Tag: Data

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Averages by John Hawkhead

mean median mode
learning my average
did not measure up

By John Hawkhead

In mathematics mean, mode and medium are different types of averages from a data set:

  • Mean is the average of a data set, calculated by adding all the data set numbers and then dividing the result by the total of values in the set.
  • Median is the middle value of a data set ordered from least to greatest.
  • Mode is the value that appears the most times in a set of data.

Further reading:

‘Central tendency’, Wikipedia article: https://en.wikipedia.org/wiki/Central_tendency

Author bio:

John Hawkhead (@HawkheadJohn) has been writing haiku and illustrating for over 25 years. His work has been published all over the world and he has won a number of haiku competitions. John’s books of haiku and senryu, ‘Small Shadows’ and ‘Bone Moon’, are now available from Alba Publishing (http://www.albapublishing.com/).

Enjoyed John’s sciku? Check out more of his sciku here: ‘Dark matter’, ‘Chirality’, ‘Spooky Interaction’, ‘Dancing’, ‘Planetarium’, ‘Empty Space’, ‘New Beginning’, ‘Interactions’, ‘Surface Tension’, and ‘Shell Game’.

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Low-rank Representation by Dr David Keyes

Vast sea of numbers,

Can you be described by few,

As bones define flesh?

 

Many data objects, such as matrices, which are traditionally described by providing a high precision number for every (row,column) entry, can be represented to usefully high precision by many fewer numbers. This so-called “data sparsity” holds for the mathematical descriptions of many physical and statistical phenomena whose effects or correlations decay smoothly with distance.

An apparently complex interaction or relationship is, with a special perspective, much simpler. In an extreme limit, we can lump the moon’s gravitational effect on the Earth by assuming that all of its distributed mass is concentrated at a single point. The potential to represent dense matrices by products of a small number of vectors (the number needed is called the “rank”) is analogous to this and leads to huge savings in memory and operations when manipulating such objects. The effect of the whole can be represented by a carefully defined abstraction. One version of this technique is called “skeletonization,” which suggests the Sciku above. For an example of this philosophy, see Yokota et al, 2014.

Original research:  https://doi.org/10.14529/jsfi140104

David Keyes directs the Extreme Computing Research Center at KAUST, where he was a founding dean in 2009. He inhabits the intersection of Mathematics, Computer Science, and applications, with a focus on colonizing emerging energy-efficient architectures for scientific computations. He is a Fellow of SIAM and AMS and has received the ACM Gordon Bell Prize and the IEEE Sidney Fernbach Award. As a lover of poetry, he is delighted to discover the Sciku community.

Enjoyed this sciku? Check out David’s other sciku: Algorithmic complexity.