An adaptive k-nearest neighbor graph building technique with applications to hyperspectral imagery

Abstract

The analysis of remotely sensed spectral imagery has a variety of applications in both the public and private sectors, including tracking urban development, monitoring the spread of diseased crops, and mapping environmental disasters. The high spatial and spectral resolutions in hyperspectral imagery (HSI) make it particularly desirable for these types of analyses, as HSI sensors capture “color” information beyond what the human eye can see; this allows for greater differentiation between materials. However, those same properties can make HSI more difficult to analyze: traditional statistical or linear data models are not always able to well-model the high-dimensional HSI data for materially cluttered scenes. In recent years, the literature has shown an increase in the use of graph theory-based models for HSI analysis. These models are often used as the foundation for data transformations and manifold learning algorithms including Locally Linear Embedding, Commute Time Distance, and ISOMAP. A challenge associated with the graph building techniques used in these transformations is that they are typically k-nearest neighbor (kNN) graphs, which requires the user to designate a universal k value for the dataset. There is a need for an adaptive approach to building a kNN graph for HSI analysis so as to handle the particular characteristics of hyperspectral data in the spectral space, such as the sparse regions of data due to anomalies or rare targets in the scene, and the dense regions of data due to background clusters. Here, we present adaptive nearest neighbors, or ANN, which identifies a different k value for each pixel, so that pixels in denser regions have a higher k value and pixels in sparser regions have a lower k value. The resulting ANN graphs will be compared against kNN, and will be shown for synthetic data as well as hyperspectral data. While the focus here is on HSI, the ANN technique is applicable to any type of data analysis using a graph-based model.