Xiquan Shi, PhD
xshi [at] desu.edu
Ph.D. in Computational Mathematics, Jilin University, December 1988
B.S. in Computational Mathematics, Jilin University, December 1984
Clustering Analysis, Wavelet, Image Processing, Special Function.
Brief Non-technical Description of Research (for layperson)
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data mining, and a common technique for statistical data analysis, used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, bioinformatics, data compression, and computer graphics.
Wavelet or wavelet analysis is a profound development of Fourier analysis. Generally, wavelet is more efficient than Fourier Analysis to extract information from the unknown portions.
Image processing is a method to convert an image into digital form and perform some operations on it, in order to get an enhanced image or to extract some useful information from it. It is a type of signal dispensation in which input is image, like video frame or photograph and output may be image or characteristics associated with that image.
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications. There is no general formal definition, but the list of mathematical functions contains functions which are commonly accepted as special.
Recent Courses Taught
- Calculus I, Calculus II, Calculus III, Advanced Calculus I, Advanced Calculus II, Business Calculus
- Complex Analysis
- Functional Analysis
- College Algebra
Selected Recent Publications (3)
- Peng Zheng and Xiquan Shi, The use of the dyadic partition in elementary real analysis. Journal of Computational and Applied Mathematics, Volume 329, P 344-352, 2018
- Xiquan Shi, The Haar Wavelet Analysis of Matrices and its Applications, Journal of Mathematical Research with Applications, Vol. 37 No. 1 (No. 162), 2017, 19-28.
- Peng Zheng, Keni Zheng, Fengshan Liu, Xiquan Shi, Image registration by using mult-variate spline functions, Scientia Sinica Mathematica, 2015, 45: 1599-1610, doi: 10.1360/N012015-00024.