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72 lines
2.4 KiB
Markdown
72 lines
2.4 KiB
Markdown
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# Dimensionality Reduction Study
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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.
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## Introduction to Dimensionality Reduction (0.5 Week)
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- Motivations for dimensionality reduction
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- Advantages of dimensionality reduction
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- Disadvantages of dimensionality reduction
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## Feature Selection (3 Weeks)
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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.
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### Metaheuristic Methods (1.5 Weeks)
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- Filter Method
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- Wrapper Method
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- Embedded Method
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### Optimality Criteria (0.5 Weeks)
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- Bayesian Information Criterion
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- Mallow's C
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- Akaike Information Criterion
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### Other Feature Selection Techniques (1 Week)
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- Subset Selection
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- Minimum-Redundancy-Maximum-Relevance (mRMR) feature selection
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- Global Optimization Formulations
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- Correlation Feature Selection
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### Applications of Metaheuristic Techniques (0.5 Weeks)
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- Stepwise Regression
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- Branch and Bound
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## Feature Extraction (6 Weeks)
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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.
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### Linear Dimensionality Reduction (3 Weeks)
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- Principal Component Analysis (PCA)
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- Singular Value Decomposition (SVD)
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- Non-Negative Matrix Factorization
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- Linear Discriminant Analysis (LDA)
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- Multidimensional Scaling (MDS)
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- Canonical Correlation Analysis (CCA) [If Time Permits]
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- Linear Independent Component Analysis [If Time Permits]
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- Factor Analysis [If Time Permits]
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### Non-Linear Dimensionality Reduction (3 Weeks)
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One approach to the simplification is to assume that the data of interest lie on an embedded non-linear manifold within higher-dimensional space.
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- Kernel Principal Component Analysis
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- Nonlinear Principal Component Analysis
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- Generalized Discriminant Analysis (GDA)
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- T-Distributed Stochastic Neighbor Embedding (T-SNE)
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- Self-Organizing Map
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- Multifactor Dimensionality Reduction (MDR)
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- Isomap
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- Locally-Linear Embedding
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- Nonlinear Independent Component Analysis
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- Sammon's Mapping [If Time Permits]
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- Hessian Eigenmaps [If Time Permits]
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- Diffusion Maps [If Time Permits]
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- RankVisu [If Time Permits]
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