On the Use of Continuous Wavelet Transforms to Analyse Accelerometer Data Collected by the NAT Device to Characterise Parkinson's Disease

Parkinson’s disease (PD) is treated using drugs with powerful side-effects, and has similar symptoms to a range of other diseases. It is therefore important to diagnose PD accurately, and then to monitor its progression, to avoid mis-prescribing and under- and over-prescription of these drugs. Although diagnosis by experts in PD is fairly accurate, there is certainly room for improvement, and most initial diagnoses are carried out by non-expert medical staff with a much lower degree of accuracy. It is therefore desirable that automatic methods of diagnosis and monitoring be developed, and this Thesis examines the use of wavelets like those used in the Continuous Wavelet Transform (CWT), using wavelets extracted from the data itself, to try and detect features in the data pertaining to PD patients and controls. We believe that we have successfully automatically detected distinct features, with the proviso that this has been done with very little data, opening up the possibility of tracking the development of the disease as different characteristics alter in importance, or of distinguishing subtypes of PD (analyses of the genome have determined that such subtypes exist). However, the CWTs generated by wavelets corresponding to individual features, do not suffice as a basis for diagnosis, as the features may only be intermittently present. In combination, either with other wavelets of the same type, or other methods entirely, diagnosis remains a possibility. We used Neural Acquisition Tracker (NAT) devices to obtain tri-axial accelerometer data as input to these methods, and will analyse the effect of finite bandwidth on their performance. We believe the following list sums up the main novelty of our techniques: Libraries of motion shapes: at least within the field of the analysis of the motion of PD subjects; Representing motion shapes: by equivalence classes of piecewise polynomial wavelet triplets, which are invariant under rotations and reflections; Distance functions: working out the form of a distance based on the L_2 distance between individual functions, but which works on the equivalence classes mentioned above; hierarchical k-medoids: an approximation to k-medoids, using the clustering of cluster centres, which runs faster than k-medoids.