2013
DOI: 10.1109/tpami.2012.270
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Schroedinger Eigenmaps for the Analysis of Biomedical Data

Abstract: Abstract-We introduce Schroedinger Eigenmaps, a new semi-supervised manifold learning and recovery technique. This method is based on an implementation of graph Schroedinger operators with appropriately constructed barrier potentials as carriers of labeled information. We use our approach for the analysis of standard bio-medical datasets and new multispectral retinal images.Index Terms-Schroedinger Eigenmaps, Laplacian Eigenmaps, Schroedinger operator on a graph, barrier potential, dimension reduction, manifol… Show more

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Cited by 66 publications
(29 citation statements)
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(38 reference statements)
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“…An alternative to using only a single band is to apply a dimension reduction technique to the entire multispectral image, in order to combine the individual bands into a single representative image. Possible techniques for this are linear methods, such as PCA, and nonlinear methods, such as Laplacian eigenmaps [46] and related graph-kernel methods [47]. Taking as the input image the first principal component in the case of PCA, or the first eigenvector in the case of Laplacian eigenmaps, and then registering this to the reference image using our algorithm, is one approach to extending our method to full multispectral and hyperspectral images.…”
Section: Multispectral-to-panchromatic Registration Experimentsmentioning
confidence: 99%
“…An alternative to using only a single band is to apply a dimension reduction technique to the entire multispectral image, in order to combine the individual bands into a single representative image. Possible techniques for this are linear methods, such as PCA, and nonlinear methods, such as Laplacian eigenmaps [46] and related graph-kernel methods [47]. Taking as the input image the first principal component in the case of PCA, or the first eigenvector in the case of Laplacian eigenmaps, and then registering this to the reference image using our algorithm, is one approach to extending our method to full multispectral and hyperspectral images.…”
Section: Multispectral-to-panchromatic Registration Experimentsmentioning
confidence: 99%
“…Applications of MSI have shown promising results in different areas of biomedical image analysis ranging from human forearm imaging to skin chromophore mapping, [34][35][36][37][38] with several applied to retinal image analysis. [39][40][41][42] A recent study on retinal vein occlusion demonstrated that MSI was able to define vascular abnormalities at a comparable performance as fundus photography, fundus fluorescein angiography, and optical coherence tomography. 43 In MSI, image data are captured at specific nonoverlapping frequency bands.…”
Section: Resultsmentioning
confidence: 99%
“…Deep learning models have several drawbacks, such as the need for huge amounts of training data, high training time, large memory usage, and the complicated design of a suitable network. A semi-supervised technique was developed by Zheng et al 4 (see also Chen et al, 5 Xu et al, 6 and Wilkins et al; 7 for general learning techniques, we refer to Grady, 8 Czaja and Ehler, 9 Schölkopf and Smola, 10 and Roweis and Saul 11 ). Here we shall provide an efficient method with a fast learning part and low memory needs based on dimension reduction techniques.…”
Section: Introductionmentioning
confidence: 99%