Local biplots for multi-dimensional scaling, with application to the microbiome

by   Julia Fukuyama, et al.

We present local biplots, a an extension of the classic principal components biplot to multi-dimensional scaling. Noticing that principal components biplots have an interpretation as the Jacobian of a map from data space to the principal subspace, we define local biplots as the Jacobian of the analogous map for multi-dimensional scaling. In the process, we show a close relationship between our local biplot axes, generalized Euclidean distances, and generalized principal components. In simulations and real data we show how local biplots can shed light on what variables or combinations of variables are important for the low-dimensional embedding provided by multi-dimensional scaling. They give particular insight into a class of phylogenetically-informed distances commonly used in the analysis of microbiome data, showing that different variants of these distances can be interpreted as implicitly smoothing the data along the phylogenetic tree and that the extent of this smoothing is variable.



There are no comments yet.


page 1

page 2

page 3

page 4


Closed-Loop Data Transcription to an LDR via Minimaxing Rate Reduction

This work proposes a new computational framework for learning an explici...

Multi-dimensional Skyline Query to Find Best Shopping Mall for Customers

This paper presents a new application for multi-dimensional Skyline quer...

Implementation Strategies for Multidimensional Spreadsheets

Seasoned Excel developers were invited to participate in a challenge to ...

Modeling high-dimensional dependence among astronomical data

Fixing the relationship among a set of experimental quantities is a fund...

New Interpretation of Principal Components Analysis

A new look on the principal component analysis has been presented. First...

A Flexible Framework for Parallel Multi-Dimensional DFTs

Multi-dimensional discrete Fourier transforms (DFT) are typically decomp...

Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inference

In this paper, we study statistical inference of change-points (CPs) in ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.