Showing papers on "Euclidean distance published in 2015"

Learning descriptors for object recognition and 3D pose estimation

Abstract: Detecting poorly textured objects and estimating their 3D pose reliably is still a very challenging problem. We introduce a simple but powerful approach to computing descriptors for object views that efficiently capture both the object identity and 3D pose. By contrast with previous manifold-based approaches, we can rely on the Euclidean distance to evaluate the similarity between descriptors, and therefore use scalable Nearest Neighbor search methods to efficiently handle a large number of objects under a large range of poses. To achieve this, we train a Convolutional Neural Network to compute these descriptors by enforcing simple similarity and dissimilarity constraints between the descriptors. We show that our constraints nicely untangle the images from different objects and different views into clusters that are not only well-separated but also structured as the corresponding sets of poses: The Euclidean distance between descriptors is large when the descriptors are from different objects, and directly related to the distance between the poses when the descriptors are from the same object. These important properties allow us to outperform state-of-the-art object views representations on challenging RGB and RGB-D data.

Image segmentation by generalized hierarchical fuzzy C-means algorithm

Abstract: Fuzzy c-means (FCM) has been considered as an effective algorithm for image segmentation. However, it still suffers from two problems: one is insufficient robustness to image noise, and the other is the Euclidean distance in FCM, which is sensitive to outliers. In this paper, we propose two new algorithms, generalized FCM (GFCM) and hierarchical FCM (HFCM), to solve these two problems. Traditional FCM can be considered as a linear combination of membership and distance from the expression of its mathematical formula. GFCM is generated by applying generalized mean on these two items. We impose generalized mean on membership to incorporate local spatial information and cluster information, and on distance function to incorporate local spatial information and image intensity value. Thus, our GFCM is more robust to image noise with the spatial constraints: the generalized mean. To solve the second problem caused by Euclidean distance (l2 norm), we introduce a more flexibility function which considers the distance function itself as a sub-FCM. Furthermore, the sub-FCM distance function in HFCM is general and flexible enough to deal with non-Euclidean data. Finally, we combine these two algorithms to introduce a new generalized hierarchical FCM (GHFCM). Experimental results demonstrate the improved robustness and effectiveness of the proposed algorithm.

Euclidean Distance Matrices: Essential theory, algorithms, and applications

Abstract: Euclidean distance matrices (EDMs) are matrices of the squared distances between points. The definition is deceivingly simple; thanks to their many useful properties, they have found applications in psychometrics, crystallography, machine learning, wireless sensor networks, acoustics, and more. Despite the usefulness of EDMs, they seem to be insufficiently known in the signal processing community. Our goal is to rectify this mishap in a concise tutorial. We review the fundamental properties of EDMs, such as rank or (non)definiteness, and show how the various EDM properties can be used to design algorithms for completing and denoising distance data. Along the way, we demonstrate applications to microphone position calibration, ultrasound tomography, room reconstruction from echoes, and phase retrieval. By spelling out the essential algorithms, we hope to fast-track the readers in applying EDMs to their own problems. The code for all of the described algorithms and to generate the figures in the article is available online at http://lcav.epfl.ch/ivan.dokmanic. Finally, we suggest directions for further research.

Modified Distance Calculation in Generational Distance and Inverted Generational Distance

Abstract: In this paper, we propose the use of modified distance calculation in generational distance (GD) and inverted generational distance (IGD). These performance indicators evaluate the quality of an obtained solution set in comparison with a pre-specified reference point set. Both indicators are based on the distance between a solution and a reference point. The Euclidean distance in an objective space is usually used for distance calculation. Our idea is to take into account the dominance relation between a solution and a reference point when we calculate their distance. If a solution is dominated by a reference point, the Euclidean distance is used for their distance calculation with no modification. However, if they are non-dominated with each other, we calculate the minimum distance from the reference point to the dominated region by the solution. This distance can be viewed as an amount of the inferiority of the solution (i.e., the insufficiency of its objective values) in comparison with the reference point. We demonstrate using simple examples that some Pareto non-compliant results of GD and IGD are resolved by the modified distance calculation. We also show that IGD with the modified distance calculation is weakly Pareto compliant whereas the original IGD is Pareto non-compliant.

Log-Euclidean Metric Learning on Symmetric Positive Definite Manifold with Application to Image Set Classification

Abstract: The manifold of Symmetric Positive Definite (SPD) matrices has been successfully used for data representation in image set classification. By endowing the SPD manifold with Log-Euclidean Metric, existing methods typically work on vector-forms of SPD matrix logarithms. This however not only inevitably distorts the geometrical structure of the space of SPD matrix logarithms but also brings low efficiency especially when the dimensionality of SPD matrix is high. To overcome this limitation, we propose a novel metric learning approach to work directly on logarithms of SPD matrices. Specifically, our method aims to learn a tangent map that can directly transform the matrix logarithms from the original tangent space to a new tangent space of more discriminability. Under the tangent map framework, the novel metric learning can then be formulated as an optimization problem of seeking a Mahalanobis-like matrix, which can take the advantage of traditional metric learning techniques. Extensive evaluations on several image set classification tasks demonstrate the effectiveness of our proposed metric learning method.

Comprehensive analysis of distance and similarity measures for Wi-Fi fingerprinting indoor positioning systems

Abstract: We introduce a study in depth of distance/similarity measures for indoor location.Alternative measures provide better results than commonly used Euclidean distance.Choosing an appropriate non-linear representation is crucial for intensity values.Very low intensity values are representative and they should not be filtered.All the experiments are validated with a public database, so they are reproducible. Recent advances in indoor positioning systems led to a business interest in those applications and services where a precise localization is crucial. Wi-Fi fingerprinting based on machine learning and expert systems are commonly used in the literature. They compare a current fingerprint to a database of fingerprints, and then return the most similar one/ones according to: 1) a distance function, 2) a data representation method for received signal strength values, and 3) a thresholding strategy. However, most of the previous works simply use the Euclidean distance with the raw unprocessed data. There is not any previous work that studies which is the best distance function, which is the best way of representing the data and which is the effect of applying thresholding. In this paper, we present a comprehensive study using 51 distance metrics, 4 alternatives to represent the raw data (2 of them proposed by us), a thresholding based on the RSS values and the public UJIIndoorLoc database. The results shown in this paper demonstrate that researchers and developers should take into account the conclusions arisen in this work in order to improve the accuracy of their systems. The IPSs based on k-NN are improved by just selecting the appropriate configuration (mainly distance function and data representation). In the best case, 13-NN with Sorensen distance and the powed data representation, the error in determining the place (building and floor) has been reduced in more than a 50% and the positioning accuracy has been increased in 1.7 m with respect to the 1-NN with Euclidean distance and raw data commonly used in the literature. Moreover, our experiments also demonstrate that thresholding should not be applied in multi-building and multi-floor environments.

Kinetic Distance and Kinetic Maps from Molecular Dynamics Simulation

Abstract: Characterizing macromolecular kinetics from molecular dynamics (MD) simulations requires a distance metric that can distinguish slowly interconverting states. Here, we build upon diffusion map theory and define a kinetic distance metric for irreducible Markov processes that quantifies how slowly molecular conformations interconvert. The kinetic distance can be computed given a model that approximates the eigenvalues and eigenvectors (reaction coordinates) of the MD Markov operator. Here, we employ the time-lagged independent component analysis (TICA). The TICA components can be scaled to provide a kinetic map in which the Euclidean distance corresponds to the kinetic distance. As a result, the question of how many TICA dimensions should be kept in a dimensionality reduction approach becomes obsolete, and one parameter less needs to be specified in the kinetic model construction. We demonstrate the approach using TICA and Markov state model (MSM) analyses for illustrative models, protein conformation dynamics in bovine pancreatic trypsin inhibitor and protein-inhibitor association in trypsin and benzamidine. We find that the total kinetic variance (TKV) is an excellent indicator of model quality and can be used to rank different input feature sets.

Automatic Liver Segmentation Based on Shape Constraints and Deformable Graph Cut in CT Images

Abstract: Liver segmentation is still a challenging task in medical image processing area due to the complexity of the liver’s anatomy, low contrast with adjacent organs, and presence of pathologies. This investigation was used to develop and validate an automated method to segment livers in CT images. The proposed framework consists of three steps: 1) preprocessing; 2) initialization; and 3) segmentation. In the first step, a statistical shape model is constructed based on the principal component analysis and the input image is smoothed using curvature anisotropic diffusion filtering. In the second step, the mean shape model is moved using thresholding and Euclidean distance transformation to obtain a coarse position in a test image, and then the initial mesh is locally and iteratively deformed to the coarse boundary, which is constrained to stay close to a subspace of shapes describing the anatomical variability. Finally, in order to accurately detect the liver surface, deformable graph cut was proposed, which effectively integrates the properties and inter-relationship of the input images and initialized surface. The proposed method was evaluated on 50 CT scan images, which are publicly available in two databases Sliver07 and 3Dircadb. The experimental results showed that the proposed method was effective and accurate for detection of the liver surface.

Deep learning-based tree classification using mobile LiDAR data

Abstract: Our work addresses the problem of extracting and classifying tree species from mobile LiDAR data. The work includes tree preprocessing and tree classification. In tree preprocessing, voxel-based upward-growing filtering is proposed to remove ground points from the mobile LiDAR data, followed by a tree segmentation that extracts individual trees via Euclidean distance clustering and voxel-based normalized cut segmentation. In tree classification, first, a waveform representation is developed to model geometric structures of trees. Then, deep learning techniques are used to generate high-level feature abstractions of the trees’ waveform representations. Quantitative analysis shows that our algorithm achieves an overall accuracy of 86.1% and a kappa coefficient of 0.8 in classifying urban tree species using mobile LiDAR data. Comparative experiments demonstrate that the uses of waveform representation and deep Boltzmann machines contribute to the improvement of classification accuracies of tree species.

Learning Hierarchical Features for Automated Extraction of Road Markings From 3-D Mobile LiDAR Point Clouds

Abstract: This paper presents a novel method for automated extraction of road markings directly from three dimensional (3-D) point clouds acquired by a mobile light detection and ranging (LiDAR) system. First, road surface points are segmented from a raw point cloud using a curb-based approach. Then, road markings are directly extracted from road surface points through multisegment thresholding and spatial density filtering. Finally, seven specific types of road markings are further accurately delineated through a combination of Euclidean distance clustering, voxel-based normalized cut segmentation, large-size marking classification based on trajectory and curb-lines, and small-size marking classification based on deep learning, and principal component analysis (PCA). Quantitative evaluations indicate that the proposed method achieves an average completeness, correctness, and F-measure of 0.93, 0.92, and 0.93, respectively. Comparative studies also demonstrate that the proposed method achieves better performance and accuracy than those of the two existing methods.

An improved WiFi indoor positioning algorithm by weighted fusion

Abstract: The rapid development of mobile Internet has offered the opportunity for WiFi indoor positioning to come under the spotlight due to its low cost. However, nowadays the accuracy of WiFi indoor positioning cannot meet the demands of practical applications. To solve this problem, this paper proposes an improved WiFi indoor positioning algorithm by weighted fusion. The proposed algorithm is based on traditional location fingerprinting algorithms and consists of two stages: the offline acquisition and the online positioning. The offline acquisition process selects optimal parameters to complete the signal acquisition, and it forms a database of fingerprints by error classification and handling. To further improve the accuracy of positioning, the online positioning process first uses a pre-match method to select the candidate fingerprints to shorten the positioning time. After that, it uses the improved Euclidean distance and the improved joint probability to calculate two intermediate results, and further calculates the final result from these two intermediate results by weighted fusion. The improved Euclidean distance introduces the standard deviation of WiFi signal strength to smooth the WiFi signal fluctuation and the improved joint probability introduces the logarithmic calculation to reduce the difference between probability values. Comparing the proposed algorithm, the Euclidean distance based WKNN algorithm and the joint probability algorithm, the experimental results indicate that the proposed algorithm has higher positioning accuracy.

Extremes on river networks

Abstract: Max-stable processes are the natural extension of the classical extreme-value distributions to the functional setting, and they are increasingly widely used to estimate probabilities of complex extreme events. In this paper we broaden them from the usual situation in which dependence varies according to functions of Euclidean distance to situations in which extreme river discharges at two locations on a river network may be dependent because the locations are flow-connected or because of common meteorological events. In the former case dependence depends on river distance, and in the second it depends on the hydrological distance between the locations, either of which may be very different from their Euclidean distance. Inference for the model parameters is performed using a multivariate threshold likelihood, which is shown by simulation to work well. The ideas are illustrated with data from the upper Danube basin.

Modelling non-Euclidean movement and landscape connectivity in highly structured ecological networks

Abstract: Summary Movement is influenced by landscape structure, configuration and geometry, but measuring distance as perceived by animals poses technical and logistical challenges. Instead, movement is typically measured using Euclidean distance, irrespective of location or landscape structure, or is based on arbitrary cost surfaces. A recently proposed extension of spatial capture-recapture (SCR) models resolves this issue using spatial encounter histories of individuals to calculate least-cost paths (ecological distance: Ecology, 94, 2013, 287) thereby relaxing the Euclidean assumption. We evaluate the consequences of not accounting for movement heterogeneity when estimating abundance in highly structured landscapes, and demonstrate the value of this approach for estimating biologically realistic space-use patterns and landscape connectivity. We simulated SCR data in a riparian habitat network, using the ecological distance model under a range of scenarios where space-use in and around the landscape was increasingly associated with water (i.e. increasingly less Euclidean). To assess the influence of miscalculating distance on estimates of population size, we compared the results from the ecological and Euclidean distance based models. We then demonstrate that the ecological distance model can be used to estimate home range geometry when space use is not symmetrical. Finally, we provide a method for calculating landscape connectivity based on modelled species-landscape interactions generated from capture-recapture data. Using ecological distance always produced unbiased estimates of abundance. Explicitly modelling the strength of the species-landscape interaction provided a direct measure of landscape connectivity and better characterised true home range geometry. Abundance under the Euclidean distance model was increasingly (negatively) biased as space use was more strongly associated with water and, because home ranges are assumed to be symmetrical, produced poor characterisations of home range geometry and no information about landscape connectivity. The ecological distance SCR model uses spatially indexed capture-recapture data to estimate how activity patterns are influenced by landscape structure. As well as reducing bias in estimates of abundance, this approach provides biologically realistic representations of home range geometry, and direct information about species-landscape interactions. The incorporation of both structural (landscape) and functional (movement) components of connectivity provides a direct measure of species-specific landscape connectivity.

Accelerating Dynamic Time Warping Clustering with a Novel Admissible Pruning Strategy

Abstract: Clustering time series is a useful operation in its own right, and an important subroutine in many higher-level data mining analyses, including data editing for classifiers, summarization, and outlier detection. While it has been noted that the general superiority of Dynamic Time Warping (DTW) over Euclidean Distance for similarity search diminishes as we consider ever larger datasets, as we shall show, the same is not true for clustering. Thus, clustering time series under DTW remains a computationally challenging task. In this work, we address this lethargy in two ways. We propose a novel pruning strategy that exploits both upper and lower bounds to prune off a large fraction of the expensive distance calculations. This pruning strategy is admissible; giving us provably identical results to the brute force algorithm, but is at least an order of magnitude faster. For datasets where even this level of speedup is inadequate, we show that we can use a simple heuristic to order the unavoidable calculations in a most-useful-first ordering, thus casting the clustering as an anytime algorithm. We demonstrate the utility of our ideas with both single and multidimensional case studies in the domains of astronomy, speech physiology, medicine and entomology.

Class-Dependent Sparse Representation Classifier for Robust Hyperspectral Image Classification

Abstract: Sparse representation of signals for classification is an active research area. Signals can potentially have a compact representation as a linear combination of atoms in an overcomplete dictionary. Based on this observation, a sparse-representation-based classification (SRC) has been proposed for robust face recognition and has gained popularity for various classification tasks. It relies on the underlying assumption that a test sample can be linearly represented by a small number of training samples from the same class. However, SRC implementations ignore the Euclidean distance relationship between samples when learning the sparse representation of a test sample in the given dictionary. To overcome this drawback, we propose an alternate formulation that we assert is better suited for classification tasks. Specifically, class-dependent sparse representation classifier (cdSRC) is proposed for hyperspectral image classification, which effectively combines the ideas of SRC and $K$ -nearest neighbor classifier in a classwise manner to exploit both correlation and Euclidean distance relationship between test and training samples. Toward this goal, a unified class membership function is developed, which utilizes residual and Euclidean distance information simultaneously. Experimental results based on several real-world hyperspectral data sets have shown that cdSRC not only dramatically increases the classification performance over SRC but also outperforms other popular classifiers, such as support vector machine.

Inverse Sparse Tracker With a Locally Weighted Distance Metric

Abstract: Sparse representation has been recently extensively studied for visual tracking and generally facilitates more accurate tracking results than classic methods. In this paper, we propose a sparsity-based tracking algorithm that is featured with two components: 1) an inverse sparse representation formulation and 2) a locally weighted distance metric. In the inverse sparse representation formulation, the target template is reconstructed with particles, which enables the tracker to compute the weights of all particles by solving only one ${\ell _{1}}$ optimization problem and thereby provides a quite efficient model. This is in direct contrast to most previous sparse trackers that entail solving one optimization problem for each particle. However, we notice that this formulation with normal Euclidean distance metric is sensitive to partial noise like occlusion and illumination changes. To this end, we design a locally weighted distance metric to replace the Euclidean one. Similar ideas of using local features appear in other works, but only being supported by popular assumptions like local models could handle partial noise better than holistic models, without any solid theoretical analysis. In this paper, we attempt to explicitly explain it from a mathematical view. On that basis, we further propose a method to assign local weights by exploiting the temporal and spatial continuity. In the proposed method, appearance changes caused by partial occlusion and shape deformation are carefully considered, thereby facilitating accurate similarity measurement and model update. The experimental validation is conducted from two aspects: 1) self validation on key components and 2) comparison with other state-of-the-art algorithms. Results over 15 challenging sequences show that the proposed tracking algorithm performs favorably against the existing sparsity-based trackers and the other state-of-the-art methods.

Segmentation of Brain Tissues from Magnetic Resonance Images Using Adaptively Regularized Kernel-Based Fuzzy C-Means Clustering

Abstract: An adaptively regularized kernel-based fuzzy -means clustering framework is proposed for segmentation of brain magnetic resonance images. The framework can be in the form of three algorithms for the local average grayscale being replaced by the grayscale of the average filter, median filter, and devised weighted images, respectively. The algorithms employ the heterogeneity of grayscales in the neighborhood and exploit this measure for local contextual information and replace the standard Euclidean distance with Gaussian radial basis kernel functions. The main advantages are adaptiveness to local context, enhanced robustness to preserve image details, independence of clustering parameters, and decreased computational costs. The algorithms have been validated against both synthetic and clinical magnetic resonance images with different types and levels of noises and compared with 6 recent soft clustering algorithms. Experimental results show that the proposed algorithms are superior in preserving image details and segmentation accuracy while maintaining a low computational complexity.

Learning Descriptors for Object Recognition and 3D Pose Estimation

Abstract: Detecting poorly textured objects and estimating their 3D pose reliably is still a very challenging problem. We introduce a simple but powerful approach to computing descriptors for object views that efficiently capture both the object identity and 3D pose. By contrast with previous manifold-based approaches, we can rely on the Euclidean distance to evaluate the similarity between descriptors, and therefore use scalable Nearest Neighbor search methods to efficiently handle a large number of objects under a large range of poses. To achieve this, we train a Convolutional Neural Network to compute these descriptors by enforcing simple similarity and dissimilarity constraints between the descriptors. We show that our constraints nicely untangle the images from different objects and different views into clusters that are not only well-separated but also structured as the corresponding sets of poses: The Euclidean distance between descriptors is large when the descriptors are from different objects, and directly related to the distance between the poses when the descriptors are from the same object. These important properties allow us to outperform state-of-the-art object views representations on challenging RGB and RGB-D data.

Generalized Precoder Design Formulation and Iterative Algorithm for Spatial Modulation in MIMO Systems With CSIT

Abstract: In this paper, we propose two generalized precoder designs to enhance the bit error rates for the general category of spatial modulation (SM) in multiple-input multiple-output (MIMO) systems with channel state information at the transmitter (CSIT). We investigate typical SM-MIMO systems and propose two optimization formulations for designing precoders. Our design rationale for the first formulation is to maximize the minimum Euclidean distance among codewords; for the second formulation, it is to minimize the total signal power for the lower-bounded Euclidean distances among codewords. Since both formulations are non-convex and their optimal solutions are generally intractable, we propose an algorithm that acquires effective solutions by iteratively solving the alternative convex problem linearized and approximated from the original non-convex problem. Discussions on complexity analysis, performance comparisons, design challenges, and robustness in imperfect CSIT are then provided. By generalizing the design formulations, the proposed precoder designs can be extended to generalized SM, which completes the investigation for virtually all SM-type systems. Simulation results show that the proposed designs improve the performance of SM-/GSM-MIMO systems and outperform existing precoding methods with a potentially higher complexity cost.

Hesitant fuzzy agglomerative hierarchical clustering algorithms

Abstract: Recently, hesitant fuzzy sets (HFSs) have been studied by many researchers as a powerful tool to describe and deal with uncertain data, but relatively, very few studies focus on the clustering analysis of HFSs. In this paper, we propose a novel hesitant fuzzy agglomerative hierarchical clustering algorithm for HFSs. The algorithm considers each of the given HFSs as a unique cluster in the first stage, and then compares each pair of the HFSs by utilising the weighted Hamming distance or the weighted Euclidean distance. The two clusters with smaller distance are jointed. The procedure is then repeated time and again until the desirable number of clusters is achieved. Moreover, we extend the algorithm to cluster the interval-valued hesitant fuzzy sets, and finally illustrate the effectiveness of our clustering algorithms by experimental results.

Modified distance calculation in generational distance and inverted generational distance

Abstract: In this paper, we propose the use of modified distance calculation in generational distance (GD) and inverted generational distance (IGD). These performance indicators evaluate the quality of an obtained solution set in comparison with a pre-specified reference point set. Both indicators are based on the distance between a solution and a reference point. The Euclidean distance in an objective space is usually used for distance calculation. Our idea is to take into account the dominance relation between a solution and a reference point when we calculate their distance. If a solution is dominated by a reference point, the Euclidean distance is used for their distance calculation with no modification. However, if they are non-dominated with each other, we calculate the minimum distance from the reference point to the dominated region by the solution. This distance can be viewed as an amount of the inferiority of the solution (i.e., the insufficiency of its objective values) in comparison with the reference point. We demonstrate using simple examples that some Pareto non-compliant results of GD and IGD are resolved by the modified distance calculation. We also show that IGD with the modified distance calculation is weakly Pareto compliant whereas the original IGD is Pareto non-compliant.

Extremes on river networks

Abstract: Max-stable processes are the natural extension of the classical extreme-value distributions to the functional setting, and they are increasingly widely used to estimate probabilities of complex extreme events. In this paper we broaden them from the usual situation in which dependence varies according to functions of Euclidean distance to situations in which extreme river discharges at two locations on a river network may be dependent because the locations are flow-connected or because of common meteorological events. In the former case dependence depends on river distance, and in the second it depends on the hydrological distance between the locations, either of which may be very different from their Euclidean distance. Inference for the model parameters is performed using a multivariate threshold likelihood, which is shown by simulation to work well. The ideas are illustrated with data from the upper Danube basin.

Automated interpretation of 3D laserscanned point clouds for plant organ segmentation

Abstract: Plant organ segmentation from 3D point clouds is a relevant task for plant phenotyping and plant growth observation. Automated solutions are required to increase the efficiency of recent high-throughput plant phenotyping pipelines. However, plant geometrical properties vary with time, among observation scales and different plant types. The main objective of the present research is to develop a fully automated, fast and reliable data driven approach for plant organ segmentation. The automated segmentation of plant organs using unsupervised, clustering methods is crucial in cases where the goal is to get fast insights into the data or no labeled data is available or costly to achieve. For this we propose and compare data driven approaches that are easy-to-realize and make the use of standard algorithms possible. Since normalized histograms, acquired from 3D point clouds, can be seen as samples from a probability simplex, we propose to map the data from the simplex space into Euclidean space using Aitchisons log ratio transformation, or into the positive quadrant of the unit sphere using square root transformation. This, in turn, paves the way to a wide range of commonly used analysis techniques that are based on measuring the similarities between data points using Euclidean distance. We investigate the performance of the resulting approaches in the practical context of grouping 3D point clouds and demonstrate empirically that they lead to clustering results with high accuracy for monocotyledonous and dicotyledonous plant species with diverse shoot architecture. An automated segmentation of 3D point clouds is demonstrated in the present work. Within seconds first insights into plant data can be deviated – even from non-labelled data. This approach is applicable to different plant species with high accuracy. The analysis cascade can be implemented in future high-throughput phenotyping scenarios and will support the evaluation of the performance of different plant genotypes exposed to stress or in different environmental scenarios.

Detection and classification of faults in transmission lines using the maximum wavelet singular value and Euclidean norm

Abstract: In this study, a novel algorithm for detecting and classifying faults in high-voltage transmission lines is proposed. The algorithm is based on the discrete wavelet transform (DWT) and singular value decomposition (SVD). The DWT is used for extracting the currents’ high-frequency components under fault conditions. Signals under each fault condition are scaled in frequency, in order to build a wavelet matrix. By means of the SVD, the maximum singular value is calculated and employed in this proposal. The attained results exhibit that the maximum singular value represents a good indicator for the issue. This novel approach for detecting and classifying faults in power systems is called maximum wavelet singular value. Phase-to-ground, two-phase to ground, and three-phase faults’ simulations under different fault impedances are carried out by DIgSILENT Power Factory. The analysed fault conditions are evaluated demonstrating that the proposal reduces the computational burden and the time detection.

Distance and similarity measures for dual hesitant fuzzy sets and their applications in pattern recognition

Abstract: Dual hesitant fuzzy set (DHFS) is a very comprehensive set which includes fuzzy set, intuition fuzzy set and hesitant fuzzy set as its special cases. Distance and similarity measures play great roles in many areas, such as decision making, pattern recognition, etc. In this paper, we introduce some distance and similarity measures for DHFSs based on Hamming distance, Euclidean distance and Hausdorff distance. Two examples are used to illustrate these distance and similarity measures and their applications in pattern recognition. Finally, the comparisons among DHFSs and the corresponding IVIFSs and HFSs are made in detail by utilizing the developed distance measures.

Cosine similarity based fingerprinting algorithm in WLAN indoor positioning against device diversity

Abstract: The fingerprinting location method is commonly used in WLAN indoor positioning system. Device diversity (DD) which leads to Received Signal Strength (RSS) value difference between the users' device and the reference device is becoming an increasingly important factor impacting the positioning accuracy. Thus, the device diversity is a key problem gained more and more attention in fingerprinting location system recently, which introduces many uncertainties to the positioning result. Traditionally, the Euclidean distance is widely adopted in fingerprinting method. However, when encountering with RSS value difference caused by device diversity, the localization performance is degraded significantly. Due to this problem, our paper proposes a method employing cosine similarity instead of the Euclidean distance to improve the positioning accuracy about 13.15% higher within 2 meters when device diversity exists in the positioning. The experiment results show that the proposed method presents a good performance without the expenses of computation caused by calibration method which is employed in many previous works.