Nearest-neighbor Graph Research Articles

On the spatial distribution of buildings for map generalization

ABSTRACTInformation on spatial distribution of buildings must be explored as part of the process of map generalization. A new approach is proposed in this article, which combines building classification and clustering to enable the detection of class differences within a pattern, as well as patterns within a class. To do this, an analysis of existing parameters describing building characteristics is performed via principal component analysis (PCA), and four major parameters (i.e. convex hull area, IPQ compactness, number of edges, and smallest minimum bounding rectangle orientation) are selected for further classification based on similarities between building characteristics. A building clustering method based on minimum spanning tree (MST) considering rivers and roads is then applied. Theory and experiments show that use of a relative neighbor graph (RNG) is more effective in detecting linear building patterns than either a nearest neighbor graph (NNG), an MST, or a Gabriel graph (GssG). Building classification and clustering are therefore conducted separately using experimental data extracted from OpenStreetMap (OSM), and linear patterns are then recognized within resultant clusters. Experimental results show that the approach proposed in this article is both reasonable and efficient for mining information on the spatial distribution of buildings for map generalization.

Orthogonal sparse linear discriminant analysis

ABSTRACTLinear discriminant analysis (LDA) is a linear feature extraction approach, and it has received much attention. On the basis of LDA, researchers have done a lot of research work on it, and many variant versions of LDA were proposed. However, the inherent problem of LDA cannot be solved very well by the variant methods. The major disadvantages of the classical LDA are as follows. First, it is sensitive to outliers and noises. Second, only the global discriminant structure is preserved, while the local discriminant information is ignored. In this paper, we present a new orthogonal sparse linear discriminant analysis (OSLDA) algorithm. The k nearest neighbour graph is first constructed to preserve the locality discriminant information of sample points. Then, L2,1-norm constraint on the projection matrix is used to act as loss function, which can make the proposed method robust to outliers in data points. Extensive experiments have been performed on several standard public image databases, and the experiment results demonstrate the performance of the proposed OSLDA algorithm.

Object Shapes from Regular Curves through Sparse Representations

Robotics coupled with image processing algorithms have led to more advanced control systems in varied applications. Object detection systems are used in multiple places like warehouses where detecting the object faster, makes efficient warehouse management. In this work, an object detection algorithm which uses shape as an object representation is presented. The algorithm uses semi-local contour grouping which is based on gradient maps generated from G-Let filters. The algorithm offers a computationally simpler solution as the original gradient map is reduced to a sparse representation using different thresholding techniques. The sparse representation of the object is modeled as a neighbor graph and the shape is constructed using alpha-hull of the nearest neighbor graph. The construction of a gradient map and working with its local curvatures simplifies the shape detection problem, from building hierarchical structures of local-to-global contour relationships to nearest neighbor calculations on a graph and fixing their boundary.

A novel clustering method to identify cell types from single cell transcriptional profiles

With the advancement of the high throughput single cell techniques, transcriptomics data generation at the single cell level becomes very easy. Analysis of this single cell expression values can reveal lots of unprecedented information about complex cellular heterogeneity and tissue composition. To date, different statistical methods are applied to analyze expression data at the cellular level, but there is still pretty much scope for the development of new bioinformatics tools. In this article, a graph theoretic clustering algorithm is proposed to identify cellular states from single cell gene expression data. The proposed algorithm first generates a shared nearest neighbor graph from the single cell RNA-seq dataset and then applies minimum spanning tree based clustering method to cluster the graph nodes. To compare our proposed algorithm’s performance with other unsupervised clustering methods, we used three real scRNA-seq datasets (human cancer cells, human embryonic cells and mouse embryonic cells). From the comparison result, it is evident that the proposed algorithm outperforms other standard single cell analysis methods.

Using NearestGraph QoS Prediction Method for Service Recommendation in the Cloud

With the advent of the mobile network, the fusion of cloud computing and fog computing is becoming feasible to promise lower latency and short‐fat connection. However, there are a lot of redundant cloud‐aware services with identical functionalities but a different quality of service (QoS) in the fog cloud environment. In fact, since QoS information is stored in distributed fog servers rather than remote cloud, it is hard for individuals to make recommendation and selection with sparse QoS information. Collaborative filtering is an important method for the sparsity problems and has been widely adopted on the prediction of missing QoS values. Focusing on the fact that existing researchers often ignore the QoS fluctuation in a wide range in the fog cloud environment, a novel neighbor‐based QoS prediction method is proposed for service recommendation, in which a concept and calculation method is put forward to describe the stable status of services and users with quantifiable QoS values, and a NearestGraph algorithm is further designed to recognize stable or unstable candidate along with their popularity by a nearest neighbor graph structure which can help to make missing QoS values prediction in a certain order to improve final prediction accuracy. Experimental results confirm that the proposed method is effective in predicting unknown QoS values in terms of service recommendation accuracy and efficiency.

Distributed Information Retrieval Based On Metaheuristic Search and Query Expansion

Distributed information retrieval DIR is a model enables a user to access many searchable databases reside in different locations. DIR is more complex than the centralized information retrieval IR . It requires addressing two significant additional problems that are the resource selection and the results merging. Many techniques for addressing the two problems have been published in the literature. However they still have a negative impact on retrieving quality and response time. This paper aims to improve the DIR efficiency through using a meta heuristic algorithm and improving the result quality through a query expansion. The algorithm has been strengthened using the nearest neighbor graph in order to improve the search performance.

Parallel cosine nearest neighbor graph construction

The nearest neighbor graph is an important structure in many data mining methods for clustering, advertising, recommender systems, and outlier detection. Constructing the graph requires computing up to n2 similarities for a set of n objects. This high complexity has led researchers to seek approximate methods, which find many but not all of the nearest neighbors. In contrast, we leverage shared memory parallelism and recent advances in similarity joins to solve the problem exactly. Our method considers all pairs of potential neighbors but quickly filters pairs that could not be a part of the nearest neighbor graph, based on similarity upper bound estimates. The filtering is data dependent and not easily predicted, which poses load balance challenges in parallel execution. We evaluated our methods on several real-world datasets and found they work up to two orders of magnitude faster than existing methods, display linear strong scaling characteristics, and incur less than 1% load imbalance during filtering.

Fast approximate minimum spanning tree based clustering algorithm

Minimum Spanning Tree (MST) based clustering algorithms have been employed successfully to detect clusters of heterogeneous nature. Given a dataset of n random points, most of the MST-based clustering algorithms first generate a complete graph G of the dataset and then construct MST from G. The first step of the algorithm is the major bottleneck which takes O(n2) time. This paper proposes an algorithm namely MST-based clustering on partition-based nearest neighbor graph for reducing the computational overhead. By using a centroid based nearest neighbor rule, the proposed algorithm first generates a sparse Local Neighborhood Graph (LNG) and then the approximate MST is constructed from LNG. We prove that both size and computational time to construct the graph (LNG) is O(n3/2), which is a O(n) factor improvement over the traditional algorithms. The approximate MST is constructed from LNG in O(n3/2lgn) time, which is asymptotically faster than O(n2). Experimental analysis on both synthetic and real datasets demonstrates that the computational time has been reduced significantly by maintaining the quality of clusters obtained from the approximate MST.

Variants of k-regular nearest neighbor graph and their construction

Neighborhood graph and its construction play an important role in numerous problems. Many methods have been proposed to improve the classic k-NN construction based on various criteria. Recently, a new structure named k-regular nearest neighbor (k-RNN) graph has been proposed not only to minimize the sum of edge weights (for keeping the creditable neighborhood relationships), but also to require the node degree to be approximately k. However, the proposed graph construction algorithm is highly heuristic, which neither minimizes the cost (sum of edge weights) in an explicit manner nor formalizes the node degree requirement. In this work we formalize the essential requirements behind k-RNN. Several variants of this formalization will be studied, all being formulated as problems of energy function minimization with efficient greedy solutions. An experimental evaluation is also presented to demonstrate the effectiveness of our methods and superior performance compared to previous works.

Node Attribute-enhanced Community Detection in Complex Networks

Community detection involves grouping the nodes of a network such that nodes in the same community are more densely connected to each other than to the rest of the network. Previous studies have focused mainly on identifying communities in networks using node connectivity. However, each node in a network may be associated with many attributes. Identifying communities in networks combining node attributes has become increasingly popular in recent years. Most existing methods operate on networks with attributes of binary, categorical, or numerical type only. In this study, we introduce kNN-enhance, a simple and flexible community detection approach that uses node attribute enhancement. This approach adds the k Nearest Neighbor (kNN) graph of node attributes to alleviate the sparsity and the noise effect of an original network, thereby strengthening the community structure in the network. We use two testing algorithms, kNN-nearest and kNN-Kmeans, to partition the newly generated, attribute-enhanced graph. Our analyses of synthetic and real world networks have shown that the proposed algorithms achieve better performance compared to existing state-of-the-art algorithms. Further, the algorithms are able to deal with networks containing different combinations of binary, categorical, or numerical attributes and could be easily extended to the analysis of massive networks.

Manifold matching using shortest-path distance and joint neighborhood selection

Matching datasets of multiple modalities has become an important task in data analysis. Existing methods often rely on the embedding and transformation of each single modality without utilizing any correspondence information, which often results in sub-optimal matching performance. In this paper, we propose a nonlinear manifold matching algorithm using shortest-path distance and joint neighborhood selection. Specifically, a joint nearest-neighbor graph is built for all modalities. Then the shortest-path distance within each modality is calculated from the joint neighborhood graph, followed by embedding into and matching in a common low-dimensional Euclidean space. Compared to existing algorithms, our approach exhibits superior performance for matching disparate datasets of multiple modalities.

Deep learning for polyp recognition in wireless capsule endoscopy images.

Wireless capsule endoscopy (WCE) enables physicians to examine the digestive tract without any surgical operations, at the cost of a large volume of images to be analyzed. In the computer-aided diagnosis of WCE images, the main challenge arises from the difficulty of robust characterization of images. This study aims to provide discriminative description of WCE images and assist physicians to recognize polyp images automatically. We propose a novel deep feature learning method, named stacked sparse autoencoder with image manifold constraint (SSAEIM), to recognize polyps in the WCE images. Our SSAEIM differs from the traditional sparse autoencoder (SAE) by introducing an image manifold constraint, which is constructed by a nearest neighbor graph and represents intrinsic structures of images. The image manifold constraint enforces that images within the same category share similar learned features and images in different categories should be kept far away. Thus, the learned features preserve large intervariances and small intravariances among images. The average overall recognition accuracy (ORA) of our method for WCE images is 98.00%. The accuracies for polyps, bubbles, turbid images, and clear images are 98.00%, 99.50%, 99.00%, and 95.50%, respectively. Moreover, the comparison results show that our SSAEIM outperforms existing polyp recognition methods with relative higher ORA. The comprehensive results have demonstrated that the proposed SSAEIM can provide descriptive characterization for WCE images and recognize polyps in a WCE video accurately. This method could be further utilized in the clinical trials to help physicians from the tedious image reading work.

Route Selection for Cabling Considering Cost Minimization and Earthquake Survivability Via a Semi-Supervised Probabilistic Model

This paper focuses on an important and fundamental problem of connecting two points by a cable, subject to a tradeoff between cost and earthquake survivability. In particular, we address the problem of selecting a route for laying a cable under arbitrary topography, based on earthquake data. First, we derive a semi-supervised probability density estimation model for the likelihood of earthquake disaster. Based on this probabilistic model, we generate a nearest neighbor graph. The graph represents each data point with a four-dimensional space formed by the three-dimensional undersea coordinates and the one-dimensional data of earthquake disaster level. It then forms the weight on graph between any positions. The data used in this study are all real data of undersea topography and earthquake information of the Taiwan Strait. As a result, both the undersea topology and the earthquake level can be transferred into a distance for shortest route finding. Finally, Dijkstra's algorithm is used for finding the optimal shortest route for cabling between the two given points on the graph. Extensive simulations based on a synthetic dataset and the Taiwan Strait real-world dataset corroborate the effectiveness of the proposed method.

Estimation of the Number of Endmembers in a Hyperspectral Image via the Hubness Phenomenon

Estimation of the number of endmembers (NOE) is an important first step in many hyperspectral unmixing applications. We present a new method for solving this problem, based on the statistics of the indegree distribution (IDD) of the data nearest neighbor graph. It is known that this IDD shows a high dependence on the intrinsic dimensionality (ID) of the data, and becomes skewed for increasing dimensionality. This effect is known as the hubness phenomenon, and we propose a technique that exploits this effect to derive an estimate for the NOE in a hyperspectral data set. While this number should have a trivial relation with the ID of the data set, this relation is often obscured by the large correlations that exist between endmember spectra and adjacent spectral bands. The proposed technique circumvents this problem by building representative statistics based on simulated hyperspectral data sets, and therefore performs much better than alternative techniques. Also several types of nonlinearly mixed data sets can be treated by the proposed technique, which is illustrated with bilinear data sets.

Functional brain segmentation using inter-subject correlation in fMRI.

The human brain continuously processes massive amounts of rich sensory information. To better understand such highly complex brain processes, modern neuroimaging studies are increasingly utilizing experimental setups that better mimic daily-life situations. A new exploratory data-analysis approach, functional segmentation inter-subject correlation analysis (FuSeISC), was proposed to facilitate the analysis of functional magnetic resonance (fMRI) data sets collected in these experiments. The method provides a new type of functional segmentation of brain areas, not only characterizing areas that display similar processing across subjects but also areas in which processing across subjects is highly variable. FuSeISC was tested using fMRI data sets collected during traditional block-design stimuli (37 subjects) as well as naturalistic auditory narratives (19 subjects). The method identified spatially local and/or bilaterally symmetric clusters in several cortical areas, many of which are known to be processing the types of stimuli used in the experiments. The method is not only useful for spatial exploration of large fMRI data sets obtained using naturalistic stimuli, but also has other potential applications, such as generation of a functional brain atlases including both lower- and higher-order processing areas. Finally, as a part of FuSeISC, a criterion-based sparsification of the shared nearest-neighbor graph was proposed for detecting clusters in noisy data. In the tests with synthetic data, this technique was superior to well-known clustering methods, such as Ward's method, affinity propagation, and K-means ++. Hum Brain Mapp 38:2643-2665, 2017. © 2017 Wiley Periodicals, Inc.

Tree-based localized fuzzy twin support vector clustering with square loss function

Twin support vector machine (TWSVM) is an efficient supervised learning algorithm, proposed for the classification problems. Motivated by its success, we propose Tree-based localized fuzzy twin support vector clustering (Tree-TWSVC). Tree-TWSVC is a novel clustering algorithm that builds the cluster model as a binary tree, where each node comprises of proposed TWSVM-based classifier, termed as localized fuzzy TWSVM (LF-TWSVM). The proposed clustering algorithm Tree-TWSVC has efficient learning time, achieved due to the tree structure and the formulation that leads to solving a series of systems of linear equations. Tree-TWSVC delivers good clustering accuracy because of the square loss function and it uses nearest neighbour graph based initialization method. The proposed algorithm restricts the cluster hyperplane from extending indefinitely by using cluster prototype, which further improves its accuracy. It can efficiently handle large datasets and outperforms other TWSVM-based clustering methods. In this work, we propose two implementations of Tree-TWSVC: Binary Tree-TWSVC and One-against-all Tree-TWSVC. To prove the efficacy of the proposed method, experiments are performed on a number of benchmark UCI datasets. We have also given the application of Tree-TWSVC as an image segmentation tool.

Multi-view learning via multiple graph regularized generative model

Topic models, such as probabilistic latent semantic analysis (PLSA) and latent Dirichlet allocation (LDA), have shown impressive success in many fields. Recently, multi-view learning via probabilistic latent semantic analysis (MVPLSA), is also designed for multi-view topic modeling. These approaches are instances of generative model, whereas they all ignore the manifold structure of data distribution, which is generally useful for preserving the nonlinear information. In this paper, we propose a novel multiple graph regularized generative model to exploit the manifold structure in multiple views. Specifically, we construct a nearest neighbor graph for each view to encode its corresponding manifold information. A multiple graph ensemble regularization framework is proposed to learn the optimal intrinsic manifold. Then, the manifold regularization term is incorporated into a multi-view topic model, resulting in a unified objective function. The solutions are derived based on the Expectation Maximization optimization framework. Experimental results on real-world multi-view data sets demonstrate the effectiveness of our approach.

Percolation and convergence properties of graphs related to minimal spanning forests

Lyons, Peres and Schramm have shown that minimal spanning forests on randomly weighted lattices exhibit a critical geometry in the sense that adding or deleting only a small number of edges results in a radical change of percolation properties. We show that these results can be extended to a Euclidean setting by considering families of stationary super- and subgraphs that approximate the Euclidean minimal spanning forest arbitrarily closely, but whose percolation properties differ decisively from those of the minimal spanning forest. Since these families can be seen as generalizations of the relative neighborhood graph and the nearest-neighbor graph, respectively, our results provide a new perspective on known percolation results from literature. We argue that the rates at which the approximating families converge to the minimal spanning forest are closely related to geometric characteristics of clusters in critical continuum percolation, and we show that convergence occurs at a polynomial rate.

Spectral clustering based on local PCA

We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weigh...

Robust Nonparametric Nearest Neighbor Random Process Clustering

We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their generative models without prior knowledge of the model statistics and the number of generative models. Two algorithms, both using the $L^1$-distance between estimated power spectral densities (PSDs) as a measure of dissimilarity, are analyzed. The first one, termed nearest neighbor process clustering (NNPC), relies on partitioning the nearest neighbor graph of the observations via spectral clustering. The second algorithm, simply referred to as $k$-means (KM), consists of a single $k$-means iteration with farthest point initialization and was considered before in the literature, albeit with a different dissimilarity measure. We prove that both algorithms succeed with high probability in the presence of noise and missing entries, and even when the generative process PSDs overlap significantly, all provided that the observation length is sufficiently large. Our results quantify the tradeoff between the overlap of the generative process PSDs, the observation length, the fraction of missing entries, and the noise variance. Finally, we provide extensive numerical results for synthetic and real data and find that NNPC outperforms state-of-the-art algorithms in human motion sequence clustering.