This document discusses techniques for making recommendations in real-time using co-occurrence analysis. It describes how interaction cut and frequency cut downsampling allow batch co-occurrence analysis to scale to large datasets. These same techniques also enable an online approach to updating recommendations in real-time with each new user interaction. The key insights are that limiting user histories and item frequencies results in a bounded number of updates needed for each new data point, allowing real-time recommendations using MapR's distributed data platform.

1. © 2014 MapR Technologies 1© 2014 MapR Technologies

2. © 2014 MapR Technologies 2
Who I am
Ted Dunning, Chief Applications Architect, MapR Technologies
Email tdunning@mapr.com tdunning@apache.org
Twitter @Ted_Dunning
Apache Mahout https://mahout.apache.org/
Twitter @ApacheMahout

3. © 2014 MapR Technologies 3
Agenda
• Background – recommending with puppies and ponies
• Speed tricks
• Accuracy tricks
• Moving to real-time

4. © 2014 MapR Technologies 4
Puppies and Ponies

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Cooccurrence AnalysisCooccurrence Analysis

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How Often Do Items Co-occur
How often do items co-occur?
¢A A
A

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Which Co-occurrences are Interesting?
Which cooccurences are interesting?
Each row of indicators becomes a field in a
search engine document
¢A A
sparsify ¢A A( )

8. © 2014 MapR Technologies 8
Recommendations
Alice got an apple and
a puppyAlice

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Recommendations
Alice got an apple and
a puppyAlice
Charles got a bicycleCharles

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Recommendations
Alice got an apple and
a puppyAlice
Charles got a bicycleCharles
Bob Bob got an apple

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Recommendations
Alice got an apple and
a puppyAlice
Charles got a bicycleCharles
Bob What else would Bob like?

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Recommendations
Alice got an apple and
a puppyAlice
Charles got a bicycleCharles
Bob A puppy!

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By the way, like me, Bob also
wants a pony…

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Recommendations
?
Alice
Bob
Charles
Amelia
What if everybody gets a
pony?
What else would you recommend for
new user Amelia?

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Recommendations
?
Alice
Bob
Charles
Amelia
If everybody gets a pony, it’s
not a very good indicator of
what to else predict...

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Problems with Raw Co-occurrence
• Very popular items co-occur with everything or why it’s not very
helpful to know that everybody wants a pony…
– Examples: Welcome document; Elevator music
• Very widespread occurrence is not interesting to generate indicators
for recommendation
– Unless you want to offer an item that is constantly desired, such as
razor blades (or ponies)
• What we want is anomalous co-occurrence
– This is the source of interesting indicators of preference on which to
base recommendation

17. © 2014 MapR Technologies 17
Overview: Get Useful Indicators from Behaviors
1. Use log files to build history matrix of users x items
– Remember: this history of interactions will be sparse compared to all
potential combinations
2. Transform to a co-occurrence matrix of items x items
3. Look for useful indicators by identifying anomalous co-occurrences to
make an indicator matrix
– Log Likelihood Ratio (LLR) can be helpful to judge which co-
occurrences can with confidence be used as indicators of preference
– ItemSimilarityJob in Apache Mahout uses LLR

18. © 2014 MapR Technologies 18
Which one is the anomalous co-occurrence?
A not A
B 13 1000
not B 1000 100,000
A not A
B 1 0
not B 0 10,000
A not A
B 10 0
not B 0 100,000
A not A
B 1 0
not B 0 2

19. © 2014 MapR Technologies 19
Which one is the anomalous co-occurrence?
A not A
B 13 1000
not B 1000 100,000
A not A
B 1 0
not B 0 10,000
A not A
B 10 0
not B 0 100,000
A not A
B 1 0
not B 0 2
0.90 1.95
4.52 14.3
Dunning Ted, Accurate Methods for the Statistics of Surprise and Coincidence,
Computational Linguistics vol 19 no. 1 (1993)

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Collection of Documents: Insert Meta-Data
Search Engine
Item
meta-data
Document for
“puppy”
id: t4
title: puppy
desc: The sweetest little puppy
ever.
keywords: puppy, dog, pet
Ingest easily via NFS
✔ indicators: (t1)

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Cooccurrence Mechanics
• Cooccurrence is just a self-join
for each user, i
for each history item j1 in Ai*
for each history item j2 in Ai*
count pair (j1, j2)
aij1
aij2
= ¢A A
i
å

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Cross-occurrence Mechanics
• Cross occurrence is just a self-join of adjoined matrices
for each user, i
for each history item j1 in Ai*
for each history item j2 in Bi*
count pair (j1, j2)
aij1
bij2
= ¢A B
i
å A | B[ ]¢ A | B[ ] =
¢A A ¢A B
¢B A ¢B B
é
ë
ê
ù
û
ú

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A word about scaling

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A few pragmatic tricks
• Downsample all user histories to max length (interaction cut)
– Can be random or most-recent (no apparent effect on accuracy)
– Prolific users are often pathological anyway
– Common limit is 300 items (no apparent effect on accuracy)
• Downsample all items to limit max viewers (frequency limit)
– Can be random or earliest (no apparent effect)
– Ubiquitous items are uninformative
– Common limit is 500 users (no apparent effect)
Schelter, et al. Scalable similarity-based neighborhood methods with MapReduce.
Proceedings of the sixth ACM conference on Recommender systems. 2012

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But note!
• Number of pairs for a user history with ki distinct items is ≈ ki
2/2
• Average size of user history increases with increasing dataset
– Average may grow more slowly than N (or not!)
– Full cooccurrence cost grows strictly faster than N
– i.e. it just doesn’t scale
• Downsampling interactions places bounds on per user cost
– Cooccurrence with interaction cut is scalable
t µ ki
2
i
å Î o(N)
t µ min kmax
2
,ki
2
( )< Nkmax
2
i
å Î O(N)

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0 200 400 600 800 1000
0123456
Benefit of down−sampling
User Limit
Pairs(x109
)
Without down−sampling
Track limit = 1000
500
200
Computed on 48,373,586 pair−wise triples
from the million song dataset
●
●

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Batch Scaling in Time Implies Scaling in Space
• Note:
– With frequency limit sampling, max cooccurrence count is small (<1000)
– With interaction cut, total number of non-zero pairs is relatively small
– Entire cooccurrence matrix can be stored in memory in ~10-15 GB
• Specifically:
– With interaction cut, cooccurrence scales in size
– Without interaction cut, cooccurrence does not scale size-wise
¢A A 0
Î O(N)
¢A A 0
Îw(N)

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Impact of Interaction Cut Downsampling
• Interaction cut allows batch cooccurrence analysis to be O(N) in
time and space
• This is intriguing
– Amortized cost is low
– Could this be extended to an on-line form?
• Incremental matrix factorization is hard
– Could cooccurrence be a key alternative?
• Scaling matters most at scale
– Cooccurrence is very accurate at large scale
– Factorization shows benefits at smaller scales

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Online update

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Requirements for Online Algorithms
• Each unit of input must require O(1) work
– Theoretical bound
• The constants have to be small enough on average
– Pragmatic constraint
• Total accumulated data must be small (enough)
– Pragmatic constraint

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Log Files
Search
Technology
Item
Meta-Data
via
NFS
MapR Cluster
via
NFS PostPre
Recommendations
New User
History
Web
Tier
Recommendations
happen in real-time
Batch co-
occurrence
Want this to be real-time
Real-time recommendations using MapR data platform

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Space Bound Implies Time Bound
• Because user histories are pruned, only a limited number of
value updates need be made with each new observation
• This bound is just twice the interaction cut kmax
– Which is a constant
• Bounding the number of updates trivially bounds the time

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Implications for Online Update
A+eij( )¢ A+eij( )- ¢A A = ¢eij A+ ¢A eij +djj
=
0
Ai*
0
é
ë
ê
ê
ê
ù
û
ú
ú
ú
+ 0 Ai*( )¢ 0
é
ë
ê
ù
û
ú+djj

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Ai* + Ai*( )¢ +dii
0
£ 2kmax -1Î O(1)
With interaction cut at kmax

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But Wait, It Gets Better
• The new observation may be pruned
– For users at the interaction cut, we can ignore updates
– For items at the frequency cut, we can ignore updates
– Ignoring updates only affects indicators, not recommendation query
– At million song dataset size, half of all updates are pruned
• On average ki is much less than the interaction cut
– For million song dataset, average appears to grow with log of frequency
limit, with little dependency on values of interaction cut > 200
• LLR cutoff avoids almost all updates to index
• Average grows slowly with frequency cut

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0 200 400 600 800 1000
05101520253035
Interaction cut (kmax)
kave
Frequency cut = 1000
= 500
= 200

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0 200 400 600 800 1000
05101520253035
Frequency cut
kave

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Recap
• Cooccurrence-based recommendations are simple
– Deploying with a search engine is even better
• Interaction cut and frequency cut are key to batch scalability
• Similar effect occurs in online form of updates
– Only dozens of updates per transaction needed
– Data structure required is relatively small
– Very, very few updates cause search engine updates
• Fully online recommendation is very feasible, almost easy

39. © 2014 MapR Technologies 40
More Details Available
available for free at
available for free at
http://www.mapr.com/practical-machine-learning

40. © 2014 MapR Technologies 41
Who I am
Ted Dunning, Chief Applications Architect, MapR Technologies
Email tdunning@mapr.com tdunning@apache.org
Twitter @Ted_Dunning
Apache Mahout https://mahout.apache.org/
Twitter @ApacheMahout
Apache Drill http://incubator.apache.org/drill/
Twitter @ApacheDrill

41. © 2014 MapR Technologies 42
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tdunning@mapr.com
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