A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks

In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel hypercomplex number systems referred to as real-part associative hypercomplex number systems. Real-part associative hypercomplex number systems generalize the well-known Cayley-Dickson algebras and real Clifford algebras and include the systems of real numbers, complex numbers, dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as particular instances. Apart from the novel hypercomplex number systems, we introduce a family of hypercomplex-valued activation functions called $\mathcal{B}$-projection functions. Broadly speaking, a $\mathcal{B}$-projection function projects the activation potential onto the set of all possible states of a hypercomplex-valued neuron. Using the theory presented in this paper, we confirm the stability analysis of several discrete-time hypercomplex-valued Hopfield-type neural networks from the literature. Moreover, we introduce and provide the stability analysis of a general class of Hopfield-type neural networks on Cayley-Dickson algebras

Global exponential synchronization of quaternion-valued memristive neural networks with time delays

This paper extends the memristive neural networks (MNNs) to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established, and the problem of drive-response global synchronization of this type of networks is investigated in this paper. Two cases are taken into consideration: one is with the conventional differential inclusion assumption, the other without. Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques. Finally, corresponding simulation examples are presented to demonstrate the correctness of the proposed results derived in this paper

Real to H-space Encoder for Speech Recognition

International audienceDeep neural networks (DNNs) and more precisely recurrent neural networks (RNNs) are at the core of modern automatic speech recognition systems, due to their efficiency to process input sequences. Recently, it has been shown that different input representations, based on multidimensional algebras, such as complex and quaternion numbers, are able to bring to neural networks a more natural, compressive and powerful representation of the input signal by outperforming common real-valued NNs. Indeed, quaternion-valued neural networks (QNNs) better learn both internal dependencies, such as the relation between the Mel-filter-bank value of a specific time frame and its time derivatives, and global dependencies, describing the relations that exist between time frames. Nonetheless, QNNs are limited to quaternion-valued input signals, and it is difficult to benefit from this powerful representation with real-valued input data. This paper proposes to tackle this weakness by introducing a real-to-quaternion encoder that allows QNNs to process any one dimensional input features, such as traditional Mel-filter-banks for automatic speech recognition

Bicomplex neural networks with hypergeometric activation functions

Bicomplex convolutional neural networks (BCCNN) are a natural extension of the quaternion convolutional neural networks for the bicomplex case. As it happens with the quaternionic case, BCCNN has the capability of learning and modelling external dependencies that exist between neighbour features of an input vector and internal latent dependencies within the feature. This property arises from the fact that, under certain circumstances, it is possible to deal with the bicomplex number in a component-wise way. In this paper, we present a BCCNN, and we apply it to a classification task involving the colorized version of the well-known dataset MNIST. Besides the novelty of considering bicomplex numbers, our CNN considers an activation function a Bessel-type function. As we see, our results present better results compared with the one where the classical ReLU activation function is considered.publishe

Neural Computing in Quaternion Algebra

兵庫県立大学201

Learning Speech Emotion Representations in the Quaternion Domain

The modeling of human emotion expression in speech signals is an important, yet challenging task. The high resource demand of speech emotion recognition models, combined with the the general scarcity of emotion-labelled data are obstacles to the development and application of effective solutions in this field. In this paper, we present an approach to jointly circumvent these difficulties. Our method, named RH-emo, is a novel semi-supervised architecture aimed at extracting quaternion embeddings from real-valued monoaural spectrograms, enabling the use of quaternion-valued networks for speech emotion recognition tasks. RH-emo is a hybrid real/quaternion autoencoder network that consists of a real-valued encoder in parallel to a real-valued emotion classifier and a quaternion-valued decoder. On the one hand, the classifier permits to optimize each latent axis of the embeddings for the classification of a specific emotion-related characteristic: valence, arousal, dominance and overall emotion. On the other hand, the quaternion reconstruction enables the latent dimension to develop intra-channel correlations that are required for an effective representation as a quaternion entity. We test our approach on speech emotion recognition tasks using four popular datasets: Iemocap, Ravdess, EmoDb and Tess, comparing the performance of three well-established real-valued CNN architectures (AlexNet, ResNet-50, VGG) and their quaternion-valued equivalent fed with the embeddings created with RH-emo. We obtain a consistent improvement in the test accuracy for all datasets, while drastically reducing the resources' demand of models. Moreover, we performed additional experiments and ablation studies that confirm the effectiveness of our approach. The RH-emo repository is available at: https://github.com/ispamm/rhemo.Comment: Paper Submitted to IEEE/ACM Transactions on Audio, Speech and Language Processin

Applied Mathematics and Computational Physics

As faster and more efficient numerical algorithms become available, the understanding of the physics and the mathematical foundation behind these new methods will play an increasingly important role. This Special Issue provides a platform for researchers from both academia and industry to present their novel computational methods that have engineering and physics applications

Human Promoter Prediction Using DNA Numerical Representation

With the emergence of genomic signal processing, numerical representation techniques for DNA alphabet set {A, G, C, T} play a key role in applying digital signal processing and machine learning techniques for processing and analysis of DNA sequences. The choice of the numerical representation of a DNA sequence affects how well the biological properties can be reflected in the numerical domain for the detection and identification of the characteristics of special regions of interest within the DNA sequence. This dissertation presents a comprehensive study of various DNA numerical and graphical representation methods and their applications in processing and analyzing long DNA sequences. Discussions on the relative merits and demerits of the various methods, experimental results and possible future developments have also been included. Another area of the research focus is on promoter prediction in human (Homo Sapiens) DNA sequences with neural network based multi classifier system using DNA numerical representation methods. In spite of the recent development of several computational methods for human promoter prediction, there is a need for performance improvement. In particular, the high false positive rate of the feature-based approaches decreases the prediction reliability and leads to erroneous results in gene annotation.To improve the prediction accuracy and reliability, DigiPromPred a numerical representation based promoter prediction system is proposed to characterize DNA alphabets in different regions of a DNA sequence.The DigiPromPred system is found to be able to predict promoters with a sensitivity of 90.8% while reducing false prediction rate for non-promoter sequences with a specificity of 90.4%. The comparative study with state-of-the-art promoter prediction systems for human chromosome 22 shows that our proposed system maintains a good balance between prediction accuracy and reliability. To reduce the system architecture and computational complexity compared to the existing system, a simple feed forward neural network classifier known as SDigiPromPred is proposed. The SDigiPromPred system is found to be able to predict promoters with a sensitivity of 87%, 87%, 99% while reducing false prediction rate for non-promoter sequences with a specificity of 92%, 94%, 99% for Human, Drosophila, and Arabidopsis sequences respectively with reconfigurable capability compared to existing system