some important streaming algorithms you should know about-(ted dunning, mapr)
TRANSCRIPT
®© 2014 MapR Technologies 1
®
© 2014 MapR Technologies
Ted Dunning
®© 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
®© 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
®© 2014 MapR Technologies 4
Key Trick - Hashing
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0.0 0.2 0.4 0.6 0.8 1.0
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1.0
hash(ix)
®© 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
®© 2014 MapR Technologies 6
Hyper log log!
®© 2014 MapR Technologies 7
min(x)
Repeated Minimum
10 samples
Min is ~ 0.1
®© 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
®© 2014 MapR Technologies 9
Count min sketch!
®© 2014 MapR Technologies 10
Increment Hashed Locations to Insert
a
hi(a)
®© 2014 MapR Technologies 11
Probe Using min of Counts
mini"k[hi(a)]
®© 2014 MapR Technologies 12
Leaky counters!
®© 2014 MapR Technologies 13
frequency@100 = 1e6
frequency@1000 = 80e3
Frequencies drop off fast
®© 2014 MapR Technologies 14
Streaming k-means!
®© 2014 MapR Technologies 15
Typical k-means Failure
Bad initial conditions cause cluster splitting
®© 2014 MapR Technologies 16
Many Clusters in Sketch is Fine
®© 2014 MapR Technologies 17
Lots of Clusters Approximate Anything
®© 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
®© 2014 MapR Technologies 19
Finally, t-digest!
®© 2014 MapR Technologies 20
Should a new point be added to an existing cluster?
Or form a new one?
®© 2014 MapR Technologies 21
0.0 0.2 0.4 0.6 0.8 1.0
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q
Clus
ter S
izeVariable Cluster Size for Constant Relative Accuracy
Small clusters give high accuracy
Large clusters give coarse accuracy
®© 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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®© 2014 MapR Technologies 23
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0.0 0.2 0.4 0.6 0.8 1.0
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Transformation
near q = 0.5
Centroids are widely spaced
q = 0 or q = 1and tightly near
to k-scale
Size Limits via Constant Steps in k-scale
®© 2014 MapR Technologies 24
0.0 0.2 0.4 0.6 0.8 1.0
020
4060
80100
q
kTranslation Between Quantile and Cluster #
k1 − k2 ≤1
k = sin−1(2q−1)+π / 2
πδ
Centroid size can be controlled using translation to centroid scale
®© 2014 MapR Technologies 25
Actual Results
®© 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
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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
®© 2014 MapR Technologies 27
®© 2014 MapR Technologies 28
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