mirror of
https://github.com/Brandon-Rozek/website.git
synced 2025-10-29 21:31:12 +00:00
73 lines
2.4 KiB
Markdown
73 lines
2.4 KiB
Markdown
---
|
|
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]
|
|
|