Undergraduate Projects
Title Coming Soon
Emma Clifton, Hillsdale College
Honors Thesis 2019-2020
Abstract: In preparation
Regression based models for lineup performance and NBA player ratings
Jonathan Peters, Hillsdale College
Laureates 2018, Honors Thesis 2018-2019
Abstract: In a collaborative setting, it is useful to be able to assign credit for group outcomes to individual members, to identify individual contributions, and to predict the performance of the group. Here, we explore statistical methods for evaluating individual performances of professional basketball players based on lineup performance. Using data from the 2016-17 NBA season, we analyzed the effectiveness of various models for assessing individual offensive and defensive abilities and predicting the outcome of each possession based on the ten players on the floor. We show that commonly-used regularized adjusted plus minus models can be improved by regularizing each players’ ratings based on their total possessions played. We also show that classification models (logistic models) can outperform regression models when estimating defensive contributions.
Classification of audio signals through machine learning
Justin Rogers, Hillsdale College
Honors Thesis 2017-2018
Abstract: A four-second audio file contains at least 64000 separate data points. If the sound is a musical note, there is a much more succinct description: “Saxophone playing B4.” Our goal is to complete this classification algorithmically: can we give a computer a good ear for music? In this project, we examined the NSynth Dataset and applied techniques from topological data analysis to construct persistence diagrams, which provide geometric descriptions of the frequency spectrum. This reduces file size by a factor of 600, with negligible information loss. Using the persistent approach, we introduce several novel algorithms for pitch classification. In particular, the “PersistFFT2” algorithm is significantly more accurate than the other algorithms, indicating an advantage of the topological approach. To attain our final results, we use an ensemble learning technique to combine all our algorithms. This classifier was trained on a low dimensional representation of the original data and was able to determine the pitch and instrument with 90% and 91% accuracy respectively during cross validation exceeding the performance of each of its components.
Spontaneous synchrony on graphs and the emergence of order from Disorder
Dylan Linville,Rose-Hulman Institute of Technology; Daniel Trugillo Martins Fontes, University of Sao Paolo
R-Surf Program, Summer 2016
Abstract: From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior,
called oscillators, are found in a variety of different settings. When oscillators adjust their behavior
in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the
same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which
describes oscillators as dynamical systems on a graph and has been used to study synchronization
in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical
methods used to investigate the governing system of differential equations and the conditions that
lead to synchronization, and demonstrate that perfect synchronization occurs only under strict
conditions and for specific graph structures. We also present results from an experiment with coupled
metronomes in which spontaneous emergence of synchronization, consistent with the mathematical
theory, can be observed in a real-world setting.