6,502 research outputs found
Differential quadrature method for space-fractional diffusion equations on 2D irregular domains
In mathematical physics, the space-fractional diffusion equations are of
particular interest in the studies of physical phenomena modelled by L\'{e}vy
processes, which are sometimes called super-diffusion equations. In this
article, we develop the differential quadrature (DQ) methods for solving the 2D
space-fractional diffusion equations on irregular domains. The methods in
presence reduce the original equation into a set of ordinary differential
equations (ODEs) by introducing valid DQ formulations to fractional directional
derivatives based on the functional values at scattered nodal points on problem
domain. The required weighted coefficients are calculated by using radial basis
functions (RBFs) as trial functions, and the resultant ODEs are discretized by
the Crank-Nicolson scheme. The main advantages of our methods lie in their
flexibility and applicability to arbitrary domains. A series of illustrated
examples are finally provided to support these points.Comment: 25 pages, 25 figures, 7 table
Unsupervised Feature Selection with Adaptive Structure Learning
The problem of feature selection has raised considerable interests in the
past decade. Traditional unsupervised methods select the features which can
faithfully preserve the intrinsic structures of data, where the intrinsic
structures are estimated using all the input features of data. However, the
estimated intrinsic structures are unreliable/inaccurate when the redundant and
noisy features are not removed. Therefore, we face a dilemma here: one need the
true structures of data to identify the informative features, and one need the
informative features to accurately estimate the true structures of data. To
address this, we propose a unified learning framework which performs structure
learning and feature selection simultaneously. The structures are adaptively
learned from the results of feature selection, and the informative features are
reselected to preserve the refined structures of data. By leveraging the
interactions between these two essential tasks, we are able to capture accurate
structures and select more informative features. Experimental results on many
benchmark data sets demonstrate that the proposed method outperforms many state
of the art unsupervised feature selection methods
A convex formulation for semi-supervised multi-label feature selection
Copyright © 2014, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Explosive growth of multimedia data has brought challenge of how to efficiently browse, retrieve and organize these data. Under this circumstance, different approaches have been proposed to facilitate multimedia analysis. Several semi-supervised feature selection algorithms have been proposed to exploit both labeled and unlabeled data. However, they are implemented based on graphs, such that they cannot handle large-scale datasets. How to conduct semi-supervised feature selection on large-scale datasets has become a challenging research problem. Moreover, existing multi-label feature selection algorithms rely on eigen-decomposition with heavy computational burden, which further prevent current feature selection algorithms from being applied for big data. In this paper, we propose a novel convex semi-supervised multi-label feature selection algorithm, which can be applied to large-scale datasets. We evaluate performance of the proposed algorithm over five benchmark datasets and compare the results with state- of-the-art supervised and semi-supervised feature selection algorithms as well as baseline using all features. The experimental results demonstrate that our proposed algorithm consistently achieve superiors performances
Improved Spectral Clustering via Embedded Label Propagation
Spectral clustering is a key research topic in the field of machine learning and data mining. Most of the existing spectral clustering algorithms are built upon Gaussian Laplacian matrices, which are sensitive to parameters. We propose a novel parameter free, distance consistent Locally Linear Embedding. The proposed distance consistent LLE promises that edges between closer data points have greater weight.Furthermore, we propose a novel improved spectral clustering via embedded label propagation. Our algorithm is built upon two advancements of the state of the art:1) label propagation,which propagates a node\'s labels to neighboring nodes according to their proximity; and 2) manifold learning, which has been widely used in its capacity to leverage the manifold structure of data points. First we perform standard spectral clustering on original data and assign each cluster to k nearest data points. Next, we propagate labels through dense, unlabeled data regions. Extensive experiments with various datasets validate the superiority of the proposed algorithm compared to current state of the art spectral algorithms
Balanced k-Means and Min-Cut Clustering
Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their simplicity and efficacy. The classical k-means algorithm partitions a number of data points into several subsets by iteratively updating the clustering centers and the associated data points. By contrast, a weighted undirected graph is constructed in min-cut algorithms which partition the vertices of the graph into two sets. However, existing clustering algorithms tend to cluster minority of data points into a subset, which shall be avoided when the target dataset is balanced. To achieve more accurate clustering for balanced dataset, we propose to leverage exclusive lasso on k-means and min-cut to regulate the balance degree of the clustering results. By optimizing our objective functions that build atop the exclusive lasso, we can make the clustering result as much balanced as possible. Extensive experiments on several large-scale datasets validate the advantage of the proposed algorithms compared to the state-of-the-art clustering algorithms
A convex formulation for spectral shrunk clustering
Copyright © 2015, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning in the original space. However, the manifold in reduced-dimensional subspace is likely to exhibit altered properties in contrast with the original space. Thus, applying manifold information obtained from the original space to the clustering process in a low-dimensional subspace is prone to inferior performance. Aiming to address this issue, we propose a novel convex algorithm that mines the manifold structure in the low-dimensional subspace. In addition, our unified learning process makes the manifold learning particularly tailored for the clustering. Compared with other related methods, the proposed algorithm results in more structured clustering result. To validate the efficacy of the proposed algorithm, we perform extensive experiments on several benchmark datasets in comparison with some state-of-the-art clustering approaches. The experimental results demonstrate that the proposed algorithm has quite promising clustering performance
Photo-based automatic 3D reconstruction of train accident scenes
Railway accidents place significant demands on the resources of, and support from, railway emergency management departments. Once an accident occurs, an efficient incident rescue plan needs to be delivered as early as possible to minimise the loss of life and property. However, in the railway sector, most relevant departments currently face a challenge in drawing up a rescue scheme effectively and accurately with the insufficient information collected from the scene of a train accident. To assist with the rescue planning, we propose a framework which can rapidly and automatically construct a 3D virtual scene of a train accident by utilising photos of the accident spot. The framework uses a hybrid 3D reconstruction method to extract the position and pose information of the carriages involved in an accident. It adopts a geographic information system and a 3D visualisation engine to model and display the landscapes and buildings at the site of a train accident. In order to assess and validate our prototype, we quantitatively evaluate our main algorithm and demonstrate the usage of our technology with two case studies including a simulated scene with an in-lab setting and a real train derailment scene from on-site pictures. The results of both are accoun table with high accuracy and represent the ability of timely modelling and visualisation of a train accident scene
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