Szepesva ri Cs, Bala zs L, Lo rincz A. Topology learning solved by extended objects: A neural network model. Neural Computations 1994; 6: 441--448  Home/Search   Document Not in Database   Summary   Related Articles   Check

....function enables the learning of the 3 dimensional geometry of a world, from two of 2 dimensional projections of 3 dimensional extended objects. I. Introduction The system to be described is an application of the artificial neural network architecture we developed for 2 dimensional (2D) images [7]. Here two of 2D projections of 3 dimensional (3D) objects guide the network to wire in the 3D geometry of the external world. The basis of the system is a selforganizing competitive artificial neural network [4] that receives, as inputs, images of the external world. The primary building block of ....

....neuron of largest activity. The stored vector of the winning neuron l is then modified with the help of the update rule: Deltaw l = ff(x Gamma w l ) where ff is the so called feedforward learning parameter; 0 ff 1: In earlier simulations, we presented 2D objects of a 2D space to the network [7]. Input vectors were derived by computing the overlap of the local, extended, randomly positioned objects and the pixels of digitization. The inputted local, extended objects as well as the winner take all mechanism result in local spatial filters. This is the consequence of the correlations of ....

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C. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. Neural Computation, 1993. in press.

.... path planning approaches that are based on the diffusion equation (Lei, 1990; Connolly and Grupen, 1993, Glasius et al. 1995; Glasius et al. 1996; Marshall and Tarassenko, 1994) These works were extended by Lorincz et al. in a series of publications that provides a self organizing formulation (Szepesv ari et al. 1994; Szepesv ari and Lorincz, 1996; Rozgonyi et al. 1996) to the path planning architecture and provides a direct inverse system identification stage of associative nature for controlling (Fomin et al. 1994; Szepesv ari and Lorincz, 1996a) The approach has the advantage that it provides a natural ....

.... neighboring connections have followed two routes, the one that used a WTA competition between the connections themselves (Martinetz, 1993; Martinetz and Schulten, 1994) and the other one that used leaky learning for the connections and assumed local extended objects (Szepesv ari and Lorincz, 1993; Szepesv ari et al. 1994; Szepesv ari and Lorincz, 1996) Here it suffices to use the method of Martinetz and Schulten (Martinetz, 1993; Martinetz and Schulten, 1994) which they termed competitive Hebbian learning (CHL) Below, the concepts developed by Martinetz and Schulten are shortly reviewed. In the case of a WTA ....

C. Szepesv'ari, L. Bal'azs and A. Lorincz 1994, "Topology learning solved by extended objects: A neural network model," Neural Comput. 6, 439--456.

....where this information is used to create better interpolation [15, 8, 3] This paper summarizes the recent advances in the theory of self organizing development of approximate geometry representations based on the use of neural networks. The first results of this field were published in [24, 9, 36, 34]. Some theoretical results were developed in [23] and [32] Part of this work is based on the theoretical approach of [32] which is different from that of [23] and also is somewhat more general. The Martinetz approach [23] treats signals provided by artificial neuron like entities whereas the ....

....representation. The resolution of our geometry representation does not depend on the number of neurons but rather on the local nature of the training objects. Geometry representation is important since (i) Kohonen type neighbour training may be introduced with the help of these connections [34, 35], ii) the connection structure may be used for path planning [21, 4, 25, 11] as well as for learning motion control [35] and (iii) for feature extraction that utilizes geometry information [2, 22] ....

Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. Neural Computation, 6(3):441--458, 1994.

....is said to be local on the camera if its size is small compared to that of the camera. Numerical simulations with learning rule given in (1) show that the equilibrium prototype vectors represent localized areas on the camera (Fig. 2) provided that localized input vectors are presented (see e.g. [27, 33]) Schulten et al. have put forward a heuristic argument [30, 27] to show that localized input vectors result in localized prototype vectors. The learning equation they used is slightly different from ours in that they normalized the prototype vectors after each learning step. It was argued ....

Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. In Proc. of ICANN'93, page 678, Springer-Verlag, London, Amsterdam, The Netherlands, September 1993.

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Szepesva ri Cs, Bala zs L, Lo rincz A. Topology learning solved by extended objects: A neural network model. Neural Computations 1994; 6: 441--448

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Cs. Szepesvari, L. Balazs and A. Lorincz 1994, "Topology learning solved by extended objects: a neural network model," Neural Computation 6, 439--456.

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Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. submitted to Neural Computation, 1992.

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Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. In S. Gielen and B. Kappen, editors, Proc. of ICANN'93, page 678, Amsterdam, The Netherlands, September 1993. Springer-Verlag, London.

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Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. Neural Computation, 6(3):441--458, 1994. 22

....e.g. when using geometry representing networks one may introduce neighbour training without the loss of generality provided that the inverse dynamics function is smooth. Another attractive property of the scheme lies in its learning properties. The GDL can be formed in a self organizing fashion [15,16,17]. The PDA map is formed via an associative learning method when the training data are given in the form of action response pairs. That is, it is possible to apply SDS Control during learning, if the effective (SDS) control signal is used for association. Note, that 1 Control with the ....

Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. Neural Computation, 6(3):441--458, 1994.

.... Moody and Darken (Moody and Darken, 1989) Poggio and Girosi (Poggio and Girosi, 1990) Nowlan (Nowlan, 1990) Benaim and Tomasini (Benaim and Tomasini, 1991,Benaim and Tomasini, 1992) Martinetz and Schulten (Martinetz and Schulten, 1991) Fomin et al. Fomin et al. 1994) Szepesv ari et al. (Szepesv ari et al. 1994), Joutsensalo et al. Joutsensalo et al. 1995) and Michaels (Michaels, 1995) to name but a few. N 1 N 2 v u x y Figure 1: Single hidden layer cascaded network The weight u of subnetwork N 1 is trained independently of the weight v of subnetwork N 2 . We investigate in this article if ....

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....system Tremendous amount of sensory input information coming from the external world should be reduced to a set of high or low bits in order to build up an efficient internal representation. Systems considered here are categorizing systems of soft competition, such as the where system [11, 4] with spatial filters that reduce the high resolution image to a few positions and thus we assume a grid system. The recognition of objects, the what system, may be built by several methods, e.g. 2, 9, 8, 3, 7] Both subsystems have bit string outputs and it is the task of the agent to find out ....

Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. Neural Computation, 6(3):441--458, 1994.

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Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. Neural Computation, 6(3):441-- 458, 1994.

....of the topology of the space to be discretized and can take advantage of the neighbour training. Two other methods that were proposed and that provide correct representation of topological spaces are: the method of learning with the help of extended input objects [Szepesv ari and Lorincz, 1993, Szepesv ari et al. 1994] and the method of Voronoi polygons [Martinetz, 1993] Both methods are capable of building up spatial filters and can develop interneural connections to represent the correct neighbourhood relations of these filters. It has been shown that in the case of local extended input objects [Szepesv ari ....

....Voronoi polygons [Martinetz, 1993] Both methods are capable of building up spatial filters and can develop interneural connections to represent the correct neighbourhood relations of these filters. It has been shown that in the case of local extended input objects [Szepesv ari and Lorincz, 1993, Szepesv ari et al. 1994] interneural connections may be used for Kohonen like cooperative neighbour training. In this way one may return to the original idea of the Kohonen network without prescribing the neighbourhood relations of neurons. In many cases input objects of different sizes should be distinguished, even if ....

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Szepesv'ari, C., Bal'azs, L., and Lorincz, A. (1994). Topology learning solved by extended objects: a neural network model. Neural Computation, 6:441--458.

....internal representation of sensory events, iv) a prewired goal system, v) the algorithm that designs action plans, and (vi) a decision system (see Fig. 1) ffl The dimension reducing system (DRS) Systems considered here are categorizing systems of soft competition, such as the where system [6, 3] with spatial filters that reduce the high resolution image to a few positions and we can assume a grid system. The recognition of objects may be per Cs. Szepesv ari and A. Lorincz are with the Department of Photophysics, Institute of Isotopes, The Hungarian Academy of Sciences, Budapest, ....

C. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. Neural Computation, 1993. in press.

....of the world. The drawbacks of the model are: i) it may be applied if the topology of both the work place and the control space fit the prewired topology of the Kohonen network, ii) it does not lead to self organized path planning and is thus unprotected against obstacles. Our first solution ([2]) that overcomes problem (i) applies a combination of Competitive learning for spatial filter (SF) formation and develops geometry connections between neurons via Hebbian (H) learning. The competitive part may than be weakened to soft competition with the help of Kohonen like neighbour training ....

Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. Neural Computation, 1993. in press.

....blocks for neural network and neural network hierarchy fabrications, and ffl they tend to form a redundant representation, which is an inherently robust feature. Another advantage of HAH networks against some other soft competitive networks, e.g. the network of Szepesv ari, Bal azs and Lorincz [16] is that there is no need for a winner take all (WTA) subsystem. WTA needs precise prewiring of inhibitory connections. Here the question of tolerance in network parameters is the subject of investigation. In the case of self organized learning the definition of performance is not ....

....was set to 1 16, i.e. it was set somewhat above the inverse of the number of neurons. That favours, through Eq. 6) one or sometimes two neurons to fire (become high) at a time. The network produced circular local filters in a similar way to the competitive net of Szepesv ari, Bal azs and Lorincz [16]. The left hand side of Fig. 3 shows the receptive field of one of the neurons for the TM network. The filter size corresponds to the average object size. It may be worth noting that the local filters represent the simplest correlations of the different input patterns that the competing neurons ....

[Article contains additional citation context not shown here]

Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. Neural Computation,

....of Photophysics, Institute of Isotopes The Hungarian Academy of Sciences, Budapest, Hungary z Department of Physics, Attila J ozsef University, Szeged, Hungary I. Introduction Competing neurons are able to create spatial filters of circular shape and of equal sizes, as it was shown in [1]. Our goal was to develop a neural network, that creates filters of different sizes in order to distinguish among patterns of different sizes, even if they are positioned to the same place in the input space. Such network could solve fast segmentation tasks in parallel. There are evidences that ....

Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. Neural Computation, 1993. in press.

....of possible images was discretized by the discretization layer. The feedforward weights of every neuron of the discretization layer form a localized Gaussian shaped spatial filter. The proximity relations between discretizing neurons are based on the neighborhood relations of their spatial filters (Szepesv ari et al. 1994; Szepesv ari and Lorincz, 1996a) The spatial filters and the proximity relations between them can be learnt by self organization (Szepesv ari et al. 1994; Szepesv ari and Lorincz, 1996a) In these experiments, however, the spatial filters, the proximity relations as well as the control commands ....

....shaped spatial filter. The proximity relations between discretizing neurons are based on the neighborhood relations of their spatial filters (Szepesv ari et al. 1994; Szepesv ari and Lorincz, 1996a) The spatial filters and the proximity relations between them can be learnt by self organization (Szepesv ari et al. 1994; Szepesv ari and Lorincz, 1996a) In these experiments, however, the spatial filters, the proximity relations as well as the control commands stored by the interneurons were prewired in an ideal fashion in order to limit the range of possible errors to structural approximation errors only. In ....

Szepesv'ari, Cs., Bal'azs, L., and Lorincz, A. (1994). Topology learning solved by extended objects: a neural network model. Neural Computation, 6(3):441--458.

....to form generalized flow fields (i.e. temporal associations) and thus may be used to fill the missing point of the DCR architecture. Another way of establishing temporal associations is as follows. 1) Self organizing means are capable of developing an approximate geometry representation [31, 32]. 2) The secondary sensors can be built onto the geometry representing directed connections that bridge the local approximator units [33, 10, 11] 3) The secondary sensors related to the neighbour connections are appropriate devices for measuring the projection of the local flow vector onto the ....

Cs. Szepesv'ari, L. Bal'azs, and A. Lorincz. Topology learning solved by extended objects: a neural network model. Neural Computation, 6:439--456, 1994.

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