Learning Input and Recurrent Weight Matrices in Echo State Networks

Echo State Networks (ESNs) are a special type of the temporally deep network model, the Recurrent Neural Network (RNN), where the recurrent matrix is carefully designed and both the recurrent and input matrices are fixed. An ESN uses the linearity of the activation function of the output units to simplify the learning of the output matrix. In this paper, we devise a special technique that take advantage of this linearity in the output units of an ESN, to learn the input and recurrent matrices. This has not been done in earlier ESNs due to their well known difficulty in learning those matrices. Compared to the technique of BackPropagation Through Time (BPTT) in learning general RNNs, our proposed method exploits linearity of activation function in the output units to formulate the relationships amongst the various matrices in an RNN. These relationships results in the gradient of the cost function having an analytical form and being more accurate. This would enable us to compute the gradients instead of obtaining them by recursion as in BPTT. Experimental results on phone state classification show that learning one or both the input and recurrent matrices in an ESN yields superior results compared to traditional ESNs that do not learn these matrices, especially when longer time steps are used.

Sparse Representation-based Image Quality Assessment

A successful approach to image quality assessment involves comparing the structural information between a distorted and its reference image. However, extracting structural information that is perceptually important to our visual system is a challenging task. This paper addresses this issue by employing a sparse representation-based approach and proposes a new metric called the \emph{sparse representation-based quality} (SPARQ) \emph{index}. The proposed method learns the inherent structures of the reference image as a set of basis vectors, such that any structure in the image can be represented by a linear combination of only a few of those basis vectors. This sparse strategy is employed because it is known to generate basis vectors that are qualitatively similar to the receptive field of the simple cells present in the mammalian primary visual cortex. The visual quality of the distorted image is estimated by comparing the structures of the reference and the distorted images in terms of the learnt basis vectors resembling cortical cells. Our approach is evaluated on six publicly available subject-rated image quality assessment datasets. The proposed SPARQ index consistently exhibits high correlation with the subjective ratings on all datasets and performs better or at par with the state-of-the-art.