Clustering and its uses in Earthquakes

Shubhankar, , (2013) Clustering and its uses in Earthquakes. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS Dissertation of Shubhankar) Shubhankar-07MS20-MS_Thesis.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

We will here consider the problem of determining the structure of a clustered data, without any prior knowledge of the number of clusters/components or any other information about their structure. Data are represented by a mixture models in which each component or group represents a different cluster. Here we will take general as well as heuristic approaches towards finding out structures of such clusters and then use the same to analyze simulated as well as natural data and hence extract qualitative information about earth quakes. If we make a simplistic assumption that most naturally occurring data follow normal distributions then using various parameterizations and cross cluster constraints we can make models with varying geometric properties. Partitions are determined by the expectation-maximization (EM) algorithm for maximum likelihood, with initial values from agglomerative hierarchical clustering. We use a totally stochastic approach for calculation of optimal number of clusters, the Bayesian Information criterion, which allows us to compare multiple models at the same time and it is quite unlike the significance test. Besides, the Expectation Maximization technique used here also provides a good scale for the measurement of uncertainty of allocation of a data point. In the heuristic approach we propose another (a little coarse) pattern recognition method that is able to reconstruct the 3D structure of the active part of a fault network using the spatial locations of earth-quakes. This method is a generalization of the so-called ‘Dynamic Clustering Method’, which originally partitions a set of data-points into clusters, using a global minimization criterion over the spatial inertia of those clusters. The new method improves on ‘Dynamic Clustering Method’ by taking into account the full spatial inertia tensor of each cluster, in order to partition the dataset into fault-like, anisotropic clusters.

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