Diffusion bases dimensionality reduction

The overflow of data is a critical contemporary challenge in many areas such as hyper-spectral sensing, information retrieval, biotechnology, social media mining, classification etc. It is usually manifested by a high dimensional representation of data observations. In most cases, the information that is inherent in high-dimensional datasets is conveyed by a small number of parameters that correspond to the actual degrees of freedom of the dataset. In order to efficiently process the dataset, one needs to derive these parameters by embedding the dataset into a low-dimensional space. This process is commonly referred to as dimensionality reduction or feature extraction. We present a novel algorithm for dimensionality reduction - diffusion bases - which explores the connectivity among the coordinates of the data and is dual to the diffusion maps algorithm. The algorithm reduces the dimensionality of the data while maintaining the coherency of the information that is conveyed by the data.