Methods For Large-Scale Data Analysis & Machine Learning For Intelligent Image Processing

This project originates from research on methods and techniques for real time analysis and handling of large dimensional data with respect to the presence of uncertainties and scarce rates of sampling. The main applicational focus is the development of methods of object detection in the basis of higher dimensional representation of objects in their relative feature spaces. During these studies, it became clear that due to internal uncertainties and biases in the small amount of data available for this task, a theory for improving performance of generic AI systems regarding the minimisation of misclassifications is required for this project. Recently discovered phenomenon in stochastic separation theorems [1] have offered a way to remedy issues with errors in generic AI systems, providing that decision variables in the AI systems are sufficiently high dimensional [2], [3], [4], [5]. At the time work on this thesis started, these results were limited to only a few sets of practically relevant distributions. The theoretical focus of this work was to develop existing methods by generalising the results to k-tuples in product measure distributions and to overcome the concentration limit found in a later work [6]. The main application areas of these theories include but are not limited to:

1. Computational complexity in real time processing of high dimensional data.

2. Insufficient richness or quality of data.

3. Computational complexity of training a detector in real time.

4. Ensuring invariance to different methods of detection.

This thesis assesses these problem and describes recent developments in theoretical and practical results over the last four years. Section II introduces machine learning and the main associated problems. An overview of classification techniques precedes formal definitions of the remaining issues as mathematical problems to be solved. Section III details examples of tactile language classification through hardware and software. Section IV presents the main theoretical body of the thesis, culminating in two methods of classifying sign language gestures through an automated error corrector appended to a core AI going from a 82.4% success to 100% success with enough error clusters and a general separability measure to distinguish higher dimensional representations of projected data through kernel feature maps. Finally, Section V concludes this thesis with future outlooks for research and possible applications for the acquired results.