Page 30 - Undergraduate Research Opportunities Program Proceedings 2017-18

School of Science
Department of Mathematics

Department of Mathematics

Low-Rank and Sparsity Reconstruction in Data Science

Supervisor: CAI Jianfeng / MATH Co-Supervisor: YE Guibo / MATH
Student: JIANG Bo / MATH-SFM Course: UROP1100, Fall
ZHOU Weixuan / ECOF UROP1100, Fall

This paper tends to provide a brief analysis and some implementations of a popular algorithm in object detection,
namely, max-margin object detection (MMOD). To introduce this algorithm, a quick review of Platt’s fast training of
support vector machines (SVM) using sequential minimal optimization (SMO) will be provided. Some background
knowledge in Histograms of Oriented Gradients (HOG) and Convolutional Neural Network (CNN) will also be discussed.
Then this paper will analyze the main algorithms of MMOD and, using the publicly available library, implement the
algorithms and display the main results visually. Our results show that MMOD generally works well in avoiding false-
alarm, while there is still room for improvement in missed detections.

Combinatorial Studies of Gauss-Bonnet and Hopf Theorems
Supervisor: CHEN Beifang / MATH
Student: WAN Jingbo / MATH-IRE Course: UROP1100, Spring

This report focus on the classical Poincare-hopf theorem for vector field on 2-dim manifold and its generalization on
directed graph. The classical Poincare-hopf theorem is a theorem concerning the relation between isolated zeros of
smooth vector field and the topology of the smooth 2-manifold. Is is very surprise that the sum of index of any vector
field is a topological invariance. More precisely,

for any smooth vector field v on M. The significance of this poincare-hopf theorem is that χ(M) is a purely topology
quantity of the manifold, where the index of vector field is an analytic concept of a manifold, and this means poincare-
hopf theorem gives a relation between the topology or geometry and the analytic information of the manifold.

Statistical Analysis in Portfolio Construction

Supervisor: CHEN Kani / MATH
Student: ZHANG Kao / MATH Course: UROP2100, Fall

In this report, we first try to look at the drawback of classic portfolio construction methods such Markowitz’s risk-return.
Then we provide a self-contained 4-step routine to formulate an automated and general portfolio selection process,
taking the advantage of deep learning structure. Afterwards, we try to verify and demonstrate our theory in an example
of IBB Index. And finally, we conclude and would like to put down a few ideas of potential improvement.

Statistical Analysis in Competition Data

Supervisor: CHEN Kani / MATH
Student: ZHANG Yi / COMP Course: UROP1100, Summer

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