A. Saha and J. D. Keeler, "Algorithms for better representation and faster learning in radial basis function networks," in Advances in Neural Information Processing Systems, D. S. Touretzky, Ed., San Mateo, CA, 1990, vol. 2, pp. 482--489, Morgan Kaufmann Publishers.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....using the above described method with # =3is shown in Figure 3. We computed the Bayes error by obtaining the kernel estimate of the density, i.e. by the sum of Gaussian s centered at each pattern and with variance equal to the RMS value of distance between each pattern and its nearest neighbor [7]. The two pdf s corresponding to the example shown in Figure 3 are shown in Figure 4. 4 2 0 2 4 6 8 10 12 0 10 20 30 40 50 60 70 80 90 100 x Class1 Class2 Figure 3: Data distribution with # = 3. To shown it clearly, we plot one dimension data in two dimension by adding the pattern ....

A. Saha and J. D. Keeler, "Algorithms for better representation and faster learning in radial basis function networks," in Advances in Neural Information Processing Systems, D. S. Touretzky, Ed., San Mateo, CA, 1990, vol. 2, pp. 482--489, Morgan Kaufmann Publishers.

....trained to output i for the images in the training set. The r parameter of the Gaussian basis units, which governs the tradeoff between satisfactory performance on the training set and generalization to novel inputs, was set to the value of the mean distance among the members of the training set [24]. This choice of r caused the output of a recognizer for a given person to be always greater for the (training set) images of the same person than for images of the other people in joe tha bil ba dav foo .1 0, 0,1 0,2 1,0 0,1 if joe pas ob sta ste tha te vmb wav 8,1 8,2 8,4 8,5 8,3 ....

A. Saha and J. D. Keeler. Algorithms for better representation and faster learning in Radial Basis Function networks. In D. Touretzky, editor, Neural Information Processing Systems, volume 2, pages 482 489. Morgan Kaufmann, San Mateo, CA, 1990.

....(RCE) and the algorithm presented in this work. 100 instances of the database were used as training data and 50 as testing data. The RBF network was trained using a kernel unit for each training vector and s was calculated for each kernel as the RMS distance to its neighbors, as suggested in [21]. The RCE network was trained using an initial q (threshold or radius of each kernel) equal to half of the dimension of the feature space. Both networks used 4 input units (one for each attribute) and 3 output units (one for each class) For the rule extraction algorithm, membership functions of ....

Saha A. and Keeler J., Algorithms for better representation and faster learning in Radial Basis Function networks, Advances in Neural Information Processing Systems, 2, pp. 482--489, 1990.

....(RCE) and the algorithm presented in this work. 100 instances of the database were used as training data and 50 as testing data. The RBF network was trained using a kernel unit for each training vector and oe was calculated for each kernel as the RMS distance to its neighbors, as suggested in [21]. The RCE network was trained using an initial (threshold or radius of each kernel) equal to half of the dimension of the feature space. Both networks used 4 input units (one for each attribute) and 3 output units (one for each class) For the rule extraction algorithm, membership functions of ....

A. Saha and J. Keeler. Algorithms for better representation and faster learning in radial basis function networks. Advances in Neural Information Processing Systems, 2:482--489, 1990.

....vector (input x) together with the 3 coefficients that describe each hand posture (output y) is then used for supervised training. 3 The LLM Network Architecture In our approach we make use of LLM networks [15, 16] This type of network, related to selforganizing maps [3] and the GRBF approach [11, 13, 17], is computationally efficient and learns fast [8, 18] Basically, it approximates a non linear transformation by a set of locally valid, linear mappings (Fig.2) where mapping r (r = 1 . N , N being the number of units of the network) is given by y r = w (out) r A r (x Gamma w (in) r ....

Saha, A., Keeler, J.D. (1990), "Algorithms for Better Representation and Faster Learning in Radial Basis Function Networks", in Advances in Neural Information Processing Systems 2 , ed. D.S. Touretzky, pp. 482--489, Morgan Kaufman Publishers, San Mateo, CA.

....Note that the tree is not completely explored: only branches which store patterns that are closer to the input pattern than their radius are then searched. We call this mode of extended search backtracking . Another way to extend the search is to force a bigger radius than the stored radius [5]. The factor by which the radii are multiplied is called the external search factor. Experimentally, the results show that extending the search using these methods is efficient in terms of performance while allowing to keep a good speed up factor ff. 3.2.2 Rejection Rejection is provided in ....

A. Saha and J.D. Keeler, Algorithms for better representation and faster learning in radial basis function networks, Neural Information Processing Systems, ed. D. Touretzky, Morgan Kaufmann, San Mateo, CA , 482-489, (1990).

....10 Distinct Sub Nets 3. 1 Radii Setting The setting of radii values is also a significant factor for the design of RBF NNs and such determination is still one of the open issues [9, 10] In the simulation work, we have investigated the individual setting of radii values using 1 nearest neighbour [11], however, the recognition performance using this technique did not yield better results than the radii setting with fixed values. In this paper, fixed radii values for the respective RBFs are therefore used and set equal according to the following modified radii setting found in [10] oe = d N ....

A. Saha and J. D. Keeler, "Algorithms for better representation and faster learning in radial basis function networks", In: "Advances in Neural Information Processing Systems 2", Ed. D. S. Touretzky, pp.482-489, San Mateo, CA: Morgan Kaufmann, 1990.

....for tuning the centers were developed by [13] 14] and by [37] However, most of these techniques are computationally expensive. 2. For proper setting of the standard deviation, oe, heuristics are necessary. 23] suggests to use a value proportional to the maximum distance between centers. In [33] each hidden neuron has a different oe, calculated as a function of the distance between its center and the center of its nearest neighbor. Adaptation formulae for learning oe from examples can be found in [17] IEEE TRANSACTIONS ON NEURAL NETWORKS 814 ....

Saha, A. and Keeler, J.D. (1990). Algorithms for Better Representation and Faster Learning in Radial Basis Function Networks. In Advances in Neural Information Processing Systems 2 (D.S. Touretzky), San Mateo, CA, Morgan Kaufmann, 482--489

....and slight changes in the view of the object. 3. Feature Classification by a LLM network For feature classification we chose a Local Linear Map network, which is a computationally efficient means for nonlinear function approximation. It is related to the selforganizing map [2] and the GRBF [4, 5, 7] approach. It approximates the nonlinear function by a set of locally valid linear mappings, for details see e.g. 6] Here we use a winner takes all network. In this case for a given input only one node, the best match or winner node, contributes to the output vector. For the classification ....

A. Saha and J. Keeler. Algorithms for better representation and faster learning in radial basis function networks. In D. Touretzky, editor, Advances in Neural Information Processing Systems 2, pages 482--489. Morgan Kaufman Publishers, San Mateo, CA, 1990.

....approach such as Hummel s recent implementation of the Recognition By Components theory (Hummel and Biederman, 1992) 4 The value of oe was computed as follows. First, the mean separation S of the vectors in the entire ensemble of inputs was computed (this is the value of oe recommended by (Saha and Keeler, 1990)) Second, oe was set to either 0:5, 1:0, or 2:0 times S. 4 Conclusions and future work The present work studied the interaction between class similarity and viewpoint dependence in recognition. Intuitively, one expects an increased sensitivity to viewpoint in the discrimination between highly ....

Saha, A. and Keeler, J. D. (1990). Algorithms for better representation and faster learning in Radial Basis Function networks. In Touretzky, D., editor, Neural Information Processing Systems, volume 2, pages 482--489. Morgan Kaufmann, San Mateo, CA.

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