objective case are presented and compared on synthetic data, with a novel method based on bootstrapping of the training data shown to significantly improve generalization ability. Finally experimental evidence is presented in this study demonstrating the general application potential of the framework by generating populations of ENNs for forecasting 37 different international stock indexes.

Riemannian elasticity: a statistical regularization framework for non-linear registration

Abstract: In inter-subject registration, one often lacks a good model of the transformation variability to choose the optimal regularization. Some works attempt to model the variability in a statistical way, but the re-introduction in a registration algorithm is not easy. In this paper, we interpret the elastic energy as the distance of the Green-St Venant strain tensor to the identity, which reflects the deviation of the local deformation from a rigid transformation. By changing the Euclidean metric for a more suitable Riemannian one, we define a consistent statistical framework to quantify the amount of deformation. In particular, the mean and the covariance matrix of the strain tensor can be consistently and efficiently computed from a population of non-linear transformations. These statistics are then used as parameters in a Mahalanobis distance to measure the statistical deviation from the observed variability, giving a new regularization criterion that we called the statistical Riemannian elasticity. This new criterion is able to handle anisotropic deformations and is inverse-consistent. Preliminary results show that it can be quite easily implemented in a non-rigid registration algorithms.

A HOL theory of euclidean space

Abstract: We describe a formalization of the elementary algebra, topology and analysis of finite-dimensional Euclidean space in the HOL Light theorem prover. (Euclidean space is ${\mathbb R}^{N}$ with the usual notion of distance.) A notable feature is that the HOL type system is used to encode the dimension N in a simple and useful way, even though HOL does not permit dependent types. In the resulting theory the HOL type system, far from getting in the way, naturally imposes the correct dimensional constraints, e.g. checking compatibility in matrix multiplication. Among the interesting later developments of the theory are a partial decision procedure for the theory of vector spaces (based on a more general algorithm due to Solovay) and a formal proof of various classic theorems of topology and analysis for arbitrary N-dimensional Euclidean space, e.g. Brouwer's fixpoint theorem and the differentiability of inverse functions.

Euclidean distortion and the sparsest cut

Abstract: We prove that every n-point metric space of negative type (in particular, every n-point subset of L1) embeds into a Euclidean space with distortion O(√log n log log n), a result which is tight up to the O(log log n) factor. As a consequence, we obtain the best known polynomial-time approximation algorithm for the Sparsest Cut problem with general demands. If the demand is supported on a subset of size k, we achieve an approximation ratio of O(√log k log log k).

Adaptive Content-Based Image Retrieval with Relevance Feedback

Abstract: Retrieval of images, based on similarities between feature vectors of querying image and those from database, is considered The searching procedure was performed through the two basic steps: an objective one, based on the Euclidean distances and a subjective one based on the user's relevance feedback Images recognized from user as the best matched to a query are labeled and used for updating the query feature vector through a RBF (radial basis function) neural network The searching process is repeated from such subjectively refined feature vectors In practice, several iterative steps are sufficient, as confirmed by intensive simulations

Clustering using a random walk based distance measure

Abstract: This work proposes a simple way to improve a clustering algo- rithm. The idea is to exploit a new distance metric called the \Euclidian Commute Time" (ECT) distance, based on a random walk model on a graph derived from the data. Using this distance measure instead of the usual Euclidean distance in a k-means algorithm allows to retrieve well- separated clusters of arbitrary shape, without working hypothesis about their data distribution. Experimental results show that the use of this new distance measure signiflcantly improves the quality of the clustering on the tested data sets.

Novel self-configurable positioning technique for multihop wireless networks

Abstract: Geographic location information can effectively improve the performance (e.g., in routing or intelligent coordination) of large wireless networks. In this paper, we propose a novel self-configurable positioning technique for multihop wireless networks, based on a Euclidean distance estimation model and a coordinates establishment scheme. A number of nodes serve as the landmarks to establish a coordinates system. Specifically, any pair of landmarks estimate their Euclidean distance according to the shortest path length between them and establish the coordinates system by minimizing an error objective function. Other nodes in the network can accordingly contact the landmarks and determine their own coordinates. The proposed technique is independent of the Global Navigation Satellite Systems (GNSSs), and the established coordinates can be easily tuned to GNSS if at least one node in the network is equipped with GNSS receiver. Our simulation results show that the proposed self-configurable positioning technique is highly fault-tolerable to measurement inaccuracy and can effectively establish the coordinates for multihop wireless networks. More landmarks yield more accurate results. With the rectification of our Euclidean distance estimation model, four to seven landmarks are usually sufficient to meet the accuracy requirement in a network with hundreds of nodes. The computing time for coordinates establishment is in the order of milliseconds for a GHz CPU, acceptable for most applications in the mobile ad hoc networks as well as the sensor networks.

On the Generalization Ability of GRLVQ Networks

Abstract: We derive a generalization bound for prototype-based classifiers with adaptive metric. The bound depends on the margin of the classifier and is independent of the dimensionality of the data. It holds for classifiers based on the Euclidean metric extended by adaptive relevance terms. In particular, the result holds for relevance learning vector quantization (RLVQ) [4] and generalized relevance learning vector quantization (GRLVQ) [19].

Material metric, connectivity and dislocations in continua

Abstract: In this paper, we present a framework within which the role of the initial material structure of a body, or its developing structure in the course of deformation, is accounted for in the constitutive equation of the material. The problem is dealt with at the local level, i.e., at the material neighborhood. If a neighborhood has structure then its geometry cannot be represented by a Euclidean metric. The entire body may thus be non–Euclidean. We formulate the constitutive equation for large deformation in the case where either a neighborhood is non–Euclidean because of its initial structure, or it becomes so by virtue of irreversible internal motion and/or induced dislocation fields, which we discuss at some length. In the formulation of the theory, questions of connectivity arise and are dealt with in the text.

A Multidimensional Filter Algorithm for Nonlinear Equations and Nonlinear Least-Squares

Abstract: We introduce a new algorithm for the solution of systems of nonlinear equations and nonlinear least-squares problems that attempts to combine the efficiency of filter techniques and the robustness of trust-region methods. The algorithm is shown, under reasonable assumptions, to globally converge to zeros of the system, or to first-order stationary points of the Euclidean norm of its residual. Preliminary numerical experience is presented that shows substantial gains in efficiency over the traditional monotone trust-region approach.

A symbolic representation of time series

Abstract: Various representations have been proposed for time series to facilitate similarity searches and discovery of interesting patterns. Although the Euclidean distance and its variants have been most frequently used as similarity measures, they are relatively sensitive to noise and fail to provide meaningful information in many cases. Moreover, for time series with high dimensionality, the similarity calculation may be extremely inefficient. To solve this problem, we introduce a new method which gives a symbolic representation of the time series and can dramatically reduce its dimensionality. The method employs Vector Quantization to encode time series using symbols prior to performing similarity analysis. Due to the symbolic representation, we can apply string matching algorithms to calculate the similarities more efficiently and accurately. We propose a similarity measure that is based on the Longest Common Subsequence (LCSS) model. The experimental results on real and simulated data demonstrate the utility and efficiency of the proposed technique.