A Study of Dimensionality Reduction Techniques and its Analysis on Climate Data

Abstract

Dimensionality reduction is a significant problem across a wide variety of domains such as pattern recognition, data compression, image segmentation and clustering. Different methods exploit different features in the data to reduce dimensionality. Principle component Analysis is one such method that exploits the variance in data to embed data onto a lower dimensional space called the principle component space. These are linear techniques which can be expressed in the form B=TX where T is the transformation matrix that acts on the data matrix X to the reduced dimensionality representation B. Other linear techniques explored are Factor Analysis and Dictionary Learning. In many problems, the observations are high-dimensional but we may have reason to believe that the they lie near a lower-dimensional manifold. In other words, we may believe that high-dimensional data are multiple, indirect measurements of an underlying source, which typically cannot be directly measured. Learning a suitable low-dimensional manifold from high-dimensional data is essentially the same as learning this underlying source. Techniques such as ISOMAP, Locally Linear Embedding, Laplacian EigenMaps (LEMs) and many others try to embed the high-dimensional observations in the non-linear space onto a low dimensional manifold. We will explore these methods making comparative studies and their applications in the domain of climate science.