Daniel Mckenzie.

About me.

From 2019--2022 I will be an Assistant Adjunct Professor (ie. a postdoc) within the Computational and Applied Mathematics group at UCLA . My primary advisor is Wotao Yin . I received my PhD from the University of Georgia in May 2019. My advisor was Ming-Jun Lai . Prior to that I was an undergraduate at University of Cape Town from where I also received my Master's degree. In between Cape Town and Athens, Georgia I spent a semester at the University of Bayreuth in Germany, working with Professor Fabrizio Catanese and his Lehrstuhl. You can find a copy of my CV here . On the right is a photo of me and my dad; I am the one on the left.

Research Interests.

I am primarily interested in applied and computational mathematics. I enjoy using techniques from compressed sensing, graph theory and geometry to provide theoretically sound solutions to problems of practical interest in data science.

Publications:

  1. Compressive Sensing for cut improvement and local clustering. , joint with Ming-Jun Lai.
    • Abstract: We show how one can phrase the cut improvement problem for graphs as a sparse recovery problem, whence one can use algorithms originally developed for use in compressive sensing. We use this new cut improvement approach as an algorithmic primitive to design new methods for local clustering and semi-supervised clustering.
    • Accepted for publication in the SIAM journal on the Mathematics of Data Science (SIMODS).
    • Final draft available here .
    • (MATLAB) code for this project available here .
    • Note this paper subsumes earlier versions, available here and here .
  2. Power Weighted Shortest Paths for Clustering Euclidean Data , joint with Steven Damelin.
    • Abstract: We study the use of power weighted shortest path distance functions for clustering high dimensional Euclidean data, under the assumption that the data is drawn from a collection of disjoint low dimensional manifolds. We argue, theoretically and experimentally, that this leads to higher clustering accuracy. We also present a fast algorithm for computing these distances
    • Journal Reference: Foundations of Data Science, September 2019
    • Click here for the journal version and here for the arXiv preprint.
    • As part of this project we developed a novel, Dijkstra-like, algorithm for determining the k nearest neighbors of a Euclidean data point, with respect to any power weighted path distance or the longest leg path distance. Click here for the MATLAB code.

Teaching.

Winter 2020

Fall 2019

Fall 2018

I am not teaching this semester.

Spring 2018

Notes.

Below are links to various short expository papers written primarily for my own benefit, to my masters and honours thesis and to the slides of various talks that I have given.

Machine Learning

Geometry

Mathematical Finance

Signal Processing

Outreach.

While at the University of Cape Town I was involved with a really great organisation called SHAWCO . I worked on a project that offered after-school tuition to learners from three schools in the Kensington area of Cape Town. We found the worksheets developed by the Malati Group as well as the Answer Series Books to be very useful.

Contact.

You can reach me at [my surname]@math.ucla.edu. The email addresses [my surname]@math.uga.edu and danmac29[at]uga.edu will work until mid-2020. My office is MS 5346.