|dc.description.abstract||Raw data are usually required to be pre-processed for better representation or discrimination of classes. This pre-processing can be done by data reduction, i.e., either reduction in dimensionality or numerosity (cardinality). Dimensionality reduction can be used for feature extraction or data visualization. Numerosity reduction is useful for ranking data points or finding the most and least important data points. This thesis proposes several algorithms for data reduction, known as dimensionality and numerosity reduction, in machine learning and data science. Dimensionality reduction tackles feature extraction and feature selection methods while numerosity reduction includes prototype selection and prototype generation approaches. This thesis focuses on feature extraction and prototype selection for data reduction. Dimensionality reduction methods can be divided into three categories, i.e., spectral, probabilistic, and neural network-based methods. The spectral methods have a geometrical point of view and are mostly reduced to the generalized eigenvalue problem. Probabilistic and network-based methods have stochastic and information theoretic foundations, respectively. Numerosity reduction methods can be divided into methods based on variance, geometry, and isolation.
For dimensionality reduction, under the spectral category, I propose weighted Fisher discriminant analysis, Roweis discriminant analysis, and image quality aware embedding. I also propose quantile-quantile embedding as a probabilistic method where the distribution of embedding is chosen by the user. Backprojection, Fisher losses, and dynamic triplet sampling using Bayesian updating are other proposed methods in the neural network-based category. Backprojection is for training shallow networks with a projection-based perspective in manifold learning. Two Fisher losses are proposed for training Siamese triplet networks for increasing and decreasing the inter- and intra-class variances, respectively. Two dynamic triplet mining methods, which are based on Bayesian updating to draw triplet samples stochastically, are proposed. For numerosity reduction, principal sample analysis and instance ranking by matrix decomposition are the proposed variance-based methods; these methods rank instances using inter-/intra-class variances and matrix factorization, respectively. Curvature anomaly detection, in which the points are assumed to be the vertices of polyhedron, and isolation Mondrian forest are the proposed methods based on geometry and isolation, respectively.
To assess the proposed tools developed for data reduction, I apply them to some applications in medical image analysis, image processing, and computer vision. Data reduction, used as a pre-processing tool, has different applications because it provides various ways of feature extraction and prototype selection for applying to different types of data. Dimensionality reduction extracts informative features and prototype selection selects the most informative data instances. For example, for medical image analysis, I use Fisher losses and dynamic triplet sampling for embedding histopathology image patches and demonstrating how different the tumorous cancer tissue types are from the normal ones. I also propose offline/online triplet mining using extreme distances for this embedding. In image processing and computer vision application, I propose Roweisfaces and Roweisposes for face recognition and 3D action recognition, respectively, using my proposed Roweis discriminant analysis method. I also introduce the concepts of anomaly landscape and anomaly path using the proposed curvature anomaly detection and use them to denoise images and video frames. I report extensive experiments, on different datasets, to show the effectiveness of the proposed algorithms. By experiments, I demonstrate that the proposed methods are useful for extracting informative features and instances for better accuracy, representation, prediction, class separation, data reduction, and embedding. I show that the proposed dimensionality reduction methods can extract informative features for better separation of classes. An example is obtaining an embedding space for separating cancer histopathology patches from the normal patches which helps hospitals diagnose cancers more easily in an automatic way. I also show that the proposed numerosity reduction methods are useful for ranking data instances based on their importance and reducing data volumes without a significant drop in performance of machine learning and data science algorithms.||en