Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - contact me Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca on Twitter Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Lumondo Photography Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Pi Art Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Hilbertonians - Creatures on the Hilbert Curve
Here we are now at the middle of the fourth large part of this talk.Pepe Deluxeget nowheremore quotes

numbers: beautiful


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


visualization + design

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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 2018 Art Posters - Stitched city road maps from around the world


Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 `\pi` day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` approximation day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 `\pi` day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
All art posters are available for purchase.
I take custom requests.

And if you've got to sleep a moment on the road
I will steer for you
And if you want to work the street alone
I'll disappear for you
—Leonard Cohen (I'm Your Man)

This year's is the 30th anniversary of `\pi` day. The theme of the art is bridging the world and making friends. So myself I again team up with my long-time friend and collaborator Jake Lever. I worled with Jake on the snowflake catalogue, where we build a world of flakes.

And so, this year we also build a world. We start with all the roads in the world and stitch them together in brand new ways. And if you walk more than 1 km in this world, you'll likely to be transported somewhere completely different.

This year's `\pi` day song is Trance Groove: Paris. Why? Because it's worth to go to new places—real or imagined.

The input data set to the art are all the roads in the world, as obtained from Open Street Map.

Road segments between intersections are represented by polylines and ends at intersections are snapped together to coincide with a resolution of 5–10 meters.

There are 108,366,429 polylines and together they span about 39,930,000 km.

extracting cities

We took 44 cities and sampled a square patch of 0.6 × 0.6 degrees of roads from the data set centered on the longitude and latitude coordinates below. This roughly corresponds to a square of 65 km × 65 km.

These center coordinates might be slightly different from the canonical ones associated with a city—I used Google Maps to center the coordinates on what I felt was a useful center for sampling streets. Below are these coordinates along with the number of polylines extracted.

           CITY    LATITUDE      LONGITUDE  POLYLINES
--------------- ------------ -------------  ---------
      amsterdam  52.38179720    4.90840330   98,965
        bangkok  13.72635950  100.53609560  154,348
      barcelona  41.38759720    2.17333560   86,575
        beijing  39.90487690  116.39331750   49,867
         berlin  52.51864170   13.40732310   64,336
   buenos_aires -34.61566250  -58.50333750  267,432
          cairo  30.05371250   31.23528970  108,524
     copenhagen  55.67346250   12.58781160   45,025
           doha  25.28233490   51.53479620   50,458
         dublin  53.34316360   -6.24433520   44,109
      edinburgh  55.94884870   -3.18828100   34,211
      hong_kong  22.31338230  114.16994610   36,329
       istanbul  41.03592820   28.98158110  190,938
        jakarta  -6.21858830  106.85252890  253,211
   johannesburg -26.20653880   28.05113830  128,840
         lisbon  38.73064000   -9.13667460   98,118
         london  51.50838960   -0.08585320  169,164
    los_angeles  34.04362360 -118.24505510  193,899
         madrid  40.41671290   -3.70329570  112,495
      marrakesh  31.63192610   -7.98895890   17,442
      melbourne -37.88286720  145.11800540  140,817
    mexico_city  19.39741470  -99.15827060  273,477
         moscow  55.75202630   37.61531070   40,043
         mumbai  19.18775070   72.97777590   65,316
        nairobi  -1.28718700   36.83157870   31,317
      new_delhi  28.61245350   77.21369970  262,503
       new_york  40.72187290  -73.92426750  199,652
           nice  43.70006260    7.26974590   25,564
          osaka  34.66944300  135.49965600  376,652
          paris  48.85837360    2.29229260  175,028
         prague  50.08022370   14.43002100   58,659
           rome  41.89659480   12.49983650   81,370
  san_francisco  37.77526950 -122.40966350   82,462
      sao_paulo -23.57343700  -46.63341590  267,742
          seoul  37.54869140  126.99479350  169,593
       shanghai  31.22590500  121.47386710   50,036
  st_petersburg  59.93029690   30.33955910   31,186
      stockholm  59.32318770   18.07408060   48,321
         sydney -33.86772020  151.20734660   76,820
          tokyo  35.69220740  139.75613010  694,893
        toronto  43.66328030  -79.38932030   73,173
      vancouver  49.25782630 -123.19394300   34,081
         vienna  48.20740250   16.37336040   53,669
         warsaw  52.23101840   21.01639680   54,870

Each city's road coordinates were then transformed using the equirectangular projection to make the distance between longitude meridians constant with latitude. This was done by $$ \phi' \leftarrow \phi - \text{avg}(\phi) $$ $$ \lambda' \leftarrow (\lambda - avg(\lambda)) \text{cos} (avg(\phi)) $$

where `\phi` is the latitude and `\lambda` is the longitude. The average is taken over the patch of roads extracted for the city. For all steps below these transformed coordinates were used.

copenhagen

Let's look at one city—Copenhagen—to get a feel for the data set.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The roads in and around Copenhagen. (zoom)

In the zoom crop below, you can see the intersections (dots) and the individual polylines that connect the intersections.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Downtown Copenhagen. (zoom)

Zooming in even more you can see the Christiansborg Slot, one of the Danish Palaces and the seat of the Danish Parliament (corresponding Google Map view).

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
In and around Christiansborg Slot (red dot) in downtown Copenhagen. (zoom)

creating city strips

City strips were created by sampling patches of 0.015 × 0.015 degrees (after transformation). This corresponds roughly to 1.7 km.

For each position in the strip, patches were sampled in order of the digits of `\pi` only if the number of polylines in the was `40d \le N < 40(d+1)-1` where `d` is the digit of `\pi`. Patches for `d=9` only need to have `360 \le N` polylines.

For example, the first patch is assigned to `d=3` and it must have `120 \le N < 159` polylines. The second patch is sampled so that its density is `40 \le N < 79` because it is associated with the next digit, `d=1`.

Further selection on acceptable patches is performed so that the streets line up with the previous patch. Minor local adjustments and stitching are performed to make the join appear seamless.

Below is an example of a set of city strips for Amsterdam, Bangkok, Beijing, Berlin, Copenhagen, Edinburgh, Hong Kong, Johannesburg, Marrakesh and Melbourne.


Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
On the road with 10 digits of `\pi`. City strips for Moscow, Mumbai, Nairobi, New Delhi, Nice, Prague, Rome, Stockholm, Vancouver and Warsaw. (BUY ARTWORK)

Below I zoom in on a portion of the city strips above to show the result of the stitching—individual street patches are outlined in blue squares.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Close-up of stitched streets in a city strip.

It's interesting to see that some patches (e.g. 4th one on the bottom strip, which is Copenhagen) don't necessarily have roads that across the patch horizontally.

creating world patches

World patches are a two-dimension version of city strips but they use more than one city.

Patches are sampled from cities based on the order of the digits of `\pi`, as arranged on a 6 × 6 grid. For example, the first row of patches corresponds to 314159 and the second 265358. Each digit is assigned to a city from which the corresponding patch is sampled.

As for city strips, patches are selected only if they align with previous patches. This is now trickier to do in two-dimensions because we must match a selected patch with up to two other patches already placed.

Unlike for city strips, there is no selection made for street density.

Below is a world patch using the following digit-to-city assignment: 0:Amsterdam, 1:Doha, 2:Marrakesh, 3:Mumbai, 4:Nairobi, 5:Rome, 6:San Francisco, 7:Seoul, 8:Shanghai and 9:Vancouver.


Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
On the road with 36 digits of `\pi`. A world patch using Amsterdam, Doha, Marrakesh, Mumbai, Nairobi, Rome, San Francisco, Seoul, Shanghai and Vancouver (BUY ARTWORK)

Below I zoom in on patches in the center of the image and show the cities from which the patches were sampled.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Close-up of stitched streets in a world patch.
VIEW ALL

news + thoughts

Statistics vs Machine Learning

Tue 03-04-2018
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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Statistics vs machine learning. (read)

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.

...more about the Points of Significance column

Happy 2018 `\pi` Day—Boonies, burbs and boutiques of `\pi`

Wed 14-03-2018

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!

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A great 10 km run loop between Istanbul, Copenhagen, San Francisco and Dublin. Stop off for halva, smørrebrød, espresso and a Guinness on the way. (details)

Intriguing and personal patterns of urban development for each city appear in the Boonies, Burbs and Boutiques series.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
In the Boonies, Burbs and Boutiques of `\pi` we draw progressively denser patches using the digit sequence 159 to inform density. (details)

No color—just lines. Lines from Marrakesh, Prague, Istanbul, Nice and other destinations for the mind and the heart.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Roads from cities rearranged according to the digits of `\pi`. (details)

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)

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.

Background reading

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

...more about the Points of Significance column

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.

...more about the Points of Significance column

Snowflake simulation

Tue 16-01-2018
Symmetric, beautiful and unique.

Just in time for the season, I've simulated a snow-pile of snowflakes based on the Gravner-Griffeath model.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A few of the beautiful snowflakes generated by the Gravner-Griffeath model. (explore)

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.