A recent open access paper by Nicholas Tierney and Dianne Cook — professors at Monash University — deals with simpler handling, exploring, and imputation of missing values in data.They present new methodology building upon tidy data principles, with a goal to integrating missing value handling as an integral part of data analysis workflows. New data structures are defined (like the nabular) along with new functions to perform common operations (like gg_miss_case).
These new methods have bundled among others in the R packages naniar and visdat, which I highly recommend you check out. To put in the author’s own words:
The naniar and visdat packages build on existing tidy tools and strike a compromise between automation and control that makes analysis efficient, readable, but not overly complex. Each tool has clear intent and effects – plotting or generating data or augmenting data in some way. This reduces repetition and typing for the user, making exploration of missing values easier as they follow consistent rules with a declarative interface.
The below showcases some of the highly informational visuals you can easily generate with naniar‘s nabulars and the associated functionalities.
For instance, these heatmap visualizations of missing data for the airquality dataset. (A) represents the default output and (B) is ordered by clustering on rows and columns. You can see there are only missings in ozone and solar radiation, and there appears to be some structure to their missingness.
Another example is this upset plot of the patterns of missingness in the airquality dataset. Only Ozone and Solar.R have missing values, and Ozone has the most missing values. There are 2 cases where both Solar.R and Ozone have missing values.
You can also generate a histogram using nabular data in order to show the values and missings in Ozone. Values are imputed below the range to show the number of missings in Ozone and colored according to missingness of ozone (‘Ozone_NA‘). This displays directly that there are approximately 35-40 missings in Ozone.
Alternatively, scatterplots can be easily generated. Displaying missings at 10 percent below the minimum of the airquality dataset. Scatterplots of ozone and solar radiation (A), and ozone and temperature (B). These plots demonstrate that there are missings in ozone and solar radiation, but not in temperature.
Finally, this parallel coordinate plot displays the missing values imputed 10% below range for the oceanbuoys dataset. Values are colored by missingness of humidity. Humidity is missing for low air and sea temperatures, and is missing for one year and one location.
R’s standard correlation functionality (base::cor) seems very impractical to the new programmer: it returns a matrix and has some pretty shitty defaults it seems. Simon Jackson thought the same so he wrote a tidyverse-compatible new package: corrr!
Simon wrote some practical R code that has helped me out greatly before (e.g., color palette’s), but this new package is just great. He provides an elaborate walkthrough on his own blog, which I can highly recommend, but I copied some teasers below.
Diagram showing how the new functionality of corrr works.
Apart from corrr::correlate to retrieve a correlation data frame and corrr::stretch to turn that data frame into a long format, the new package includes corrr::focus, which can be used to simulteneously select the columns and filter the rows of the variables focused on. For example:
# install.packages("tidyverse")
library(tidyverse)
# install.packages("corrr")
library(corrr)
# install.packages("here")
library(here)
dir.create(here::here("images")) # create an images directory
mtcars %>%
corrr::correlate() %>%
# use mirror = TRUE to not only select columns but also filter rows
corrr::focus(mpg:hp, mirror = TRUE) %>%
corrr::network_plot(colors = c("red", "green")) %>%
ggplot2::ggsave(
filename = here::here("images", "mtcars_networkplot.png"),
width = 5,
height = 5
)
With corrr::networkplot you get an immediate sense of the relationships in your data.
Let’s try some different visualizations:
mtcars %>%
corrr::correlate() %>%
corrr::focus(mpg) %>%
dplyr::mutate(rowname = reorder(rowname, mpg)) %>%
ggplot2::ggplot(ggplot2::aes(rowname, mpg)) +
# color each bar based on the direction of the correlation
ggplot2::geom_col(ggplot2::aes(fill = mpg >= 0)) +
ggplot2::coord_flip() +
ggplot2::ggsave(
filename = here::here("images", "mtcars_mpg-barplot.png"),
width = 5,
height = 5
)
The tidy correlation data frames can be easily piped into a ggplot2 function call
corrr also provides some very helpful functionality display correlations. Take, for instance, corrr::fashion and corrr::shave:
mtcars %>%
corrr::correlate() %>%
corrr::focus(mpg:hp, mirror = TRUE) %>%
# converts the upper triangle (default) to missing values
corrr::shave() %>%
# converts a correlation df into clean matrix
corrr::fashion() %>%
readr::write_excel_csv(here::here("correlation-matrix.csv"))
Exporting a nice looking correlation matrix has never been this easy.
Finally, there is the great function of corrr::rplot to generate an amazing correlation overview visual in a wingle line. However, here it is combined with corr::rearrange to make sure that closely related variables are actually closely located on the axis, and again the upper half is shaved away:
Generate fantastic single-line correlation overviews with <code>corrr::rplot</code>
For some more functionalities, please visit Simon’s blog and/or the associated GitHub page. If you copy the code above and play around with it, be sure to work in an Rproject else the here::here() functions might misbehave.
Nicolas Rougier, Michael Droettboom, Philip Bourne wrote an open access article for the Public Library of Open Science (PLOS) in 2014, proposing ten simple rules for better figures. Below I posted these 10 rules and quote several main sentences extracted from the original article.
Rule 1: Know Your Audience
It is important to identify, as early as possible in the design process, the audience and the message the visual is to convey. The graphical design of the visual should be informed by this intent. […] The general public may be the most difficult audience of all since you need to design a simple, possibly approximated, figure that reveals only the most salient part of your research.
Rule 2: Identify Your Message
It is important to clearly identify the role of the figure, i.e., what is the underlying message and how can a figure best express this message? […] Only after identifying the message will it be worth the time to develop your figure, just as you would take the time to craft your words and sentences when writing an article only after deciding on the main points of the text.
Rule 3: Adapt the Figure to the Support Medium
Ideally, each type of support medium requires a different figure, and you should abandon the practice of extracting a figure from your article to be put, as is, in your oral presentation. […] For example, during an oral presentation, a figure will be displayed for a limited time. Thus, the viewer must quickly understand what is displayed and what it represents while still listening to your explanation.
Rule 4: Captions Are Not Optional
The caption explains how to read the figure and provides additional precision for what cannot be graphically represented. This can be thought of as the explanation you would give during an oral presentation, or in front of a poster, but with the difference that you must think in advance about the questions people would ask. […] if there is a point of interest in the figure (critical domain, specific point, etc.), make sure it is visually distinct but do not hesitate to point it out again in the caption.
Rule 5: Do Not Trust the Defaults
All plots require at least some manual tuning of the different settings to better express the message, be it for making a precise plot more salient to a broad audience, or to choose the best colormap for the nature of the data.
Rule 6: Use Color Effectively
As explained by Edward Tufte [1], color can be either your greatest ally or your worst enemy if not used properly. If you decide to use color, you should consider which colors to use and where to use them. […] However, if you have no such need, you need to ask yourself, “Is there any reason this plot is blue and not black?”
Rule 7: Do Not Mislead the Reader
What distinguishes a scientific figure from other graphical artwork is the presence of data that needs to be shown as objectively as possible. […] As a rule of thumb, make sure to always use the simplest type of plots that can convey your message and make sure to use labels, ticks, title, and the full range of values when relevant.
Example from the paper on how visualization parameters can convey a misleading message.
Rule 8: Avoid “Chartjunk”
Chartjunk refers to all the unnecessary or confusing visual elements found in a figure that do not improve the message (in the best case) or add confusion (in the worst case). For example, chartjunk may include the use of too many colors, too many labels, gratuitously colored backgrounds, useless grid lines, etc. The term was first coined by Edward Tutfe [1]; he argues that any decorations that do not tell the viewer something new must be banned: “Regardless of the cause, it is all non-data-ink or redundant data-ink, and it is often chartjunk.” Thus, in order to avoid chartjunk, try to save ink, or electrons in the computing era.
Rule 9: Message Trumps Beauty
There exists a myriad of online graphics in which aesthetic is the first criterion and content comes in second place. Even if a lot of those graphics might be considered beautiful, most of them do not fit the scientific framework. Remember, in science, message and readability of the figure is the most important aspect while beauty is only an option.
Rule 10: Get the Right Tool
Matplotlib is a python plotting library, primarily for 2-D plotting, but with some 3-D support, which produces publication-quality figures in a variety of hardcopy formats and interactive environments across platforms. It comes with a huge gallery of examples that cover virtually all scientific domains (http://matplotlib.org/gallery.html).
R is a language and environment for statistical computing and graphics. R provides a wide variety of statistical (linear and nonlinear modeling, classical statistical tests, time-series analysis, classification, clustering, etc.) and graphical techniques, and is highly extensible.
Inkscape is a professional vector graphics editor. It allows you to design complex figures and can be used, for example, to improve a script-generated figure or to read a PDF file in order to extract figures and transform them any way you like.
TikZ and PGF are TeX packages for creating graphics programmatically. TikZ is built on top of PGF and allows you to create sophisticated graphics in a rather intuitive and easy manner, as shown by the Tikz gallery (http://www.texample.net/tikz/examples/all/).
GIMP is the GNU Image Manipulation Program. It is an application for such tasks as photo retouching, image composition, and image authoring. If you need to quickly retouch an image or add some legends or labels, GIMP is the perfect tool.
ImageMagick is a software suite to create, edit, compose, or convert bitmap images from the command line. It can be used to quickly convert an image into another format, and the huge script gallery (http://www.fmwconcepts.com/imagemagick/index.php) by Fred Weinhaus will provide virtually any effect you might want to achieve.
D3.js (or just D3 for Data-Driven Documents) is a JavaScript library that offers an easy way to create and control interactive data-based graphical forms which run in web browsers, as shown in the gallery at http://github.com/mbostock/d3/wiki/Gallery.
Cytoscape is a software platform for visualizing complex networks and integrating these with any type of attribute data. If your data or results are very complex, cytoscape may help you alleviate this complexity.
Circos was originally designed for visualizing genomic data but can create figures from data in any field. Circos is useful if you have data that describes relationships or multilayered annotations of one or more scales.
You can download the PDF version of the full article here.
[1] Tufte EG (1983) The Visual Display of Quantitative Information. Cheshire, Connecticut: Graphics Press.
Picular.co calls itself Google, but for colors on its website. And not without good reason. On the site, you type in a color association (e.g., forest green), and it provides you an palette overview of associated colors and their hexadecimal (Hex) codes.
I don’t precisely know how it works, but it seems to work quite well!
I recently got pointed towards a 2017 paper on bioRxiv that blew my mind: three researchers at the Computational Neuroscience Laboratories at Kyoto, Japan, demonstrate how they trained a deep neural network to decode human functional magnetic resonance imaging (fMRI) patterns and then generate the stimulus images.
In simple words, the scholars used sophisticated machine learning to reconstruct the photo’s their research particpants saw based on their brain activity… INSANE! The below shows the analysis workflow, and an actual reconstructed image. More reconstructions follow further on.
Figure 1 | Deep image reconstruction. Overview of deep image reconstruction is shown. The pixels’ values of the input image are optimized so that the DNN features of the image are similar to those decoded from fMRI activity. A deep generator network (DGN) is optionally combined with the DNN to produce natural-looking images, in which optimization is performed at the input space of the DGN. [original]Three healthy young adults participated in two types of experiments: an image presentation experiment and an imagery experiment.
In the image presentation experiments, participants were presented with several natural images from the ImageNet database, with 40 images geometrical shapes, and with 10 images of black alphabetic characters. These visual stimuli were rear-projected onto a screen in an fMRI scanner bore. Data from each subject were collected over multiple scanning sessions spanning approximately 10 months. Images were flashed at 2 Hz for several seconds. In the imagery experiment, subjects were asked to visually imagine / remember one of 25 images of the presentation experiments. Subjects were
required to start imagining a target image after seeing some cue words.
In both experimental setups, fMRI data were collected using 3.0-Tesla Siemens MAGNETOM Verio scanner located at the Kokoro Research Center, Kyoto University.
The results, some of which I copied below, are plainly amazing.
Figure 2 | Seen natural image reconstructions. Images with black and gray frames show presented and reconstructed images, respectively (reconstructed from VC activity). a) Reconstructions utilizing the DGN (using DNN1–8). Three reconstructed images correspond to reconstructions from three subjects. b) Reconstructions with and without the DGN (DNN1–8). The first, second, and third rows show presented images, reconstructions with and without the DGN, respectively. c) Reconstruction quality of seen natural images (error bars, 95% confidence interval (C.I.) across samples; three subjects pooled; chance level, 50%). d) Reconstructions using different combinations of DNN layers (without the DGN). e) Subjective assessment of reconstructions from different combinations of DNN layers (error bars, 95% C.I. across samples) [original]Figure 3 | Seen artificial shape reconstructions. Images with black and gray frames show presented and reconstructed images (DNN 1–8, without the DGN). a) Reconstructions for seen colored artificial shapes (VC activity). b, Reconstruction quality of colored artificial shapes. c) Reconstructions of colored artificial shapes obtained from multiple visual areas. d) Reconstruction quality of shape and colors for different visual areas. e) Reconstructions of alphabetical letters. f) Reconstruction quality for alphabetical letters. For b, d, f, error bars indicate 95% C.I. across samples (three subjects pooled; chance level, 50%) [original] Supplementary Figure 2 | Other examples of natural image reconstructions obtained with the DGN. Images with black and gray frames show presented and reconstructed images, respectively (reconstructed from VC activity using all DNN layers). Three reconstructed images correspond to reconstructions from three subjects. [original]Supplementary Figure 3 | Reconstructions through optimization processes. Reconstructed images obtained through the optimization processes are shown (reconstructed from VC activity of Subject 1 using all DNN layers and the DGN). Images with black and gray frames show presented and reconstructed images, respectively. [original]There were many more examples of reconstructed images, as well as much more detailed information regarding the machine learning approach and experimental setup, so I strongly advise you check out the orginal paper.
I can’t even imagine what such technology would imply for society… Proper minority report stuff here.
Here’s the abstract as an additional teaser:
Abstract
Machine learning-based analysis of human functional magnetic resonance imaging
(fMRI) patterns has enabled the visualization of perceptual content. However, it has been limited to the reconstruction with low-level image bases (Miyawaki et al., 2008; Wen et al., 2016) or to the matching to exemplars (Naselaris et al., 2009; Nishimoto et al., 2011). Recent work showed that visual cortical activity can be decoded (translated) into hierarchical features of a deep neural network (DNN) for the same input image, providing a way to make use of the information from hierarchical visual features (Horikawa & Kamitani, 2017). Here, we present a novel image reconstruction method, in which the pixel values of an image are optimized to make its DNN features similar to those decoded from human brain activity at multiple layers. We found that the generated images resembled the stimulus images (both natural images and artificial shapes) and the subjective visual content during imagery. While our model was solely trained with natural images, our method successfully generalized the reconstruction to artificial shapes, indicating that our model indeed ‘reconstructs’ or ‘generates’ images from brain activity, not simply matches to exemplars. A natural image prior introduced by another deep neural network effectively rendered semantically meaningful details to reconstructions by constraining reconstructed images to be similar to natural images. Furthermore, human judgment of reconstructions suggests the effectiveness of combining multiple DNN layers to enhance visual quality of generated images. The results suggest that hierarchical visual information in the brain can be effectively combined to reconstruct perceptual and subjective images.
Past week, Analytics in HR published a guest blog about one of my People Analytics projects which you can read here. In the blog, I explain why and how I examined the turnover of management trainees in light of the international work assignments they go on.
For the analyses, I used a statistical model called a survival analysis – also referred to as event history analysis, reliability analysis, duration analysis, time-to-event analysis, or proporational hazard models. It estimates the likelihood of an event occuring at time t, potentially as a function of certain data.
The sec version of surival analysis is a relatively easy model, requiring very little data. You can come a long way if you only have the time of observation (in this case tenure), and whether or not an event (turnover in this case) occured. For my own project, I had two organizations, so I added a source column as well (see below).
Alternatively, scatterplots can be easily generated. Displaying missings at 10 percent below the minimum of the airquality dataset. Scatterplots of ozone and solar radiation (A), and ozone and temperature (B). These plots demonstrate that there are missings in ozone and solar radiation, but not in temperature.
![journal.pcbi.1003833.g006[2].png](https://paulvanderlaken.com/wp-content/uploads/2018/09/journal-pcbi-1003833-g0062.png?w=1108)
paulvanderlaken.com 