arXiv subjects

Ahmad Moniri

Publications and source records attributed to Ahmad Moniri.

3 recordsLinked to original sources

arXiv2020

Compression and Interpretability of Deep Neural Networks via Tucker Tensor Layer: From First Principles to Tensor Valued Back-Propagation

This work aims to help resolve the two main stumbling blocks in the application of Deep Neural Networks (DNNs), that is, the exceedingly large number of trainable parameters and their physical interpretability. This is achieved through a tensor valued approach, based on the proposed Tucker Tensor Layer (TTL), as an alternative to the dense weight-matrices of DNNs. This allows us to treat the weight-matrices of general DNNs as a matrix unfolding of a higher order weight-tensor. By virtue of the compression properties of tensor decompositions, this enables us to introduce a novel and efficient framework for exploiting the multi-way nature of the weight-tensor in order to dramatically reduce the number of DNN parameters. We also derive the tensor valued back-propagation algorithm within the TTL framework, by extending the notion of matrix derivatives to tensors. In this way, the physical interpretability of the Tucker decomposition is exploited to gain physical insights into the NN training, through the process of computing gradients with respect to each factor matrix. The proposed framework is validated on both synthetic data, and the benchmark datasets MNIST, Fashion-MNIST, and CIFAR-10. Overall, through the ability to provide the relative importance of each data feature in training, the TTL back-propagation is shown to help mitigate the "black-box" nature inherent to NNs. Experiments also illustrate that the TTL achieves a 66.63-fold compression on MNIST and Fashion-MNIST, while, by simplifying the VGG-16 network, it achieves a 10\% speed up in training time, at a comparable performance.

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arXiv2018

Tensor Ensemble Learning for Multidimensional Data

In big data applications, classical ensemble learning is typically infeasible on the raw input data and dimensionality reduction techniques are necessary. To this end, novel framework that generalises classic flat-view ensemble learning to multidimensional tensor-valued data is introduced. This is achieved by virtue of tensor decompositions, whereby the proposed method, referred to as tensor ensemble learning (TEL), decomposes every input data sample into multiple factors which allows for a flexibility in the choice of multiple learning algorithms in order to improve test performance. The TEL framework is shown to naturally compress multidimensional data in order to take advantage of the inherent multi-way data structure and exploit the benefit of ensemble learning. The proposed framework is verified through the application of Higher Order Singular Value Decomposition (HOSVD) to the ETH-80 dataset and is shown to outperform the classical ensemble learning approach of bootstrap aggregating.

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arXiv2018

A Data Analytics Perspective of the Clarke and Related Transforms in Power Grid Analysis

Affordable and reliable electric power is fundamental to modern society and economy, with the Smart Grid becoming an increasingly important factor in power generation and distribution. In order to fully exploit it advantages, the analysis of modern Smart Grid requires close collaboration and convergence between power engineers and signal processing and machine learning experts. Current analysis techniques are typically derived from a Circuit Theory perspective; such an approach is adequate for only fully balanced systems operating at nominal conditions and non-obvious for data scientists - this is prohibitive for the analysis of dynamically unbalanced smart grids, where Data Analytics is not only well suited but also necessary. A common language that bridges the gap between Circuit Theory and Data Analytics, and the respective community of experts, would be a natural step forward. To this end, we revisit the Clarke and related transforms from a subspace, latent component, and spatial frequency analysis frameworks, to establish fundamental relationships between the standard three-phase transforms and modern Data Analytics. We show that the Clarke transform admits a physical interpretation as a "spatial dimensionality" reduction technique which is equivalent to Principal Component Analysis (PCA) for balanced systems, but is sub-optimal for dynamically unbalanced systems, such as the Smart Grid, while the related Park transform performs further "temporal" dimensionality reduction. Such a perspective opens numerous new avenues for the use Signal Processing and Machine Learning in power grid research, and paves the way for innovative optimisation, transformation, and analysis techniques that are not accessible to arrive at from the standard Circuit Theory principles, as demonstrated in this work through the possibility of simultaneous frequency estimation and fault detection.

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