Spectral images provide a large amount of spectral information about a scene, but sometimes when studying images, we are interested in specific components. It is a difficult problem to separate the relevant information or what we call interesting from the background of a spectral image, even more so if our target objects are unknown. Anomaly detection is a process by which algorithms are designed to separate the anomalous (different) points from the background of an image. The data is complex and lives in a high dimension, manifold learning algorithms are used to analyze data that lives in a high dimensional space, but that can be represented as a lower dimensional manifold embedded in the high dimensional space. Laplacian Eigenmaps is a manifold learning algorithm that applies spectral graph theory to perform a non-linear dimensionality reduction that preserves local neighborhood information. We present an approach to reduce the dimension of the data and separate anomalous pixels in spectral images using Laplacian Eigenmaps.
Library of Congress Subject Headings
Remote sensing--Mathematics; Remote sensing--Data processing; Spectral theory (Mathematics); Graph theory; Laplacian operator; Machine learning
Department, Program, or Center
School of Mathematical Sciences (COS)
Munoz Reales, Marcela, "Laplacian eigenmaps manifold learning and anomaly detection methods for spectral images" (2010). Thesis. Rochester Institute of Technology. Accessed from
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