Incremental Time Series Algorithms for IoT Analysis: an Example from Autoregression

Debnath Mukherjee, Suman Datta

Presented by: Daniel Petrov1

IoT

2Daniel Petrov, CS3720 2

Motivation

3Daniel Petrov, CS3720 3

Time Series

4Daniel Petrov, CS3720 4

< "#$%&"'$(, *+$%,#-_/'0+% >

tuple

Time Series Analysis

5Daniel Petrov, CS3720 5

• Statistical Analysis– Moving average– Autocorrelation function– Autoregression analysis– Linear regression

• Data Mining– Frequent pattern analysis

• Time Series Search– User-specified patterns

OLAP Infrastructure

6Daniel Petrov, CS3720 6

• 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

7Daniel Petrov, CS3720 7

• Develop Smart Algorithms– Computationally cheap– Modest memory requirements

• Incremental calculations

Autoregression

8Daniel Petrov, CS3720 8

Incremental Calculation

9Daniel Petrov, CS3720 9

Incremental AR

10Daniel Petrov, CS3720 10

11Daniel Petrov, CS3720 11

Incremental AR

! ∗ # = %

Incremental AR

12Daniel Petrov, CS3720 12

Incremental ARIncremental AR

Incremental AR

13Daniel Petrov, CS3720 13

lowconv highconv

Formulas

14Daniel Petrov, CS3720 14

!"# … = !"#_'()"*! − ),-!"# − ℎ/0ℎ!"#

1,2' … = 3[… ] − ),-1,2' − ℎ/0ℎ1,2'

1,"26(… ) = 6 − 9

Complexity Analysis

15Daniel Petrov, CS3720 15

• Update the model:– O(k)

• Update coefficients– O(k3)

• Memory complexity– O(k2)

Experimental Setup

16Daniel Petrov, CS3720 16

• 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)

17Daniel Petrov, CS3720

Memory Footprint

18Daniel Petrov, CS3720

CPU Time

19Daniel Petrov, CS3720

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

20Daniel Petrov, CS3720