0000000000824666
AUTHOR
Raul V. Casana-eslava
Probabilistic quantum clustering
Abstract Quantum Clustering is a powerful method to detect clusters with complex shapes. However, it is very sensitive to a length parameter that controls the shape of the Gaussian kernel associated with a wave function, which is employed in the Schrodinger equation with the role of a density estimator. In addition, linking data points into clusters requires local estimates of covariance which requires further parameters. This paper proposes a Bayesian framework that provides an objective measure of goodness-of-fit to the data, to optimise the adjustable parameters. This also quantifies the probabilities of cluster membership, thus partitioning the data into a specific number of clusters, w…
Scalable implementation of measuring distances in a Riemannian manifold based on the Fisher Information metric
This paper focuses on the scalability of the Fisher Information manifold by applying techniques of distributed computing. The main objective is to investigate methodologies to improve two bottlenecks associated with the measurement of distances in a Riemannian manifold formed by the Fisher Information metric. The first bottleneck is the quadratic increase in the number of pairwise distances. The second is the computation of global distances, approximated through a fully connected network of the observed pairwise distances, where the challenge is the computation of the all sources shortest path (ASSP). The scalable implementation for the pairwise distances is performed in Spark. The scalable…
Quantum clustering in non-spherical data distributions: Finding a suitable number of clusters
Quantum Clustering (QC) provides an alternative approach to clustering algorithms, several of which are based on geometric relationships between data points. Instead, QC makes use of quantum mechanics concepts to find structures (clusters) in data sets by finding the minima of a quantum potential. The starting point of QC is a Parzen estimator with a fixed length scale, which significantly affects the final cluster allocation. This dependence on an adjustable parameter is common to other methods. We propose a framework to find suitable values of the length parameter σ by optimising twin measures of cluster separation and consistency for a given cluster number. This is an extension of the Se…
Robust Conditional Independence maps of single-voxel Magnetic Resonance Spectra to elucidate associations between brain tumours and metabolites.
The aim of the paper is two-fold. First, we show that structure finding with the PC algorithm can be inherently unstable and requires further operational constraints in order to consistently obtain models that are faithful to the data. We propose a methodology to stabilise the structure finding process, minimising both false positive and false negative error rates. This is demonstrated with synthetic data. Second, to apply the proposed structure finding methodology to a data set comprising single-voxel Magnetic Resonance Spectra of normal brain and three classes of brain tumours, to elucidate the associations between brain tumour types and a range of observed metabolites that are known to b…