8287323
A recurrent neural network for solving linear projection equations
Linear projection equations arise in many optimization problems and have important applications in science and engineering. In this paper, we present a recurrent neural network for solving linear projection equations in real time. The proposed neural network has two layers and is amenable to parallel implementation with simple hardware. In the theoretical aspect, we prove that the proposed neural network can converge globally to the solution set of the problem when the matrix involved in the problem is positive semidefinite and can converge exponentially to a unique solution when the matrix is positive definite. In addition, we analyze the stability of the related dynamic system in detail. As an application, we show that the proposed neural network can be used directly to solve linear and convex quadratic programming problems and linear complementary problems with positive semidefinite matrices. The validity and transient behavior of the neural network are demonstrated by using three numerical examples.
492137
Blind source extraction in various ill-conditioned cases
The paper discusses blind source extraction in various ill-conditioned cases based on a simple extraction network model. Extractability is first analyzed for the following ill-conditioned cases: the mixing matrix is square but-singular; the number of sensors is smaller than that of sources; the number of sensors is larger than that of sources, but the column rank of the mixing matrix is deficient; the number of sources is unknown and the column rank of the mixing matrix is deficient. A necessary and sufficient condition for extractability is obtained. A cost function and an unsupervised learning algorithm for the extraction network model are developed. Simulation results are also presented to show the validity of the theoretical results and the performance and characteristics of the learning algorithm.
18656960
A dual neural network for kinematic control of redundant robot manipulators
The inverse kinematics problem in robotics can be formulated as a time-varying quadratic optimization problem. A new recurrent neural network, called the dual network, is presented in this paper. The proposed neural network is composed of a single layer of neurons, and the number of neurons is equal to the dimensionality of the workspace. The proposed dual network is proven to be globally exponentially stable. The proposed dual network is also shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators.
18182406
Recurrent neural networks for minimum infinity-norm kinematic control of redundant manipulators
This paper presents two neural network approaches to minimum infinity-norm solution of the velocity inverse kinematics problem for redundant robots. Three recurrent neural networks are applied for determining a joint velocity vector with its maximum absolute value component being minimal among all possible joint velocity vectors corresponding to the desired end-effector velocity. In each proposed neural network approach, two cooperating recurrent neural networks are used. The first approach employs two Tank-Hopfield networks for linear programming. The second approach employs two two-layer recurrent neural networks for quadratic programming and linear programming, respectively. Both the minimal 2-norm and infinity-norm of joint velocity vector can be obtained from the output of the recurrent neural networks. Simulation results demonstrate that the proposed approaches are effective with the second approach being better in terms of accuracy and optimality.
6599744
A multilayer recurrent neural network for solving continuous-time algebraic Riccati equations
A multilayer recurrent neural network is proposed for solving continuous-time algebraic matrix Riccati equations in real time. The proposed recurrent neural network consists of four bidirectionally connected layers. Each layer consists of an array of neurons. The proposed recurrent neural network is shown to be capable of solving algebraic Riccati equations and synthesizing linear-quadratic control systems in real time. Analytical results on stability of the recurrent neural network and solvability of algebraic Riccati equations by use of the recurrent neural network are discussed. The operating characteristics of the recurrent neural network are also demonstrated through three illustrative examples.
31564513
Packing of Unequal Spheres and Automated Radiosurgical Treatment Planning
We study an optimization problem of packing unequal spheres into a three-dimensional (3D) bounded region in connection with radiosurgical treatment planning. Given an input (R, V, S, L), where R is a 3D bounded region, V a positive integer, S a multiset of spheres, and L a location constraint on spheres, we want to find a packing of R using the minimum number of spheres in S such that the covered volume is at least V; the location constraint L is satisfied; and the number of points on the boundary of R that are touched by spheres is maximized. Such a packing arrangement corresponds to an optimal radiosurgical treatment planning. Finding an optimal solution to the problem, however, is computationally intractable. In particular, we show that this optimization problem and several related problems are NP-hard. Hence, some form of approximations is needed. One approach is to consider a simplified problem under the assumption that spheres of arbitrary (integral) diameters are available with unlimited supply, and there are no location constraints. This approach has met with certain success in medical applications using a dynamic programming algorithm (Bourland and Wu, 1996; Wu, 1996). We propose in this paper an improvement to the algorithm that can greatly reduce its computation cost.
550060
Automatic categorization of figures in scientific documents
Figures are very important non-textual information contained in scientific documents. Current digital libraries do not provide users tools to retrieve documents based on the information available within the figures. We propose architecture for retrieving documents by integrating figures and other information. The initial step in enabling integrated document search is to categorize figures into a set of pre-defined types. We propose several categories of figures based on their functionalities in scholarly articles. We have developed a machine-learning-based approach for automatic categorization of figures. Both global features, such as texture, and part features, such as lines, are utilized in the architecture for discriminating among figure categories. The proposed approach has been evaluated on a testbed document set collected from the CiteSeer scientific literature digital library. Experimental evaluation has demonstrated that our algorithms can produce acceptable results for real- world use. Our tools can be integrated into a scientific-document digital library
21909317
Generating Concept Hierarchies from Text for Intelligence Analysis
It is important to automatically extract key information from sensitive text documents for intelligence analysis. Text documents are usually unstructured and information extraction from texts usually focuses on named entity extraction that is insufficient to reflect the concepts contained within documents. Other research on texts focuses on classifying the whole text into categories. However, texts might be diverse in subjects and suffer from classification accuracy. In this paper, our goal is to present a feasible approach to extract relevant information from texts and organize into concept hierarchies with the help of Web corpora. The approach is designed considering the need of information intelligence and the adaptation to different application domains.
40574141
Finding similar consensus between trees: an algorithm and a distance hierarchy
Abstract The problem of finding this similar consensus (also known as the largest approximately common substructures) of two trees arises in many pattern recognition applications. This paper presents a dynamic programming algorithm to solve the problem based on the distance measure originated from Tanaka and Tanaka. The algorithm runs as fast as the best-known algorithm for comparing two trees using Tanaka's distance measure when the allowed distance between the common substructures is a constant independent of the input trees. In addition, we establish a hierarchy among Tanaka's distance measure and three other edit-based distance measures published in the literature.
123309619
From fragments to salient closed boundaries: an in-depth study
This paper conducts an in-depth study on a classical perceptual-organization problem: finding salient closed boundaries from a set of boundary fragments detected in a noisy image. In this problem, a saliency boundary is formed by identifying and connecting a subset of fragments according to the simple Gestalt laws of closure, continuity, and proximity. Our specific interest is focused on the methods that aim to achieve boundary closure, an important global property of perceptual salient boundaries. In this paper, we analyze and compare three such methods that are developed in recent years: (a) Elder and Zucker's method based on the shortest-path algorithm, (b) Williams and Thornber's method combining the spectral-analysis and the strongly-connected-component algorithms, and (c) Wang, Kubota, and Siskind's method based on ratio-contour algorithm. Both theoretic analysis and experimental study show that, with a unified setting of fragment saliency, Wang, Kubota and Siskind's method more appropriately constrains the search space for the closed boundaries, and usually produces better performance than or at least comparable performance as the other two methods. Particularly, Wang, Kubota, and Siksind's method can always guarantee the boundary closure and simplicity, which may not be always hold in the other two methods. We construct and collect a variety of synthesized and real images for this comparison.