Geometry and Machine Learning: A Survey for Data Scientists and Machine Learning Researchers

Tracking #: 536-1516


Colleen FarrellyORCID logo

Responsible editor: 

Karin Verspoor

Submission Type: 

Position Paper


Many machine learning algorithms and statistical models rely heavily upon matrices and linear algebra for computation. Linear algebra is well-suited to modern computing, as operations can be computed quickly, have decent enough accuracy, and only rely on a few assumptions about the data (usually relating to linear independence of columns/rows, sample sizes being larger than the number of predictors, and determinant values of the matrix). However, assumptions sometimes fail in the real world, and accuracy is not always as good as a machine learning practitioner might need. Data may not even lie within a linear space. Fortunately, a plethora of alternatives to linear-algebra-based algorithms are being actively developed, providing machine learning researchers and data scientists with many useful tools. This new set of tools and algorithms is highlighting problem areas within many popular machine learning frameworks, creating tools that can work on extremely small datasets or datasets with many correlated predictors, and exploring the synergy between disparate fields of mathematics and computer science. Many of these algorithms rely on data and model geometry, and the methods detailed in Part 1 (algebraic geometry) and Part 2 (differential geometry) of this overview are only a small subset of those being actively explored and developed.



  • Reviewed

Data repository URLs: 


Date of Submission: 

Monday, June 11, 2018

Date of Decision: 

Friday, August 3, 2018



Solicited Reviews:


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Meta-Review by Editor

The reviewers have acknowledged that topic of the paper is relevant, and a paper which provides a comprehensive survey of the relationship between algebraic geometry and machine learning would have significant value. However, both reviewers observe that the survey is currently too shallow, and does not adequately reflect the current state of the art in the field. It is a short manuscript which does not introduce the core concepts in sufficient depth or with sufficient mathematical rigor. There are inadequate references to papers in the field, and as such cannot really be considered a "survey". The author is advised to reconsider the scope, audience, and objectives of the manuscript.

Karin Verspoor (