Data science has been transforming an enormous number of research areas. It has opened the door to new measures to analyze and extract useful information from raw data. However, while it has been applied extensively in computer science community, there has been a modest number of such applications in the field of robotics and biomedical engineering. In this dissertation, we consider the applications of data analysis and machine learning tools in two research topics: mobile robot localization and cardiovascular predictive models.In the first part of the dissertation, we tackle a problem of feature selection for appearance-based localization. Raw image is a high-dimensional source of data, and as the resolution of visual sensor has been improved rapidly, we are equipped with even higher dimensional and richer visual information. To deal with the high dimensionality problem, a common and straightforward strategy is to select the most effective visual features for the localization task, i.e., feature selection. In this dissertation, we propose two methods of feature selection. First of all, we model each dimension of the feature vector as a Gaussian process random field with the independent variables as the coordinates of the robot. Thus, the locations of the robot can be inferred by applying a maximum likelihood estimator. The optimal set of features are chosen by backward elimination scheme. Secondly, to minimize the localization error in spatial space and to select the optimal subset of features, we formulate a multivariate version of the Least Absolute Selection and Shrinkage Operator (LASSO) regression model. Under this formulation, we develop a combined localization scheme that consists of the regression and a filtering estimator.In the later part of this dissertation, we explore the use of predictive models to predict the growth of an abdominal artery under the progression of a disease, Abdominal Aortic Aneurysm (AAA). As a patient who is diagnosed with AAA, his/her artery may locally be enlarged in pathological conditions and finally ruptures, we develop two prediction approaches using two common types of AAA geometrical data: 3D shapes from computer tomography (CT) scans and 2D profile of maximal diameters over centerline. First of all, we develop our Dynamical Gaussian Process Implicit Surface (DGPIS) for 3D shape prediction. In this method, we consider a 3D surface as a manifold embedded in a scalar field over the 3D dimensional space, the changes of which propagate the changes in the surface. Thus, by utilizing a dynamic model to represent the evolution of the field over time, we can make an inference about the AAA surface in a future time. Secondly, maximal AAA diameter is a crucial criterion for making a surgery intervention decision in clinical practice. Thus, we investigate a Deep Belief Network (DBN) model that is trained on artificial data created from Probabilistic Collocation Method (PCM) and real patients based reconstructed data. Since the merit of DBN and deep structure in general depends on a massive size of training data, which is commonly rare in this application, we overcome the shortage by pre-training the DBN on simulated data generated from PCM, then fine-tuning the neural net on reconstructed data from the real patients. The experimental results illustrate the effectiveness of our proposed methods.
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