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2011/07/05

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Chernoff and the Face Value of Numbers

Posted: 05 Jul 2011 05:03 AM PDT

Herman Chernoff

A smiley-face is very expressive, statistically. By tweaking the eyes, mouth and other bits, you can literally put a meaningful face on any jumble of numbers. Herman Chernoff pointed this out in 1973 in the Journal of the American Statistical Association, in a monograph called "The Use of Faces to Represent Points in K-Dimensional Space Graphically."

Subsequently, folks took to calling these things Chernoff faces. Chernoff faces can make statistical analysis into a recognizably human activity.

Most people, when shown some statistics, sigh and get boggled. But Herman Chernoff realized that almost everyone is good at reading faces. So he devised recipes to convert any set of statistics into an equivalent bunch of smiley-face drawings.

Each data point, he wrote, "is represented by a cartoon of a face whose features, such as length of nose and curvature of mouth, correspond to components of the point. Thus every multivariate observation is visualized as a computer-drawn face. This presentation makes it easy for the human mind to grasp many of the essential regularities and irregularities present in the data."

"The Use of Faces to Represent Points in K-Dimensional Space Graphically" is one of the few statistics papers that is visually goofy, rather than arid.

One page is filled with 87 cartoon faces, each slightly different. Some faces have little beady eyes, others have big, startled-wideawake peepers. There are wide mouths, little dried-up "I'm not here, don't notice me" mouths, and middling mouths. Another page shows off some of the cartoony variety that's possible: roundish simpleton heads, jowly alien-visitor heads, and a smattering of noggins that look froggy. Elsewhere, the study perhaps inevitably includes conventional statistics machinery — charts of numbers, differential and intergral calculus equations, and plenty of technical lingo.

Chernoff discovered, by experiment, that people could comfortably interpret a face that expresses quite large amounts of data. "At this point," he wrote, "one can treat up to 18 variables, but it would be relatively easy to increase that number by adding other features such as ears, hair, [and] facial lines."

Chernoff faces made from data gathered by measuring rocks, and presented in Chernoff's original paper in the Journal of the American Statistical Association. The paper explains that "Eight measurements were made on each of 88 nummulited specimens from the Eocene Yellow Limestone Formation of northwestern Jamaica."

The world has gone on to employ Chernoff faces a little, but not yet a lot. A 1981 report in the Journal of Marketing, for example, used them to display corporate financial data, with this explanation: "From Year 5 to Year 1, the nose narrows as well as increases in length, and the eccentricity of the eyes increases. Respectively, these facial features represent a decrease in total assets, an increase in the ratio of retained earnings to total assets, and an  increase in cash flow."

A note at the very end of Chernoff's 1973 paper hints at a practical reason why his idea would not catch on immediately: "At this time the cost of drawing these faces is about 20 to 25 cents per face on the IBM 360-67 at Stanford University using the Calcomp Plotter. Most of this cost is in the computing, and I believe that it should be possible to reduce it considerably."

Chernoff faces representing data about a series of Swiss bank notes, some real, some forged, from Bernhard Flury and Hans Riedwyl,'s 1981 study in the Journal of the American Statistical Association. The main variables are:
Xl length of the bank note
X2 width of the bank note, measured on the left side
X3 width of the bank note, measured on the right side
X4 width of the lower margin
X5 width of the upper margin
X6 length of the print diagonal from the lower left to the upper right corner

References
"The Use of Faces to Represent Points in K-Dimensional Space Graphically," Herman Chernoff, Journal of the American Statistical Association, vol. 68, no. 342, 1973, pp. 361–8.

"Facial Representation of Multivariate Data," David L. Huff, Vijay Mahajan and William C. Black, Journal of Marketing, vol. 45, no. 4, Autumn 1981, pp. 53-9.

"Use of Chernoff Faces to Follow Trends in Laboratory Data," John A. Lott and Timothy C. Durbridge, Journal of Clinical Laboratory Analysis, 1990, pp. 459-63. The authors are at Ohio State University in the USA and the Institute of Medical and Veterinary Sciences in Adelaide, Australia.

"Graphical Representation of Multivariate Data by Means of Asymmetrical Faces," Bernhard Flury and Hans Riedwyl, Journal of the American Statistical Association, vol. 76, no. 376, December 1981, pp. 757-65. The authors are at the University of Berne, Switzerland.

_____________________

This article is republished with permission from the July-August 2010 issue of the Annals of Improbable Research. You can download or purchase back issues of the magazine, or subscribe to receive future issues. Or get a subscription for someone as a gift!

Visit their website for more research that makes people LAUGH and then THINK.

Egypt's Art Of Revolution

Posted: 05 Jul 2011 04:21 AM PDT

A new exhibition in London’s Mica Gallery will feature contemporary Egyptian art, much of which depicts themes and imagery from the Arab revolution. The exhibit includes graffiti from the streets of Cairo re-created on a gallery wall and a mummified man wrapped in pages from the Qur’an. Read more about this exhibition at the Guardian link.

Link

Monkeys Try Their Hand At Photography

Posted: 05 Jul 2011 04:17 AM PDT

Photographer David Slater had his picture taken by a crested black macaque in an Indonesian national park when the curious little critter figured out how to trigger the shutter release button on his tripod mounted camera. Soon, it seemed as if the monkeys actually knew that they were on to something, and they continued to snap shot after shot, showing an intelligence and problem solving ability macaques had been assumed not to possess. What’s next for the shutterbug macaque, a job directing in Hollywood?

Link

Unmanned Glider May Hold Secret To Perpetual Flight

Posted: 05 Jul 2011 04:14 AM PDT

Engineers from the Australian Centre for Field Robotics in Sydney are working on an autopilot system for gliders that senses thermals and adjusts its course, utilizing the thermal currents to stay aloft. Couple that ability with the technique of dynamic soaring, where the glider flies between high and lower speed air currents to keep it aloft when thermals aren’t readily available, and perpetual flight might become a reality sooner than we ever could have imagined.

Link

The Sound of A Sleeping Seal

Posted: 05 Jul 2011 02:44 AM PDT

(Video Link)

Who knew seal snores were so adorable?

Via BuzzFeed

A Collection of Pictures of Basset Hounds Running

Posted: 05 Jul 2011 01:19 AM PDT

We’ve already showed one of these great pictures of basset hounds running, but it’s hard to get enough of these floppy-faced pups. Check out more pics over at BuzzFeed.

Link

College Professor Makes Action Figures of Co-Workers

Posted: 05 Jul 2011 01:11 AM PDT

Over at the Neatoshop, we have some cool personalized bobbleheads and portraits, but I can’t help but wish that we were able to add Dr. Jesse Weiss’ custom action figures to our shop, but for now we will have to appreciate his collection of action figures based on his colleagues at The University of the Ozarks.

Link Via The Mary Sue

How Fireworks Work

Posted: 05 Jul 2011 12:34 AM PDT

If watching all the fireworks shows last night got you wondering how those balls of light are actually created and manipulated, this great infographic can help fill you in on the details. Be sure to click the link to view the whole graphic.

Link

15 Cool Outdoor Barbeques

Posted: 04 Jul 2011 11:39 PM PDT

I know the Forth of July is pretty much over by now, but summer sure leaves us with plenty of time for grilling and while many of us are ok with the classic dome-grills, these 15 awesome grills on WebUrbanist are certainly a lot more stylish. I’m a particularly big fan of this wall-mounted grill.

Link

Manhattan in Miniature

Posted: 04 Jul 2011 11:07 PM PDT

Randy Hage is a Los Angeles-based artist on a mission to preserve the crumbling storefronts of Manhattan–one 1/12-scale miniature at a time. The project started when Hage noticed the generic and mass-produced logos of chain stores and restaurants shoving the small, worn shopfronts right out of the city. "My goal is to document and bring greater attention to those disappearing storefronts," he said. There are more examples of Hage’s awesome miniatures in the capsule he curated for How to Be a Retronaut. Link

Chestnut Wins Fifth Hot Dog Title

Posted: 04 Jul 2011 05:12 PM PDT

The annual July 4th hot dog eating contest was held today in front of Nathan’s Famous Hot Dogs in Coney Island. And once again, American Joey Chestnut defeated all the others by scarfing down 62 hot dogs.

It wasn’t a personal best for the 27-year-old nicknamed Jaws, but it was enough to out-eat second-place finisher Patrick Bertoletti by nine wieners. Chestnut, of San Jose, Calif., won $10,000 and the coveted mustard-yellow belt.

“I feel great!” he said after the contest, adding that he was going to drink a lot of water and avoid hot dogs for a few days.

In a separate division for women, Sonya Thomas ate 40 hot dogs to claim the pink belt championship. Chestnut’s longtime rival, Takeru Kobayashi, did not participate because he refused to sign a contract with the eating league. Link -via J-Walk Blog

Paparazzi Shades

Posted: 04 Jul 2011 01:19 PM PDT

Paparazzi Shades | $9.95

Protect yourself against embarrassing photos by setting a black rectangle over your eyes -before your picture is taken- with Paparazzi Shades from the NeatoShop! Censor bars hide your identity even in real life, so your fans (and friends) can snap away while your anonymity is protected. Paparazzi Shades make a great gift, too!

Check out other pranks and gag gifts from the NeatoShop!

4th of July for Math Nerds

Posted: 04 Jul 2011 01:16 PM PDT


(YouTube link)

Josh Sundquist shares some charts and graphs about fireworks, pie, and other Independence Day traditions. -via Buzzfeed

Melvin the Magical Mixed Media Machine

Posted: 04 Jul 2011 11:59 AM PDT

(Vimeo link)

HEYHEYHEY, the studio behind Melvin the Magical Mixed Media Machine (or just Melvin the Machine, or just Melvin)  designed this Rube Goldberg machine with a bit of a twist–instead of just performing simple tasks with mind-bending inefficiency, Melvin’s also in the business of self-promotion. While Melvin is performing, he takes pictures, makes videos of his audience, then uploads them to his blog, Facebook and Twitter accounts. He also screen-prints merchandise. All of these things can be found on Melvin’s site. Link

via G.TDW

Spider Weaves a Web in Space

Posted: 04 Jul 2011 09:33 AM PDT

(Video link)

A national education program being carried out right now on the International Space Station involves watching the behavior or animals and insects in microgravity. This video is of Esmerelda, a golden silk orb-weaver spider (Nephila clavipes), weaving a web in her new low-gravity home. Typically, an orb-weaver will spin an asymmetrical web, but researchers have noticed that those spun by the two spiders on the ISS are becoming more circular. In addition, the spiders no longer sit at the tops of their webs facing downwards, and are instead hanging out in all sorts of positions to look out for their captured prey–something that doesn’t happen here on Earth.

Read more about the experiment and the oddities in Esmeralda’s behavior on New Scientist. Link

Other People’s Papers

Posted: 04 Jul 2011 09:04 AM PDT

An article at The New Inquiry is a conversation between a college-level philosophy teacher and a person who writes college papers for money. Much of it concerns the prevalence, ease, and mechanics of cheating on papers, whether the work is plagiarized or commissioned. But this explanation of why so many students cheat saddened me:

I think that the system, grading in general, grading as a gold standard of employability, college as the necessary step between high school and employment, all of these things alone aren't necessarily wrong. But when you get them all together in this network, and college is going to define your future, the grades will determine where you go, one, for a fifth of you, those of you who are going to grad school or law school or med school. For the rest of you, to get that job, you need that paper that says, "Diploma," which means you need to pass. That's all that matters.

If the only purpose in going to college is to get a diploma (not knowledge, not an education, and not good grades), then its no wonder students assume that you should get one just for paying the tuition and arranging for the required papers by any means necessary. Link -via TYWKIWDBI, where you can join the discussion.

(Image credit: The “Gold Guys”)

Unicorn Sneeze

Posted: 04 Jul 2011 07:07 AM PDT

A Tweet from @ProdigalSam gives us this adorable Twaggie drawn by David Barneda. Like all Twaggies, you can buy it on a t-shirt if you like. Link

Star-Spangled Cosplay

Posted: 04 Jul 2011 06:51 AM PDT

Who looks more patriotically American: Superman, Captain America, or Wonder Woman? Take a close look at a gallery of cosplay photographs of these and other heroes posted to celebrate the Fourth of July at Geeks Are Sexy and decide for yourself! Link

Camera Attached to Fireworks

Posted: 04 Jul 2011 06:49 AM PDT


(YouTube link)

Jeremiah Warren attached a small (and tough) camera to fireworks and captured quite a few POV sequences. Some launches had the camera facing up and some were facing down. -via Cynical-C

The Shocking True Tale Of The Mad Genius Who Invented Sea-Monkeys

Posted: 04 Jul 2011 06:48 AM PDT

Did you ever order Sea Monkeys from an ad in the back of a comic book? The man behind the “Bowlfull of Happiness” was Harold von Braunhut, who’s life was so much more than sea monkeys.

The accounts Von Braunhut gave of his adventures in American kitsch are consistently winning. Granted, he makes some claims that a skeptic is inclined to independently confirm. At some point in the years after he raced motorcycles as The Green Hornet, von Braunhut worked as a talent agent of sorts. He tells Planet X about a stunt performer he used to manage—the article has von Braunhut calling him "a fella by the name of Henry Lamore"—who would dive from a height of 40 feet into a kiddie pool filled with 12 inches of water. I began to lose faith while trying to verify this doozy, but it turns out that the Internet allows you to watch a man named Henri LaMothe still pulling off this feat at 71 years old, as an opening act for Evel Knievel.

As anyone sold by the Sea-Monkey ads could tell you, it was hard to say exactly where von Braunhut was walking on the terrain between truth, embellishment and con. That was his gift. He convinced us to look at the jazz hands and lose sight of the footwork. Von Braunhut's inventions were not quite what they seemed to be. Neither was he.

Von Braunhut was best known for his Sea Monkeys, but it was only one of his 195 patents. Even more unusual was his association with the Aryan Nation. Link -via Nag on the Lake

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