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... tables, samples of a chosen sigmoid are put into a ROM or RAM to store the desired activation function. Alternatively, we use simplified activation functions that approximate the chosen activation ... sigmoidal functions are a typical choice for MLPs, several other functions have been considered. Recently, the use of polynomial activation functions has been proposed (Chon and Cohen 1997; Piazz...

Ngày tải lên: 21/01/2014, 15:20

... statistical and optimisation theories 2 SOME IMPORTANT DATES IN THE HISTORY OF CONNECTIONISM (Cichocki and Unbehauen 1993; Zhang and Constantinides 1992), neural networks are becoming one of the ... rigorous analysis of the perceptron. The work of Grossberg in 1976 was based on biological and psychological evidence. He proposed several new architectures of nonlinear dynamical systems (Grossbe...

Ngày tải lên: 21/01/2014, 15:20

... network or a penalty term for excessive increase in the weights of the adaptive system or some other chosen function (Tikhonov et al. 1998). An example of such an objective function for online learning is J(k)= 1 N N  i=1 (e 2 (k ... weights based upon the instantaneous error • Stop if some prescribed error performance is reached The choice of the type of learning is very much dependent upon...

Ngày tải lên: 21/01/2014, 15:20

... and ˜y µ,j (0) = 0, for all j  0. The form of the equation is, moreover, a convex mixture. The choice of µ controls the trade-off between depth and resolution; small µ provides low-depth and high-resolution ... ,q. A taxonomy of recurrent neural networks architectures is presented by Tsoi and Back (1997). The choice of structure depends upon the dynamics of the signal, learning algorithm and...

Ngày tải lên: 21/01/2014, 15:20

... are described by nonlinear difference equations, have been introduced (Billings 1980; Chon and Cohen 1997; Chon et al. 1999; Connor 1994). Unlike the Volterra–Wiener representation, the NARMAX ... therefore modelling is based upon a chosen set of known functions. In addition, if the model is to approximate the system with an arbitrary accuracy, the set of chosen nonlinear continuous functions...

Ngày tải lên: 26/01/2014, 13:20

... developed for neural adaptive system identifiers and predictors. Finally, issues concerning the choice of a neural architecture with respect to the bias and variance of the prediction performance ... would provide a compromise between the bias and the variance of the prediction error achieved by a chosen model. An analogy with 112 LEARNING ALGORITHMS AND THE BIAS/VARIANCE DILEMMA Table 6.1 Ter...

Ngày tải lên: 26/01/2014, 13:20

... three neurons and six external input signals and a logistic activation function. Solution. Let us choose the initial values X 0 = rand(10, 1)∗1, W = rand(10, 3)∗2−1, using the notation of MATLAB, ... theory. The study of probabilistic operator theory and its applications was initiated by the Prague school under the direction of Antonin Spacek, in the 1950s (Bharucha-Reid 1976). They recognise...

Ngày tải lên: 26/01/2014, 13:20

... samples, as described in Mandic et al. (1998) and Bal- tersee and Chambers (1998). The network chosen for the analysis was with N =2 neurons and one external input signal to the network. Such ... Convergence curves for such a reiterated LMS algorithm for a data-reusing FIR filter applied to echo cancellation are shown in Fig- ure 8.1. The averaged squared prediction error becomes smaller ... p...

Ngày tải lên: 26/01/2014, 13:20

... performance of the NRTRL is highly dependent on the choice of the constant C in the denominator of the optimal learning rate. Dependent on the choice of C, the NRTRL can have worse, similar or ... practical applications. Therefore, the optimal learning rate for practical applications should be chosen to be smaller than the one derived above. This is one of the reasons why there is a need ......

Ngày tải lên: 26/01/2014, 13:20

... nonlinearities, and it affects the cost function to be minimised. Error nonlinearities are mostly chosen to be sign-preserving (Sethares 1992). Let us assume additive noise q(k) ∼N(0, σ 2 q ) in ... the mean square convergence of the RTRL algorithm for a recurrent perceptron. Depending on the choice of γ, this is directly applicable for learning algorithms for both feedforward and recurrent

Ngày tải lên: 26/01/2014, 13:20