MCM美国大学生数学建模竞赛题目与答案：运动与措施，音乐的发展和音乐影响.pdf
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2023-08-21
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Problem Chosen
D
2021
MCM/ICM
Summary Sheet
Team Control Number
2125654
The music industry is an extraordinarily complex system of influence between songs, artists, and
genres that grows with each passing year. We examine this system and its components in an effort to
understand how influence shapes the landscape of the music world. Our procedures utilize data
provided by Spotify’s API, containing information about influencers and followers and various
metrics describing the musical nature of artists and their songs.
We construct a directed network based on artist influence data and use it to examine the structure and
meaning of influence within a genre. We also employ neural networks to predict artists’ genres and
influencers. Additionally, we apply descriptive procedures to various data on musical metrics for
individual songs and artists, allowing us to study inter- and intra-genre trends over time and the
defining characteristics of genres. We also introduce our own measure of similarity based on the
Euclidean distance between a subset of these metrics, useful in assessing similarity between songs,
artists and genres.
We first observe some key global trends, including a rise in the prominence of high-energy genres
over time, and a decline in global acousticness consistent with the development timeline of relevant
technology. We also examine trends in individual metrics within individual genres, which provide
insight into the global trends.
In order to investigate the nature of genres, we create a neural network that uses the provided metrics
to predict the genre of an artist given their time period. Our technique yielded an approximately 80
percent success rate in predicting whether a song is of the pop/rock genre, which may suggest that the
data provided on artists and songs may be good indicators of genre. When running our neural network
on R&B versus country songs, we found that the neural network more accurately classified the R&B
songs as non-pop/rock than country, suggesting similarities between the two genres according to the
given metrics during this time period.
We also directly examine the metrics of songs by genre to illustrate these similarities and differences.
Beginning in this portion, we apply the techniques in these broad analyses, to a closer study of the
pop/rock genre. We examine trends in pop/rock song metrics, and how these trends change when data
is weighted by artist popularity, giving insight into the unique traits of top influencers.
We also explore trends in influence, including but not limited to changes in the primary sources of
influence and the dynamic tendency of followers to deviate from their influencers’ genre. From this,
we discovered that majority of pop/rock followers were classified themselves as pop/rock, warranting
further study. Moreover, we discover that over time, the most influential artists in a given time period
become less influential overall, indicating that artists may be taking influence from a broader scope of
artists.
We then employ a subnetwork within modern pop/rock to study the degree similarity between
influencers and their followers. Using a second neural network, we attempt to predict whether an
artist is a follower of a given influencer. This may suggest that the given metrics alone are not capable
of indicating influence alone; we recommend further analysis.
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