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A good distance metric is instrumental on the performance of many tasks including classification and data retrieval. However, designing an optimal distance function is very challenging, especially when the data has high dimensions.Recently, a number of algorithms have been proposed to learn an optimal distance function in a supervised manner, using data with class labels. In this thesis we proposed methods to learn an optimal distance function that can also indicate the importance of attributes.Specifically, we present several ways to define idealized distance functions, two of which involving distance error correction involving KNN classification, and another involving a two-constant defined distance function. Then we use multiple linear regression to produce regression formulas to represent the idealized distance functions. Experiments indicate that distances produced by our approaches have classification accuracy that are fairly comparable to existing methods. Importantly, our methods have added bonus of using weights on attributes to indicate the importance of attributes in the constructed optimal distance functions. Finally, the thesis presents importance of attributes on a number of datasetsfrom the UCI repository.

In the current study the pressure transient behavior of various coal samples was investigated by using the finite element approach. Finite element analyses were performed on fourteen coal samples with different physical dimensions. Two pressure transients, namely Sine-6 and A-Spike pressure pulses, were used in the research study. Fluid compressibility values of CO2 and Argon were used to perform the analyses. A fracture width of 1mm was considered for each sample to investigate the influence of fluid type on coal permeability. The influence of elastic modulus of coal sample, fracture porosity, fracture width, and fluid compressibility were investigated. The finite element analyses for each sample were performed in two different ways: (a) without considering a fracture in the coal sample and (b) considering a fracture in the coal sample. The permeability of each sample was determined by comparing numerical results with available experimental data.;The calibrated finite element models were extended to determine the permeability of fractured coal samples. The numerically determined fracture permeability is much higher than the reported permeability values obtained by assuming a homogeneous medium. The results obtained from the numerical models compare well with the available experimental data on coal permeability.