ieee cig 2016 time series clustering of free-to-play game data
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Discovering Playing Patterns:
Time Series Clustering of Free-To-Play Game Data
Alain Saas, Anna Guitart and Africa Perianez (Silicon Studio)
IEEE CIG 2016 Santorini
21 September, 2016
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About us
• Who are we?◦ Game studio and graphics
middleware company based in Tokyo◦ Research project to provide Game
Data Science as a service◦ Goals: predict player behavior, scale
to big data and intuitive resultvisualization
• Which data?◦ RPG free-to-play games◦ TS of two games◦ TS of in-app purchases and activity
behavioral data
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Challenge
Unsupervised clustering of Time Series of player activity
• Why?◦ discover temporary player patterns◦ evaluation of game events and business diagnosis◦ assess common characteristics of players belonging to the same cluster
• How?
1. representation techniques: reducing the high dimensionality of TS2. similarity measures for free-to-play game data3. hierarquical clustering4. visual validation of the results
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Representation methods
Symbolic Aggregate Approximation
Trend Extraction
Discrete Wavelet Transfrom
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Similarity measures
Dynamic Time Warping
DTW (X ,Y ) = minr∈M
(M∑
m=1
|xim − yjm|)
Correlation-based measure
COR(X ,Y ) =
∑Nn=1(xn − X )(yn − Y )√∑N
n=1(xn − X )2√∑N
n=1(yn − Y )2
Temporal Correlation and Raw ValuesBehaviors measure
CORT (X ,Y ) =
∑N−1n=1 (xn+1 − xn)(yn+1 − yn)√∑N−1
n=1 (xn+1 − xn)2√∑N−1
n=1 (yn+1 − yn)2
Complexity-Invariant Distancemeasure
CID(X ,Y ) = dist(X ,Y ) · CF (X ,Y ),
CF complexity correction factor
CF (X ,Y ) =max(CE(X ),CE(Y ))
min(CE(X ),CE(Y ))
CE is the complexity estimation
CE(X ) =
√√√√N−1∑n=1
(xn − xn+1)2
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Similarity measure comparison
Euclidean vs. Correlation Correlation vs. Complexity-Invariant Distance
Dynamic Time Warping vs.Correlation Correlation vs. Discrete Wavelet Transform
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Comparison clustering methods
• DTW Dynamic Time Warping
◦ similar player profiles with ashift on the time axis
◦ different patterns but atdifferent scale
• DWT Discrete Wavelet Transform
◦ dimensionality reduction◦ frequency of the series
• SAX Symbolic Aggregate
Approximation
◦ parameters w,a
• COR Correlation
◦ similar geometric andsynchronous profiles
◦ sensitive to noise data andoutliers
• CORT Temporal Correlation
◦ similar to COR but with timeconsideration?
• CID Complexity-Invariant distance
◦ similar complexity patterns◦ good for sparse time series
• COR+trend Correlation and trend extraction
◦ addresses COR’s sensitivity to noise◦ does not work well with sparse time series
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Hierarchical clustering
Agglomerative Ward method:Lead to a minimum increase of total within-cluster variance
Single LinkageComplete LinkageAverage LinkageCentroid MethodWard Method
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Our data
Time series measured per user per day.
Game ActivityBehavioral data
Time: The amount of time spent in the gameSessions: The total number of playing sessionsActions: The total number of actions performed
In-app Sales Purchase: The total amount of in-app purchases
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Data selection, constraints
Time Series: Multi-dimensional data⇒ selection of period P
• in our data weekly game events
• period P of length 21 days
• played time → active usersmin connections 6/7 days a week
• purchases → paying usersat least one purchase in period P
• players alive during period P
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Datasets and tests
Game Data Technique Clusters Date rangeAge of Ishtaria Daily played time COR-trend 8 Oct2014 - Jan2016Age of Ishtaria Daily purchase CID 5 Oct2014 - Jan2016Grand Sphere Daily played time COR-trend 8 Jun2015 - Mar2016
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Clustering time series of time played
1. representation method: trend extraction
2. similarity measure: correlation
3. hierarchical clustering: Ward method
4. validation of results: visualization withheatmap (raw data)
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Extraction of players characteristics
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Clustering time series of time played
Also able to extract differentiate patterns as in Age of Ishtaria
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Clustering time series of purchases
1. similarity measure:complexity-invariant distance
2. hierarchical clustering: Ward method
3. validation of results: visualization withheatmap (raw data)
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Summary and Next Steps
• Unsupervised clustering time series data from two free-to-playgames
• Evaluate several similarity measures and representation methods
• Extract meaningful behavioral patterns of players
• Assess impact of weekly game events
• Discover hidden playing dynamics regarding purchases and timeplayed
• Feature for churn prediction
• Event recommender
• Cluster level behaviour
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http://www.siliconstudio.co.jp/rd/4front/
Thank you!
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