Kernel methods and deep learning are two major branches of machine learning that have achieved numerous successes in both analytics and artificial intelligence. While having their own unique characteristics, both branches work through mapping data to a feature space that is supposedly more favorable towards the given task. This dissertation addresses the strengths and weaknesses of each mapping method through combining them and forming a family of novel deep architectures that center around the Deep Embedding Kernel (DEK). In short, DEK is a realization of a kernel function through a newly deep architecture. The mapping in DEK is both implicit (like in kernel methods) and learnable (like in deep learning). Prior to DEK, we proposed a less advanced architecture called Deep Kernel for the tasks of classification and visualization. More recently, we integrate DEK with the novel Dual Deep Learning framework to model big unstructured data. Using DEK as a core component, we further propose two machine learning models: Deep Similarity-Enhanced K Nearest Neighbors (DSE-KNN) and Recurrent Embedding Kernel (REK). Both models have their mappings trained towards optimizing data instances\u27 neighborhoods in the feature space. REK is specifically designed for time series data. Experimental studies throughout the dissertation show that the proposed models have competitive performance to other commonly used and state-of-the-art machine learning models in their given tasks
