Incremental Time Series Algorithms for IoT Analysis: an ...mosse/courses/cs3720/IOT...Incremental...
Transcript of Incremental Time Series Algorithms for IoT Analysis: an ...mosse/courses/cs3720/IOT...Incremental...
Incremental Time Series Algorithms for IoT Analysis: an Example from Autoregression
Debnath Mukherjee, Suman Datta
Presented by: Daniel Petrov1
IoT
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Motivation
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Time Series
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< "#$%&"'$(, *+$%,#-_/'0+% >
tuple
Time Series Analysis
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• Statistical Analysis– Moving average– Autocorrelation function– Autoregression analysis– Linear regression
• Data Mining– Frequent pattern analysis
• Time Series Search– User-specified patterns
OLAP Infrastructure
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• Computationally challenging tasks– Multiple data sources– Multiple parallel users– Multiple types of queries
• Cloud– (Almost) infinite computational power– (Almost) infinite amount of Memory
How about the case of IoT?
Be Smart
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• Develop Smart Algorithms– Computationally cheap– Modest memory requirements
• Incremental calculations
Autoregression
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Incremental Calculation
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Incremental AR
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Incremental AR
! ∗ # = %
Incremental AR
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Incremental ARIncremental AR
Incremental AR
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lowconv highconv
Formulas
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!"# … = !"#_'()"*! − ),-!"# − ℎ/0ℎ!"#
1,2' … = 3[… ] − ),-1,2' − ℎ/0ℎ1,2'
1,"26(… ) = 6 − 9
Complexity Analysis
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• Update the model:– O(k)
• Update coefficients– O(k3)
• Memory complexity– O(k2)
Experimental Setup
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• Windows 7 Virtual Machine
• Intel Corei5 2.67 GHz
• 1 GB Ram
• R 3.0.3 programming platform
Dataset
• 3 Synthetic Datasets– 100K (100 000 data points)– 500K (500 000 data points)– 1M (1 000 000 data points)
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Memory Footprint
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CPU Time
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Conclusions
• We presented an incremental autoregression algorithm– O(k) complexity to update the model– O(k3) complexity to update the coefficients– O(k2) memory footprint
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