The manifold learning for dimensionality reduction with hyperspectral image

Hyperspectral remote sensing image (HSI) consists of hundreds of bands that contain rich space, radiation and spectral information. The high-dimensional data can also lead to the curse of dimensionality problem making it difficult to be used effectively. In this paper, we proposed a manifold learning algorithm to reduce the dimensionality for HSI data. For high dimensional datasets with continuous variables, it is often the case that the data points are arranged along with low dimensional structures, named manifolds, in the high dimensional space. Manifold learning aims to identifying those special low dimensional structures for subsequent usage such as classification or regression. However, many manifold learning algorithms perform an eigenvector analysis on a data similarity matrix whose size is N×N, where N is the number of data points. The memory complexity of the analysis is at least O(N
²
) that is not feasible for a regular computer to compute or storage for very large datasets. To solve this problem, we used statistical sampling methods to sample a subset of data points as landmarks. A skeleton of the manifold was then identified based on the landmarks. The remaining data points were then inserted into the skeleton by Locally Linear Embedding (LLE). We tested our algorithm on AVIRIS Salinas-A data set. The experimental results showed that the HSI dataset could be reduced to a lower-dimensional space for land use classification with good performance, and the main structure was preserved well.