resources
visualizations
presentations
lunch break
Distractions and amusements, with a sandwich and coffee.
visualization + design
Hilbert Curve Art, Hilbertonians and Monkeys
I collaborated with Scientific American to create a data graphic for the September 2014 issue. The graphic compared the genomes of the Denisovan, bonobo, chimp and gorilla, showing how our own genomes are almost identical to the Denisovan and closer to that of the bonobo and chimp than the gorilla.
Here you'll find Hilbert curve art, a introduction to Hilbertonians, the creatures that live on the curve, an explanation of the Scientific American graphic and downloadable SVG/EPS Hilbert curve files.
Hilbertonians—creatures on the Hilbert Curve
Take a look at the Hilbertonian Posters and perhaps buy one. I take custom requests.
Survey of Hilbertonians
Below are some surveys that sample viable Hilbertonians. All of these Hilbertonians appear unique on the curve—they are all different with respect to rotation and flipping. Some of these have been turned into Hilbertonian posters, which you can buy.
To represent all of the 104,976 viable Hilbertonians we require that the lowest order curve on which they are drawn has at least 104,976 points.
An order 9 curve almost satisfies this requirement, with 49 = 262,144 points. So, if curves of order 9, 10 and 11 are used, they can enumerate the full set of viable Hilbertonians.
It's much easier to display all the shape-unique ones, of which there are 13,689.
To represent all 220 Hilbertonians, which includes the non-viable ones, we need to solve `4^n = 2^20` which gives `n=10`. So, if we draw curves of order 10, 11 and 12 we can show every possible Hilbertonian genome.
news + thoughts
Statistics vs Machine Learning
We conclude our series on Machine Learning with a comparison of two approaches: classical statistical inference and machine learning. The boundary between them is subject to debate, but important generalizations can be made.Inference creates a mathematical model of the datageneration process to formalize understanding or test a hypothesis about how the system behaves. Prediction aims at forecasting unobserved outcomes or future behavior. Typically we want to do both and know how biological processes work and what will happen next. Inference and ML are complementary in pointing us to biologically meaningful conclusions.
Statistics asks us to choose a model that incorporates our knowledge of the system, and ML requires us to choose a predictive algorithm by relying on its empirical capabilities. Justification for an inference model typically rests on whether we feel it adequately captures the essence of the system. The choice of pattern-learning algorithms often depends on measures of past performance in similar scenarios.
Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Statistics vs machine learning. Nature Methods 15:233–234.
Background reading
Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.
Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: supervised methods. Nature Methods 15:5–6.
Happy 2018 `\pi` Day—Boonies, burbs and boutiques of `\pi`
Celebrate `\pi` Day (March 14th) and go to brand new places. Together with Jake Lever, this year we shrink the world and play with road maps.
Streets are seamlessly streets from across the world. Finally, a halva shop on the same block!
Intriguing and personal patterns of urban development for each city appear in the Boonies, Burbs and Boutiques series.
No color—just lines. Lines from Marrakesh, Prague, Istanbul, Nice and other destinations for the mind and the heart.
The art is featured in the Pi City on the Scientific American SA Visual blog.
Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day and 2017 `\pi` Day.
Machine learning: supervised methods (SVM & kNN)
Supervised learning algorithms extract general principles from observed examples guided by a specific prediction objective.We examine two very common supervised machine learning methods: linear support vector machines (SVM) and k-nearest neighbors (kNN).
SVM is often less computationally demanding than kNN and is easier to interpret, but it can identify only a limited set of patterns. On the other hand, kNN can find very complex patterns, but its output is more challenging to interpret.
We illustrate SVM using a data set in which points fall into two categories, which are separated in SVM by a straight line "margin". SVM can be tuned using a parameter that influences the width and location of the margin, permitting points to fall within the margin or on the wrong side of the margin. We then show how kNN relaxes explicit boundary definitions, such as the straight line in SVM, and how kNN too can be tuned to create more robust classification.
Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Machine learning: a primer. Nature Methods 15:5–6.
Background reading
Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.
Human Versus Machine
Balancing subjective design with objective optimization.In a Nature graphics blog article, I present my process behind designing the stark black-and-white Nature 10 cover.
Nature 10, 18 December 2017
Machine learning: a primer
Machine learning extracts patterns from data without explicit instructions.In this primer, we focus on essential ML principles— a modeling strategy to let the data speak for themselves, to the extent possible.
The benefits of ML arise from its use of a large number of tuning parameters or weights, which control the algorithm’s complexity and are estimated from the data using numerical optimization. Often ML algorithms are motivated by heuristics such as models of interacting neurons or natural evolution—even if the underlying mechanism of the biological system being studied is substantially different. The utility of ML algorithms is typically assessed empirically by how well extracted patterns generalize to new observations.
We present a data scenario in which we fit to a model with 5 predictors using polynomials and show what to expect from ML when noise and sample size vary. We also demonstrate the consequences of excluding an important predictor or including a spurious one.
Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.
Snowflake simulation
Symmetric, beautiful and unique.Just in time for the season, I've simulated a snow-pile of snowflakes based on the Gravner-Griffeath model.
The work is described as a wintertime tale in In Silico Flurries: Computing a world of snow and co-authored with Jake Lever in the Scientific American SA Blog.
Gravner, J. & Griffeath, D. (2007) Modeling Snow Crystal Growth II: A mesoscopic lattice map with plausible dynamics.