Exploring the Intersection of Set Proximity, Parallel Computing, and Machine Learning

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My research interest lies in quantifying the similarity of sets of objects, based on their characteristic attributes and features, in a manner similar to humans performing the same task. In this regard, the focus of the proposed work is to combine my expertise in descriptively near sets and general purpose computing using GPUs (GPGPU) to augment and develop new theory for current approaches to machine learning and deep neural networks (DNN), as well as to produce further gains in the accuracy and applicability of these techniques. ******As is well known, in 2012 A. Krizhevsky et al. won the ILSVRC using a convolutional neural network driven by GPU. Their work demonstrated that the combination of GPUs, large labelled datasets, and DNN could solve a real-world image classification problem. This event, and the subsequent progress, raised the following question: had the problem of quantifying the similarity of sets of objects been effectively solved by these networks? The answer is No, and the search for new approaches forms the foundation of the proposed work. Human behaviour is much richer than simply its ability to classify objects. We have a powerfully inherent ability to make judgements on the similarity of groups of objects, which we perform seamlessly and unconsciously many times a day. Thus, there is a strong need for the combination of theoretical frameworks for quantifying similarity and the current exciting developments in the field of machine learning. The motivation of the proposed work is to develop theoretical and computational frameworks for the synthesis of human perception of the similarity of sets of objects. The mathematical foundation of this work is descriptive topology and descriptive proximity spaces (i.e. descriptive near set theory), which formalize relationships between objects, sets of objects, and collections of these sets based on features that characterize intrinsic object attributes.******As the field of descriptive topology and descriptive proximity spaces is quite new, as well as computational approaches to these concepts, the novelty of the proposed work is very high. Further, no one is working at the intersection of descriptive approaches and high performance computing (HPC) or considering how these techniques can enrich and extend current deep learning algorithms to the problem of quantifying the similarity of objects, sets of objects, and families of sets. Deep neural networks have revolutionized large swathes of society. Examples range from self-driving cars to real-time language translation. At their heart, neural networks are pattern classifiers, meaning they take an unknown pattern and place it into one of a finite number of classes. The proposed work is to quantify the similarity of sets of objects. This simple, yet different, concept has the potential to be as revolutionary as neural networks if algorithms capable of human-level performance can be achieved.