Big Data Everywhere Chicago: Getting Real with the MapR Platform (MapR)
Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)
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Transcript of Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)
![Page 1: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/1.jpg)
®© 2014 MapR Technologies 1
®
© 2014 MapR Technologies
Ted Dunning
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®© 2014 MapR Technologies 2
Contact Information Ted Dunning
Chief Applications Architect at MapR Technologies Committer & PMC for Apache’s Drill, Zookeeper & Mahout
VP of Incubator at Apache Foundation
Email [email protected] [email protected] Twitter @ted_dunning
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®© 2014 MapR Technologies 3
Must Approximate! • Many important aggregates cannot be computed on-line
– Memory cost proportional to data – Includes count distinct, heavy hitters, frequencies of top items, quantiles – Also k-means
• Most important aggregates can be approximated on-line – See all of the above
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®© 2014 MapR Technologies 4
Key Trick - Hashing
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![Page 5: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/5.jpg)
®© 2014 MapR Technologies 5
Key Trick - Sketching • Often we can build a very small sketch of the data • Carefully done, we can use the sketch to get values of interest
• All of the algorithms here use sketches of some kind
![Page 6: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/6.jpg)
®© 2014 MapR Technologies 6
Hyper log log!
![Page 7: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/7.jpg)
®© 2014 MapR Technologies 7
min(x)
Repeated Minimum
10 samples
Min is ~ 0.1
![Page 8: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/8.jpg)
®© 2014 MapR Technologies 8
Min(x)
0.00 0.02 0.04 0.06 0.08 0.10
020
4060
80 Theoretical distribution
Observed minimum value(100 samples x 10,000 replications)
Mean = 0.0099
![Page 9: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/9.jpg)
®© 2014 MapR Technologies 9
Count min sketch!
![Page 10: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/10.jpg)
®© 2014 MapR Technologies 10
Increment Hashed Locations to Insert
a
hi(a)
![Page 11: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/11.jpg)
®© 2014 MapR Technologies 11
Probe Using min of Counts
mini"k[hi(a)]
![Page 12: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/12.jpg)
®© 2014 MapR Technologies 12
Leaky counters!
![Page 13: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/13.jpg)
®© 2014 MapR Technologies 13
frequency@100 = 1e6
frequency@1000 = 80e3
Frequencies drop off fast
![Page 14: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/14.jpg)
®© 2014 MapR Technologies 14
Streaming k-means!
![Page 15: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/15.jpg)
®© 2014 MapR Technologies 15
Typical k-means Failure
Bad initial conditions cause cluster splitting
![Page 16: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/16.jpg)
®© 2014 MapR Technologies 16
Many Clusters in Sketch is Fine
![Page 17: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/17.jpg)
®© 2014 MapR Technologies 17
Lots of Clusters Approximate Anything
![Page 18: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/18.jpg)
®© 2014 MapR Technologies 18
Clustering Summary • Sketch is just lots of clusters
• Sketching can be done very approximately in one pass
• High quality clustering of the sketch is a high quality clustering of the data
![Page 19: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/19.jpg)
®© 2014 MapR Technologies 19
Finally, t-digest!
![Page 20: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/20.jpg)
®© 2014 MapR Technologies 20
Should a new point be added to an existing cluster?
Or form a new one?
![Page 21: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/21.jpg)
®© 2014 MapR Technologies 21
0.0 0.2 0.4 0.6 0.8 1.0
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ter S
izeVariable Cluster Size for Constant Relative Accuracy
Small clusters give high accuracy
Large clusters give coarse accuracy
![Page 22: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/22.jpg)
®© 2014 MapR Technologies 22
Second-Order Accuracy via Interpolation
Cumulative distribution
Centroids are spaced widely near q = 0.5
and tightly near q = 0 or q = 1
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![Page 23: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/23.jpg)
®© 2014 MapR Technologies 23
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near q = 0.5
Centroids are widely spaced
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to k-scale
Size Limits via Constant Steps in k-scale
![Page 24: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/24.jpg)
®© 2014 MapR Technologies 24
0.0 0.2 0.4 0.6 0.8 1.0
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k1 − k2 ≤1
k = sin−1(2q−1)+π / 2
πδ
Centroid size can be controlled using translation to centroid scale
![Page 25: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/25.jpg)
®© 2014 MapR Technologies 25
Actual Results
![Page 26: Some Important Streaming Algorithms You Should Know About-(Ted Dunning, MapR)](https://reader031.fdocuments.us/reader031/viewer/2022020106/55cec66cbb61eb1e308b46ed/html5/thumbnails/26.jpg)
®© 2014 MapR Technologies 26
Summary • Hashing and sketching
• Hyper log log = count distinct
• Count min = count(s)
• Streaming k-means
• Quantiles via t-digest
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0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
hash(ix)
min(x)
mini"k[hi(a)]
0.0 0.2 0.4 0.6 0.8 1.00
2040
6080
100
q
k
k1 − k2 ≤1
k = sin−1(2q−1)+π / 2
πδ
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Short Books by Ted Dunning & Ellen Friedman • Published by O’Reilly in 2014 and 2015 • For sale from Amazon or O’Reilly • Free e-books currently available courtesy of MapR
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Real World Hadoop by Ted Dunning and Ellen Friedman © Feb 2015 (published by O’Reilly)
Free copies at book signing today
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