Artificial Intelligence in Finance, Volume 1: Fundamentals and Applications
First published:
ISBN: 9781782724353
If you are a Risk.net subscriber you are entitled to 20% off your Risk books purchases. Please email enquiries@riskbooks.com for more information.
As part of your Risk.net subscription you are entitled to 20% off all of your Risk Books purchases. If you would like to place an order please email enquiries@riskbooks.com
Unsupervised learning
Miquel Noguer i Alonso, Daniel Bloch and David Pacheco Aznar
Unsupervised learning
6.1 UNIFORM MANIFOLD APPROXIMATION AND PROJECTION FOR DIMENSION REDUCTION
The UMAP is an algorithm for dimensionality reduction. It was first proposed by McInnes et al (2018) with the objective of reducing the dimensionality of the given data. That is, the algo maps data in a way that tries to fit data from one dimension to another dimension, such that ℝn → ℝd, with dimensions d < n. The main difference from other dimensionality reduction algorithms is that instead of trying to preserve global or local distances, the UMAP aims to preserve topological distances using fuzzy topology.
The way the algorithm preserves topological characteristics is by first gathering information about the data structure and then using it to modify the data in such a way that the final structure reproduces the original one.
There are three axioms that are assumed to be true (McInnes et al 2018, p. 13).
There exists a manifold on which the data will be uniformly distributed.
The underlying manifold of interest is locally connected.
The primary goal is to preserve a topological structure of the manifold.
The algorithm has three main phases.
Construct a weighted graph depending on the distributional of the original
Copyright Infopro Digital Limited. All rights reserved.
As outlined in our terms and conditions, https://www.infopro-digital.com/terms-and-conditions/subscriptions/ (point 2.4), printing is limited to a single copy.
If you would like to purchase additional rights please email info@risk.net
Copyright Infopro Digital Limited. All rights reserved.
You may share this content using our article tools. As outlined in our terms and conditions, https://www.infopro-digital.com/terms-and-conditions/subscriptions/ (clause 2.4), an Authorised User may only make one copy of the materials for their own personal use. You must also comply with the restrictions in clause 2.5.
If you would like to purchase additional rights please email info@risk.net
