Here we are now at the middle of the fourth large part of this talk.get nowheremore quotes

# piet mondrian: fun

In Silico Flurries: Computing a world of snow. Scientific American. 23 December 2017

# visualization + design

The 2018 Pi Day art celebrates the 30th anniversary of $\pi$ day and connects friends stitching road maps from around the world. Pack a sandwich and let's go!

# $\pi$ Day 2015 Art Posters

2018 $\pi$ day shrinks the world and celebrates road trips by stitching streets from around the world together. In this version, we look at the boonies, burbs and boutique of $\pi$ by drawing progressively denser patches of streets. Let's go places.
2017 $\pi$ day
2016 $\pi$ approximation day
2016 $\pi$ day
2015 $\pi$ day
2014 $\pi$ approx day
2014 $\pi$ day
2013 $\pi$ day
Circular $\pi$ art

On March 14th celebrate $\pi$ Day. Hug $\pi$—find a way to do it.

For those who favour $\tau=2\pi$ will have to postpone celebrations until July 26th. That's what you get for thinking that $\pi$ is wrong.

If you're not into details, you may opt to party on July 22nd, which is $\pi$ approximation day ($\pi$ ≈ 22/7). It's 20% more accurate that the official $\pi$ day!

Finally, if you believe that $\pi = 3$, you should read why $\pi$ is not equal to 3.

All art posters are available for purchase.
I take custom requests.

Not a circle in sight in the 2015 $\pi$ day art. Try to figure out how up to 612,330 digits are encoded before reading about the method. $\pi$'s transcendental friends $\phi$ and $e$ are there too—golden and natural. Get it?

This year's $\pi$ day is particularly special. The digits of time specify a precise time if the date is encoded in North American day-month-year convention: 3-14-15 9:26:53.

The art has been featured in Ana Swanson's Wonkblog article at the Washington Post—10 Stunning Images Show The Beauty Hidden in $\pi$.

We begin with a square and progressively divide it. At each stage, the digit in $pi$ is used to determine how many lines are used in the division. The thickness of the lines used for the divisions can be attenuated for higher levels to give the treemap some texture.

Representing a number using a tree map. Each digit of the number is used to successively divide a shape, such as a square. (zoom)

This method of encoding data is known as treemapping. Typically, it is used to encode hierarchical information, such as hard disk spac usage, where the divisions correspond to the total size of files within directories.

At each level of the tree map, more digits are encoded. Shown here are tree maps for $pi$ for the first 6 levels of division. (zoom)

This kind of treemap can be made from any number. Below I show 6 level maps for $pi$, $phi$ (Golden ratio) and $e$ (base of natural logarithm).

At each level of the tree map, more digits are encoded. Shown here are tree maps for $pi$ for the first 6 levels of division. (zoom)

The number of digits per level, $n_i$ and total digits, $N_i$ in the tree map for $pi$, $phi$ and $e$ is shown below for levels $i = 1 .. 6$.

$PI PHI e i n_i N_i n_i N_i n_i N_i 1 1 1 1 1 1 1 2 4 5 2 3 3 4 3 15 20 9 12 19 23 4 98 118 59 71 96 119 5 548 666 330 401 574 693 6 2962 3628 1857 2258 3162 3855 7 16616 20244 10041 12299 17541 21396 8 91225 111469 9 500861 612330$

## Dividing the map

In all the treemaps above, the divisions were made uniformly for each rectangle. With uniform division, the lines that divide a shape are evenly spaced. With randomized division, the placement of lines is randomized, while still ensuring that lines do not coincide.

# Machine learning: supervised methods (SVM & kNN)

Thu 18-01-2018
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.

Nature Methods Points of Significance column: Machine learning: supervised methods (SVM & kNN). (read)

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.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

# Human Versus Machine

Tue 16-01-2018
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

Thu 18-01-2018
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.

Nature Methods Points of Significance column: Machine learning: a primer. (read)

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.