Geometrical learning, descriptive geometry, and biomimetic pattern recognition

Studies on learning problems from geometry perspective have attracted an ever increasing attention in machine learning, leaded by achievements on information geometry. This paper proposes a different geometrical learning from the perspective of high-dimensional descriptive geometry. Geometrical properties of high-dimensional structures underlying a set of samples are learned via successive projections from the higher dimension to the lower dimension until two-dimensional Euclidean plane, under guidance of the established properties and theorems in high-dimensional descriptive geometry. Specifically, we introduce a hyper sausage like geometry shape for learning samples and provides a geometrical learning algorithm for specifying the hyper sausage shapes, which is then applied to biomimetic pattern recognition. Experimental results are presented to show that the proposed approach outperforms three types of support vector machines with either a three degree polynomial kernel or a radial basis function kernel, especially in the cases of high-dimensional samples of a finite size. (c) 2005 Elsevier B.V. All rights reserved.

Cancer subtypes recognition and its gene expression profiles analysis based on geometrical learning

The accurate recognition of cancer subtypes is very significant in clinic. Especially, the DNA microarray gene expression technology is applied to diagnosing and recognizing cancer types. This paper proposed a method of that recognized cancer subtypes based on geometrical learning. Firstly, the cancer genes expression profiles data was pretreated and selected feature genes by conventional method; then the expression data of feature genes in the training samples was construed each convex hull in the high-dimensional space using training algorithm of geometrical learning, while the independent test set was tested by the recognition algorithm of geometrical learning. The method was applied to the human acute leukemia gene expression data. The accuracy rate reached to 100%. The experiments have proved its efficiency and feasibility.