The 1-d manifold embedding of high-dimensional data and its application in data classification and image inpainting
Speaker:Prof. Jianzhong WANG
Department of Mathematics and Statistics
Sam Houston State University, Huntsville
Date & Time:21 May 2014 (Wednesday) 15:30 - 16:30
Venue:J319 (University of Macau)
Organized by:Department of Computer and Information Science

Abstract

Recently, the image-patch ordering method has been introduced in image processing. The method sorts patches of an image into a sequence so that on which we may apply 1-d signal processing technique. However, the sorting method above does not count the metric between the sorted data: All points on the sequence are uniformly arranged. In this talk, we introduce a 1-d manifold embedding model for the data sorting. In the model, we consider the data set residing on a curve in a high dimensional space. Then we isometrically map the data set onto a straight line so that a metric is defined on the data. Since the metric more precisely describes the similarity of the sorted data, when we apply interpolation, filtering, and other operators on the data, we will obtain more accurate results. We have applied the new model in handwritten digits classification and image inpainting and obtained better results than other existent methods.

Biography

Prof. Jianzhong Wang received his Bachelor degree in Mathematics from Peking University, China, in 1967, Master Degree in Mathematics from Zhejiang University, China, in 1981 and PhD degree in Wuhan University, China, in 1984. Since 2003, he has been working at the Department of Mathematics and Statistics, Sam Houston State University as a Professor. Currently he is the Associate Chief-Editor of the International Journal of Applicable Analysis, USA. His research areas include: 1) Splines, wavelets, and their applications; 2) Mathematical methods in image science and 3) High-dimensional data processing and dimensionality reduction.