Above are papers related to the following paper: [Paper_ID] Paper #628764. 	[Title] Approximation with neural networks: Between local and global approximation [Abstract] We investigate neural network based approximation methods. These methods depend on the locality of the basis functions. After discussing local and global basis functions, we propose a a multi-resolution hierarchical method. The various resolutions are stored at various levels in a tree. At the root of the tree, a global approximation is kept; the leafs store the learning samples themselves. Intermediate nodes store intermediate representations. In order to find an optimal partitioning of the input space, self-organising maps (SOM's) are used. The proposed method has implementational problems reminiscent of those encountered in many-particle simulations. We will investigate the parallel implementation of this method, using parallel hierarchical meth ods for many-particle simulations as a starting point. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1112929. 	[Title] Combining Linear Discriminant Functions with Neural Networks for Supervised Learning [Abstract] A novel supervised learning method is presented by combining linear discriminant functions with neural networks. The proposed method results in a tree-structured hybrid architecture. Due to constructive learning, the binary tree hierarchical architecture is automatically generated by a controlled growing process for a specific supervised learning task. Unlike the classic decision tree, the linear discriminant functions are merely employed in the intermediate level of the tree for heuristically partitioning a large and complicated task into several smaller and simpler subtasks in the proposed method. These subtasks are dealt with by component neural networks at the leaves of the tree accordingly. For constructive learning, growing and credit-assignment algorithms are developed to serve for the hybrid architecture. The proposed architecture provides an efficient way to apply existing neural networks (e.g. multi-layered perceptron) for solving a large scale problem. We have already applied the proposed method to a universal approximation problem and several benchmark classification problems in order to evaluate its performance. Simulation results have shown that the proposed method yields better results and faster training in comparison with the multi-layered perceptron. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #815073. 	[Title] Two Constructive Methods for Designing Compact Feedforward Networks of Threshold Units [Abstract] We propose two algorithms for constructing and training compact feedforward networks of linear threshold units. The Shift procedure constructs networks with a single hidden layer while the PTI constructs multilayered networks. The resulting networks are guaranteed to perform any given task with binary or real-valued inputs. The various experimental results reported for tasks with binary and real inputs indicate that our methods compare favorably with alternative procedures deriving from similar strategies, both in terms of size of the resulting networks and of their generalization properties. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #19621. 	[Title] References "Using Neural Networks to Identify Jets", Kohonen, "Self Organized Formation of Topologically Correct Feature [Abstract] 2] D. E. Rumelhart, G. E. Hinton and R. J. Williams, "Learning Internal Representations by Error Propagation", in D. E. Rumelhart and J. L. McClelland (eds.) Parallel Distributed Processing: Explorations in the Microstructure of Cognition (Vol. 1), MIT Press (1986). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1130568. 	[Title] Visual Tracking of Moving Objects using a Neural Network Controller [Abstract] For a target tracking task, the hand-held camera of the anthropomorphic OSCAR-robot manipulator has to track an object which moves arbitrarily on a table. The desired camera-joint mapping is approximated by a feedforward neural network. Through the use of time derivatives of the position of the object and of the manipulator, the controller can inherently predict the next position of the moving target object. In this paper several `anticipative' controllers are described, and successfully applied to track a moving object. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #950986. 	[Title] The locally linear Nested Network for robot manipulation [Abstract] We present a method for accurate representation of high-dimensional unknown functions from random samples drawn from its input space. The method builds representations of the function by recursively splitting the input space in smaller subspaces, while in each of these subspaces a linear approximation is computed. The representations of the function at all levels (i.e., depths in the tree) are retained during the learning process, such that a good generalisation is available as well as more accurate representations in some subareas. Therefore, fast and accurate learning are combined in this method. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #205196. 	[Title] Constructive Training Methods for Feedforward Neural Networks with Binary Weights [Abstract] DIMACS Technical Report 95-35 August 1995 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #85324. 	[Title] The optimal number of learning samples and hidden units in function approximation with a feedforward network [Abstract] This paper presents a methodology to estimate the optimal number of learning samples and the number of hidden units needed to obtain a desired accuracy of a function approximation by a feedforward network. The representation error and the generalization error, components of the total approximation error are analyzed and the approximation accuracy of a feedforward network is investigated as a function of the number of hidden units and the number of learning samples. Based on the asymptotical behavior of the approximation error, an asymptotical model of the error function (AMEF) is introduced of which the parameters can be determined experimentally. An alternative model of the error function, which include theoretical results about general bounds of approximation, is also analyzed. In combination with knowledge about the computational complexity of the learning rule an optimal learning set size and number of hidden units can be found resulting in a minimum computation time for a given desired precision of the approximation. This approach was applied to optimize the learning of the camera-robot mapping of a visually guided robot arm and a complex logarithm function approximation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #628751. 	[Title] NESTED NETWORKS FOR ROBOT CONTROL [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #815096. 	[Title] Maximizing the Robustness of a Linear Threshold Classifier with Discrete Weights [Abstract] Quantization of the parameters of a Perceptron is a central problem in hardware implementation of neural networks using a numerical technology. An interesting property of neural networks used as classifiers is their ability to provide some robustness on input noise. This paper presents efficient learning algorithms for the maximization of the robustness of a Perceptron and especially designed to tackle the combinatorial problem arising from the discrete weights. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1130586. 	[Title] Predictive Robot Control with Neural Networks [Abstract] Neural controllers are able to position the hand-held camera of the (3DOF) anthropomorphic OSCAR-robot manipulator above an object which is arbitrary placed on a table. The desired camera-joint mapping is approximated by feedforward neural networks. However, if the object is moving, the manipulator lags behind because of the required time to preprocess the visual information and to move the manipulator. Through the use of time derivatives of the position of the object and of the manipulator, the controller can inherently predict the next position of the object. In this paper several `predictive' controllers are proposed, and successfully applied to track a moving object. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #628888. 	[Title] Using Many-Particle Decomposition to get a Parallel Self-Organising Map [Abstract] We propose a method for decreasing the computational complexity of self-organising maps. The method uses a partitioning of the neurons into disjoint clusters. Teaching of the neurons occurs on a cluster-basis instead of on a neuron-basis. For teaching an N-neuron network with N 0 samples, the computational complexity decreases from O(N 0 N) to O(N 0 log N). Furthermore, we introduce a measure for the amount of order in a self-organising map, and show that the introduced algorithm behaves as well as the original algorithm. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #628766. 	[Title] Orthogonal incremental learning of a feedforward network [Abstract] Orthogonal incremental learning (OIL) is a new approach of incremental training for a feedforward network with a single hidden layer. OIL is based on the idea to describe the output weights (but not the hidden nodes) as a set of orthogonal basis functions. Hidden nodes are treated as the orthogonal representation of the network in the output weights domain. We proved that a separate training of hidden nodes does not conflict with previously optimized nodes and is described by a special relationship orthogonal backpropagation (OBP) rule. An advantage of OIL over existing algorithms is extremely fast learning. This approach can be also easily extended to build-up incrementally an arbitrary function as a linear composition of adjustable functions which are not necessarily orthogonal. OIL has been tested on `two-spirals' and `Net Talk' benchmark problems. Please summarise all the given information.

Paper #628764 has the title `Approximation with neural networks: Between local and global approximation  
` and the abstract `We investigate neural network based approximation methods. These methods depend on the locality of the basis functions. After discussing local and global basis functions, we propose a a multi-resolution hierarchical method. The various resolutions are stored at various levels in a tree. At the root of the tree, a global approximation is kept; the leafs store the learning samples themselves. Intermediate nodes store intermediate representations. In order to find an optimal partitioning of the input space, self-organising maps (SOM's) are used. The proposed method has implementational problems reminiscent of those encountered in many-particle simulations. We will investigate the parallel implementation of this method, using parallel hierarchical meth ods for many-particle simulations as a starting point.
`.
Question: Which category should Paper #628764 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #628764 has the title `Approximation with neural networks: Between local and global approximation  
` and the abstract `We investigate neural network based approximation methods. These methods depend on the locality of the basis functions. After discussing local and global basis functions, we propose a a multi-resolution hierarchical method. The various resolutions are stored at various levels in a tree. At the root of the tree, a global approximation is kept; the leafs store the learning samples themselves. Intermediate nodes store intermediate representations. In order to find an optimal partitioning of the input space, self-organising maps (SOM's) are used. The proposed method has implementational problems reminiscent of those encountered in many-particle simulations. We will investigate the parallel implementation of this method, using parallel hierarchical meth ods for many-particle simulations as a starting point.
`.
Question: Which category should Paper #628764 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks