A Survey on Linear and Non-Linear Dimensionality Reduction Techniques

Dimensionality Reduction (DR) is gaining more attention these days as a result of the increasing need to efficiently handle large amounts of data. The applications of DR cover many fields like Medical, Geographical, E-Commerce, simulation, and many more. DR plays an important part in selecting essential features. So that it reduces the dimensions of the dataset. The Dimensionality Reduction techniques were used to select the most relevant features of face recognition, Speaker identification, image annotation, and many more. Dimensionality Reductions are performed using linear and non-linear techniques. In this paper, the comparison of linear and nonlinear dimensionality reduction techniques is given based on previous analysis. Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Maximum Autocorrelation Factor (MAF), Slow Feature Analysis (SFA), Sufficient Dimension Reduction (SDR), Independent Component Analysis (ICA), Distance Metric Learning (DML), etc. are the most widely used linear dimensionality reduction techniques. The most commonly used nonlinear dimensionality reduction techniques are Locally Linear Embedding (LLE), Multidimensional scaling (MDS), Isomap, Hessian Locally Linear Embedding (HLLE), MVU, Diffusion Maps, Kernal PCA, Multilayer Autoencoder, Local Tangent Space Alignment (LTSA) and Laplacian Eigenmaps. This can be divided into Global nonlinear techniques and Local nonlinear techniques. This paper explains these techniques by pointing out flaws in current linear and nonlinear techniques and suggesting ways to improve the efficiency of linear and nonlinear dimensionality reduction techniques.