Figure 1: The proposed architecture for sequence learning. The network is composed of two parts, sequence identifiei and sequence locator. The discrimination layer contains recurrent neurons which calculate a discriminative identity number for each sequence by using f{;s which are polynomial integrating functions. Memory layer contains recurren neurons which play the role of low-pass filters with different time-constants 7;. Sequence fuzzy sets layer and Sample juzzy sets layer are composed of RBF neurons with multivariate Gaussian functions. The sequence identifier identifie: the sequence and the sequence locator detect the location of the current sample. Next, their outputs are combined in the Juzzy rules layer. After applying normalization in the normalization layer, next sample of the sequence is approximatec (Z(t + 1)) as the network output (y(¢)). In the output layer, w; to wr are output weights for each fuzzy rule. It i: assumed that the network would identify and produce the sequence after T’ samples. Therefore, there are three switches S, to $3. Initially, S; and S3 are closed and the correct sequence sample x(t) is received by the network. After 7 samples, these switches become open and 5 would be closed. Thus, the sequence locator part receives the previou: network output as the input, and the sequence identifier part receives no more inputs. Indeed, the output of the this par would remain constant after T’ samples. Figure 2: A simple example of adding a new fuzzy set in a one-dimensional input space. a The input signal is analyzed by two fuzzy sets with centers c; and cg. The total coverage for the sample x* is lower than a predefined threshold 0. b A new fuzzy set, which its center is 7*, has been added. Figure 3: Two intersected sequences with a similar part. Table 1: Parameters values for learning two intersected functions Figure 4: Comparison between the proposed architecture and the ordinary one in learning two trajectories with intersected region. a Proposed network output for the first sequence. b Proposed network output for the second sequence. c The output of an ordinary self-organizing network architecture (GDFNN) for the first sequence. d The output of an ordinary self-organizing network architecture (GDFNN) for the second sequence. One application of the proposed network is to be utilized as a pattern generator. In this experiment, the proposed network is used to learn and generate periodic patterns. Four patterns, including sine, square, triangle, and sawtooth waves are used as target sequences. The network should learn to produce one period of all patterns based on receiving the samples of the first period. Next, it would be able to reproduce them periodically, by receiving just the first period. Table 2: Parameters values for learning different patterns Figure 5: Learning four different patterns. a Sine wave. b Square wave. ¢c Triangle wave. d Sawtooth wave. Figure 6: Generating learned periodic signal with phase shift. a ¢ = 7/2. b ¢ = 7. Figure 7: Learning and generating different trajectories by the network. The first, third and fifth rows compare the desired and actual sequences. The second, fourth and sixth rows, show the corresponding noisy inputs to the network.
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