Cleaned up some old pages and uploaded some proceedings

content/notes/dimensionalityreduction/syllabus.md

@@ -0,0 +1,73 @@
+---
+title: Dimensionality Reduction Independent Study Syllabus
+---
+
+Dimensionality reduction is the process of reducing the number of random variables under consideration. This study will last for 10 weeks, meeting twice a week for about an hour.
+
+##  Introduction to Dimensionality Reduction (0.5 Week)
+
+- Motivations for dimensionality reduction
+- Advantages of dimensionality reduction
+- Disadvantages of dimensionality reduction
+
+## Feature Selection (3 Weeks)
+
+This is the process of selecting a subset of relevant features. The central premise of this technique is that many features are either redundant or irrelevant and thus can be removed without incurring much loss of information.
+
+### Metaheuristic Methods (1.5 Weeks)
+
+- Filter Method
+- Wrapper Method
+- Embedded Method
+
+### Optimality Criteria (0.5 Weeks)
+
+- Bayesian Information Criterion
+- Mallow's C
+- Akaike Information Criterion
+
+### Other Feature Selection Techniques (1 Week)
+
+- Subset Selection
+- Minimum-Redundancy-Maximum-Relevance (mRMR) feature selection
+- Global Optimization Formulations
+- Correlation Feature Selection
+
+### Applications of Metaheuristic Techniques (0.5 Weeks)
+
+- Stepwise Regression
+- Branch and Bound
+
+## Feature Extraction (6 Weeks)
+
+Feature extraction transforms the data in high-dimensional space to a space of fewer dimensions. In other words, feature extraction involves reducing the amount of resources required to describe a large set of data.
+
+### Linear Dimensionality Reduction (3 Weeks)
+
+- Principal Component Analysis (PCA)
+- Singular Value Decomposition (SVD)
+- Non-Negative Matrix Factorization
+- Linear Discriminant Analysis (LDA)
+- Multidimensional Scaling (MDS)
+- Canonical Correlation Analysis (CCA) [If Time Permits]
+- Linear Independent Component Analysis [If Time Permits]
+- Factor Analysis [If Time Permits]
+
+### Non-Linear Dimensionality Reduction (3 Weeks)
+
+One approach to the simplification is to assume that the data of interest lie on an embedded non-linear manifold within higher-dimensional space.
+
+- Kernel Principal Component Analysis
+- Nonlinear Principal Component Analysis
+- Generalized Discriminant Analysis (GDA)
+- T-Distributed Stochastic Neighbor Embedding (T-SNE)
+- Self-Organizing Map
+- Multifactor Dimensionality Reduction (MDR)
+- Isomap
+- Locally-Linear Embedding
+- Nonlinear Independent Component Analysis
+- Sammon's Mapping  [If Time Permits]
+- Hessian Eigenmaps  [If Time Permits]
+- Diffusion Maps  [If Time Permits]
+- RankVisu  [If Time Permits]
+