Chapter 1. Introduction.- Chapter 2. General Framework of Mathematics.- Chapter 3. Problem Formulation.- Chapter 4. Development of Novel Techniques of CoCoSSC Method.- Chapter 5. Further Discussions of the Proposed Method.- Chapter 6. Related Work on Geometry of Non-Convex Programs.- Chapter 7. Gradient Descent Converges to Minimizers.- Chapter 8. A Conservation Law Method Based on Optimization.- Chapter 9. Improved Sample Complexity in Sparse Subspace Clustering with Noisy and Missing Observations.- Chapter 10. Online Discovery for Stable and Grouping Causalities in Multi-Variate Time Series.- Chapter 11. Conclusion.