<p dir="ltr">Unsupervised machine learning (ML) is essential for analyzing complex data without labels. Many challenges have been identified. This dissertation addresses three key challenges: clustering initialization, unsupervised feature selection, and dimension reduction for tensors. The thesis also applies unsupervised ML to the airborne LiDAR data.</p><p dir="ltr">Chapter 2 introduces an improved initialization strategy for K-Means clustering and Gaussian Mixture Models (GMM). The proposed method improves clustering stability and accuracy.</p><p dir="ltr">Chapter 3 develops a stepwise unsupervised feature selection framework, called the Forward Partial-Variable Clustering with Full-Variable Loss (FPCFL), to improve clustering performance in high-dimensional data.</p><p dir="ltr">Chapter 4 focuses on tensor dimension reduction and feature selection in multiway data. It introduces Low-Rank Sparse Tensor Approximation (LRSTA) for efficient data compression and High-Order Orthogonal Decomposition (HOOD) for improved sparsity and interpretability, particularly in large-scale datasets like image and video analysis.</p><p dir="ltr">Chapter 5 explores unsupervised ML in airborne LiDAR data, applying clustering and dimensionality reduction to enhance ground filtering and object detection in 3D point clouds.</p><p dir="ltr">This dissertation advances unsupervised ML by improving clustering reliability, optimizing feature selection, and enhancing tensor decomposition, contributing to more effective and scalable data-driven analysis.</p>