  Classification as a supervised learning concept is an important content in
machine learning. It aims at categorizing a set of data into classes. There are
several commonly-used classification methods nowadays such as k-nearest
neighbors, random forest, and support vector machine. Each of them has its own
pros and cons, and none of them is invincible for all kinds of problems. In
this thesis, we focus on Quadratic Multiform Separation (QMS), a classification
method recently proposed by Michael Fan et al. (2019). Its fresh concept, rich
mathematical structure, and innovative definition of loss function set it apart
from the existing classification methods. Inspired by QMS, we propose utilizing
a gradient-based optimization method, Adam, to obtain a classifier that
minimizes the QMS-specific loss function. In addition, we provide suggestions
regarding model tuning through explorations of the relationships between
hyperparameters and accuracies. Our empirical result shows that QMS performs as
good as most classification methods in terms of accuracy. Its superior
performance is almost comparable to those of gradient boosting algorithms that
win massive machine learning competitions.
