Investigating Randomised Sphere Covers in Supervised Learning

c©This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with the author and that no quotation from the thesis, nor any information derived therefrom, may be published without the author’s prior, written consent. In this thesis, we thoroughly investigate a simple Instance Based Learning (IBL) classifier known as Sphere Cover. We propose a simple Randomized Sphere Cover Classifier (αRSC) and use several datasets in order to evaluate the classification performance of the αRSC classifier. In addition, we analyse the generalization error of the proposed classifier using bias/variance decomposition. A Sphere Cover Classifier may be described from the compression scheme which stipulates data compression as the reason for high generalization performance. We investigate the compression capacity of αRSC using a sample compression bound. The Compression Scheme prompted us to search new compressibility methods for αRSC. As such, we used a Gaussian kernel to investigate further data compression

Using 2k + 2 bubble searches to find single nucleotide polymorphisms in k-mer graphs

Motivation: Single nucleotide polymorphism (SNP) discovery is an important preliminary for understanding genetic variation. With current sequencing methods, we can sample genomes comprehensively. SNPs are found by aligning sequence reads against longer assembled references. De Bruijn graphs are efficient data structures that can deal with the vast amount of data from modern technologies. Recent work has shown that the topology of these graphs captures enough information to allow the detection and characterization of genetic variants, offering an alternative to alignment-based methods. Such methods rely on depth-first walks of the graph to identify closing bifurcations. These methods are conservative or generate many false-positive results, particularly when traversing highly inter-connected (complex) regions of the graph or in regions of very high coverage. Results: We devised an algorithm that calls SNPs in converted De Bruijn graphs by enumerating 2k + 2 cycles. We evaluated the accuracy of predicted SNPs by comparison with SNP lists from alignment-based methods. We tested accuracy of the SNP calling using sequence data from 16 ecotypes of Arabidopsis thaliana and found that accuracy was high. We found that SNP calling was even across the genome and genomic feature types. Using sequence-based attributes of the graph to train a decision tree allowed us to increase accuracy of SNP calls further. Together these results indicate that our algorithm is capable of finding SNPs accurately in complex sub-graphs and potentially comprehensively from whole genome graphs

Ensembles of random sphere cover classifiers

We propose and evaluate a new set of ensemble methods for the Randomised Sphere Cover (RSC) classifier. RSC is a classifier using the sphere cover method that bases classification on distance to spheres rather than distance to instances. The randomised nature of RSC makes it ideal for use in ensembles. We propose two ensemble methods tailored to the RSC classifier; RSE, an ensemble based on instance resampling and RSSE, a subspace ensemble. We compare RSE and RSSE to tree based ensembles on a set of UCI datasets and demonstrates that RSC ensembles perform significantly better than some of these ensembles, and not significantly worse than the others. We demonstrate via a case study on six gene expression data sets that RSSE can outperform other subspace ensemble methods on high dimensional data when used in conjunction with an attribute filter. Finally, we perform a set of Bias/Variance decomposition experiments to analyse the source of improvement in comparison to a base classifier