The ability to quickly calculate or query the shortest path distance between nodes on a road network is essential for many real-world applications. However, the traditional graph traversal shortest path algorithm methods, such as Dijkstra and Floyd–Warshall, cannot be extended to large-scale road networks, or the traversal speed on large-scale networks is very slow, which is computational and memory intensive. Therefore, researchers have developed many approximate methods, such as the landmark method and the embedding method, to speed up the processing time of graphs and the shortest path query. This study proposes a new method based on landmarks and embedding technology, and it proposes a multilayer neural network model to solve this problem. On the one hand, we generate distance-preserving embedding for each node, and on the other hand, we predict the shortest path distance between two nodes of a given embedment. Our approach significantly reduces training time costs and is able to approximate the real distance with a relatively low Mean Absolute Error (MAE). The experimental results on a real road network confirm these advantages.
Abstract-In this paper, we introduce a dimensionality reduction method that can be applied to clustering of high dimensional empirical distributions. The proposed approach is based on stabilized information geometrical representation of the feature distributions. The problem of dimensionality reduction on spaces of distribution functions arises in many applications including hyperspectral imaging, document clustering, and classifying flow cytometry data. Our method is a shrinkage regularized version of Fisher information distance, that we call shrinkage FINE (sFINE), which is implemented by Steinian shrinkage estimation of the matrix of Kullback Liebler distances between feature distributions. The proposed method involves computing similarities using shrinkage regularized Fisher information distance between probability density functions (PDFs) of the data features, then applying Laplacian eigenmaps on a derived similarity matrix to accomplish the embedding and perform clustering. The shrinkage regularization controls the trade-off between bias and variance and is especially well-suited for clustering empirical probability distributions of high-dimensional data sets. We also show significant gains in clustering performance on both of the UCI dataset and a spam data set. Finally we demonstrate the superiority of embedding and clustering distributional data using sFINE as compared to other state-of-the-art methods such as non-parametric information clustering, support vector machine (SVM) and sparse K-means.
Traditional plane-based clustering methods measure the cost of within-cluster and between-cluster by quadratic, linear or some other unbounded functions, which may amplify the impact of cost. This letter introduces a ramp cost function into the plane-based clustering to propose a new clustering method, called ramp-based twin support vector clustering (RampTWSVC). RampTWSVC is more robust because of its boundness, and thus it is more easier to find the intrinsic clusters than other planebased clustering methods. The non-convex programming problem in RampTWSVC is solved efficiently through an alternating iteration algorithm, and its local solution can be obtained in a finite number of iterations theoretically. In addition, the nonlinear manifold-based formation of RampTWSVC is also proposed by kernel trick. Experimental results on several benchmark datasets show the better performance of our RampTWSVC compared with other plane-based clustering methods.
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