In sa-lee/liminal: Multivariate Data Visualization with Tours and Embeddings

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(ggplot2)
theme_set(theme_bw())

This example is modified from the examples tours described in @Cook2018-jm. Here we use a tour to explore principal components space and any non-linear structure and clusters via t-SNE.

Setting up the data

Data were obtained from CT14HERA2 parton distribution function fits as used in @Cook2018-jm. There are 28 directions in the parameter space of parton distribution function fit, each point in the variables labelled X1-X56 indicate moving +- 1 standard deviation from the 'best' (maximum likelihood estimate) fit of the function. Each observation has all predictions of the corresponding measurement from an experiment. (see table 3 in that paper for more explicit details).

The remaining columns are:

• InFit: A flag indicating whether an observation entered the fit of CT14HERA2 parton distribution function
• Type: First number of ID
• ID: contains the identifier of experiment, 1XX/2XX/5XX corresponds to Deep Inelastic Scattering (DIS) / Vector Boson Production (VBP) / Strong Interaction (JET). Every ID points to an experimental paper.
• pt: the per experiment observational id
• x,mu: the kinematics of a parton. x is the parton momentum fraction, and mu is the factorisation scale.

First, we take the load the data as a data.frame:

library(liminal)
data(pdfsense)

Linear embeddings and the tour

First we can estimate all nrow(pdfsense) principal components using on the parton distribution fits:

pcs  <- prcomp(pdfsense[, 7:ncol(pdfsense)])

Using this data structure, we can produce a screeplot:

res <- data.frame(
  component = 1:56, 
  variance_explained = cumsum(pcs$sdev / sum(pcs$sdev))
)

ggplot(res, aes(x = component, y = variance_explained)) +
  geom_point() +
  scale_x_continuous(
    breaks = seq(0, 60, by = 5)
  ) +
  scale_y_continuous(
    labels = function(x) paste0(100*x, "%")
  )

Approximately 70% of the variance in the pdf fits are explained by the first 15 principal components.

Next we augment our original data with the principal components:

pdfsense <- dplyr::bind_cols(
  pdfsense, 
  as.data.frame(pcs$x)
)
pdfsense$Type <- factor(pdfsense$Type)

We can view a simple tour vialimn_tour() and color points by their experimental group

limn_tour(pdfsense, PC1:PC6, Type)

Non-Linear embeddings

Now we can set up a non-linear embedding via t-SNE, here we embed all 56 principal components.

set.seed(3099)
start <- clamp_sd(as.matrix(dplyr::select(pdfsense, PC1, PC2)), sd = 1e-4)
tsne <- Rtsne::Rtsne(
  dplyr::select(pdfsense, PC1:PC56),
  pca = FALSE, 
  normalize = TRUE,
  perplexity = 50,
  exaggeration_factor = nrow(pdfsense) / 100,
  Y_init = start
)

Once we have run t-SNE we tidy it into a data.frame, to perform a linked tour.

tsne_embedding <- as.data.frame(tsne$Y)
tsne_embedding <- dplyr::rename(tsne_embedding, tsneX = V1, tsneY = V2)
tsne_embedding$Type <- pdfsense$Type

We can view the clusters using a static scatter plot:

ggplot(tsne_embedding, 
       aes(x = tsneX, y = tsneY, color = Type)) +
  geom_point() +
  scale_color_manual(values = limn_pal_tableau10())

We can link a tour view next to the embedding to give us a clear picture of the clustering:

limn_tour_link(
  tour_data = pdfsense,
  embed_data = tsne_embedding,
  cols = PC1:PC6,
  color = Type
)

References {-}

sa-lee/liminal documentation built on June 1, 2021, 9:41 p.m.