Complex-Valued Recurrent Correlation Neural Networks

Abstract

In this paper, we generalize the bipolar recurrent correlation neural networks (RCNNs) of Chiueh and Goodman for patterns whose components are in the complex unit circle. The novel networks, referred to as complex-valued RCNNs (CV-RCNNs), are characterized by a possible nonlinear function, which is applied on the real part of the scalar product of the current state and the original patterns. We show that the CV-RCNNs always converge to a stationary state. Thus, they have potential application as associative memories. In this context, we provide sufficient conditions for the retrieval of a memorized vector. Furthermore, computational experiments concerning the reconstruction of corrupted grayscale images reveal that certain CV-RCNNs exhibit an excellent noise tolerance.

An Introduction to Quaternion-Valued Recurrent Projection Neural Networks

“…The RCNNs have been generalized for the storage and recall of complexvalued and quaternion-valued vectors [31,32]. In the following, we briefly review the quaternionic recurrent neural networks (QRCNNs).…”

“…In contrast, the continuous-valued quaternionic model proposed independently by Valle and Kobayashi always comes to rest at a stable equilibrium point under the usual conditions on the synaptic weights [29,30]. Apart from hypercomplex-valued Hopfield networks, Valle proposed a complex-valued version of the RCNNs [31]. Recently, the RCNNs have been further extended to quaternions [32].…”

“…Like our previous works[31,32], we adopted the value ε p = √ mach , where mach denotes the machine floating-point relative accuracy, in our computational implementation f p .…”

Complex Gaussian Processes for Regression

“…Signal processing for complex-valued signals has been widely studied in the linear case, see [1] and references therein. The nonlinear processing of complex-valued signals has been addressed from different points of view, such as complexvalued nonlinear adaptive filtering [2], neural networks [3], [4] and, recently, using reproducing kernel Hilbert spaces (RKHS) [5]. Some complex kernel-based algorithms have been lately proposed for classification [6], regression [7], [8], [9] and mainly for kernel principal component analysis [10].…”

Finite‐Time Synchronization for Complex‐Valued Recurrent Neural Networks with Time Delays

“…Accordingly, many fruitful achievements have been reported for this model . For example, global stability, global exponential stability, and Hopf bifurcation problems for complex-valued neural networks systems with delays or without delays were investigated in [32][33][34][35][36][37][38][39][40]. Dissipativity, 2 Complexity passivity, state estimation, exponential stability, and inputto-state stability for memristor-based complex-valued neural networks with or without delays were discussed and relative criteria were established in [43][44][45][46][47][48].…”