Generalized N-dimensional principal component analysis (GND-PCA) and its application on construction of statistical appearance models for medical volumes with fewer samples

We propose a method called generalized N-dimensional principal component analysis (GND-PCA) for the modeling of a series of multi-dimensional data in this paper. In this method, the data are directly trained as the higher-order tensor and the bases in each mode subspace are calculated to compactly represent the data. Since GND-PCA analyzes the multi-dimensional data directly on each mode better performance on generalization than PCA. Additionally, since GND-PCA can compress the data in each mode subspace, it can represent the data more efficiently, compared to the recently proposed ND-PCA method. We apply the proposed GND-PCA method to construct the appearance models for 18 MR T1-weighted brain volumes and 25 CT lung volumes, respectively. The leave-one-out experiments show that the statistical appearance models built by our method can represent an untrained data well even though the models are trained by fewer samples. & 2009 Elsevier B.V. All rights reserved.