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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