Time-series Analytics using Matrix Profile and SAX
- 4. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | Goals For Today’s Presenta&on – Explain: • Significance of the commercial problem • Challenges in using tradi&onal data mining techniques • Introduc&on to SAX and Matrix Profile • Learnings while commercializing SAX • Demo • References 4
- 7. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | Manufacturing Leading suppliers of sensing, electrical protecAon, control & power management soluAons Challenges • Delayed reac&on to degrada&on in yield and quality • Wasted Ame in root cause analysis • Inconsistent produc&vity metrics across sites, products SoluAon Components • Oracle IOT Produc&on Monitoring for real-&me visibility of calibra&on machine metrics • Analy&cs for predic&ng machine failures Benefits • Reduce producAon of bad parts by reacAng in real-Ame • Measure and improve plant efficiency across sites • Faster root cause analysis
- 8. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | 8 Root Cause Analysis Is Expensive In All Ways! Detect Problem Gather Data Develop Hypothesis Validate Hypothesis Develop Model Review Historical Related Problems Continually Monitor for Future Problems
- 10. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | Why is Root-case Analysis Challenging To Solve? (1/2) • Analysts/Process Engineering search for a pakern of &me-series samples – over a large volumes of data, in real &me – Brute force Euclidean distance comparison is expensive – need dimensionality reduc&on • It is very easy for the machine to report false posi&ves – Tradi&onal techniques to approximate matching further increase false posi&ves – Approxima&on should support lower bounding of Euclidean distance • Analysts olen start with minimal hunch on what to look – System need to iden&fy anomalies and provide predic&ons just to get started! 10
- 12. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | Introduc&on to SAX – Symbolic Aggregate Approxima&on 12 SAX allows *me series of arbitrary length n to be reduce to string of arbitrary length w Step 1: Reduce dimensionality by Piecewise Aggregate Approxima&on (PAA) It is important to normalize &me series to have a mean of zero and standard devia&on of one before applying PAA since &me series should not be compared with different offsets and amplitudes (invariances need to discounted in most cases)
- 13. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | Introduc&on to SAX – Symbolic Aggregate Approxima&on 13 SAX allows *me series of arbitrary length n to be reduce to string of arbitrary length w Step 2: Transform using breakpoints to obtain discrete representa&on • Typically, normalized &me series have a Gaussian distribu&on • Our goal is to produce symbols with equiprobability • Each symbol must produce equal-sized area under the Gaussian curve • To do so, we develop Breakpoint table for Gaussian distribu&on and number of frames
- 14. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | Introduc&on to SAX – Symbolic Aggregate Approxima&on 14 SAX allows *me series of arbitrary length n to be reduce to string of arbitrary length w Step 3: Convert PAA to string Alphabet Size is determines the number of discre&za&on levels aler PAA. Lower values may lead to loss of informa&on. Higher values are naturally desirable, but generate addi&onal computa&onal overhead. Also, experiments have found that Alphabet sizes beyond 6 rarely provide major benefits.
- 15. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | SAX Tuning Parameters • Alphabet Size determines the number of discre&za&on levels (rarely over 6) • Window length determines the number of data points to transform at a &me • Word length determines the number of frames to divide Window • Distance algorithm measures the similarity between strings We used Euclidean distance through other techniques exist (MINDIST) • Distance is useful for comparing strings. For example, “abcd” is closer to “abcc” than “abca” since their PAA values are closer -- simple string comparison will return both as equally similar 15 ( ) ( )∑ −≡ = n i ii cqCQD 1 2 ,
- 16. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | What Does SAX Enable Us To Solve? • Anomaly Detec&on • Clustering and Classifica&on • Iden&fy repeated pakerns (mo&f discovery) • Iden&fy rules in &me-series • Time-series JOINS 16
- 17. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | Learnings While Commercializing SAX • With MINDIST, smaller alphabet sizes lead to large number of false posi&ves. Very large alphabet sizes can lead to missing legi&mate matches. We feel an alphabet size of 8 should work well in most cases, but the alphabet size should not exceed 10 or be less than 6 • The number of false posi&ves is much less if the pakern is dis&nct compared to the rest of the data (for example, a strong spike). If the data changes gradually, and there are many such instances in the data, the number of false posi&ves would be very high • We should not support a tolerance value. Even with a simple MINDIST func&on, we get some false posi&ves. Adding tolerance on top of this only increased the number of reported false posi&ves. Plus, it may not be obvious to the user what is the best value of tolerance to use. Sesng it too high might further increase the number of false posi&ves • We have to configure the alphabet size depending on the amount of varia&on in the data, but for now we do not have a definite way to do this automa&cally 17
- 19. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | Compu&ng a Matrix Profile Step 1: Using a sliding window, compute distance to neighboring windows 19 • The distance matrix is symmetric • The diagonal is zero • Cells close to the diagonal are very small di,j is the distance between the ith window and the jth window of the &me series d1,1 d1,2 … … … d1,n-m+1 d2,1 d2,2 … … … d2,n-m+1 … … … … … … di,1 di,2 … di,j … di,n-m+1 … … … … … … dn-m+1,1 dn-m+1,2 … … … dn-m+1,n-m+1 ith jth D1 D2 Di Dn-m+1
- 20. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | Compu&ng a Matrix Profile Step 2: Using min(), build vector of sequence to its nearest neighbor 20 Matrix Profile: a vector of distance between each subsequence and its nearest neighbor d1,1 d1,2 … … … d1,n-m+1 d2,1 d2,2 … … … d2,n-m+1 … … … … … … di,1 di,2 … di,j … di,n-m+1 … … … … … … dn-m+1,1 dn-m+1,2 … … … dn-m+1,n-m+1 ith jth Min(D1) Min(D2) Min(Dn-m+1) Min(Di) P1 P2 … … ... Pn-m+1 D1 D2 Di Dn-m+1
- 21. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | Matrix Profile Gives Us Addi&on Insights For Free 21 0 500 1000 1500 2000 2500 3000 Must be an anomaly in the original data, in this region. Must be conserved shapes (mo&fs) in the original data, in these three regions Although similar to a self-join, it can be extended easily to an A-B join
- 22. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | There Are Techniques To Make Distance Profile Computa&on Efficient • Brute Force Algorithm O(nm) – In addi&on, the window is scanned twice (z-normaliza&on and distance calcula&on) • Just-in-&me Normaliza&on O(nm) – But we skip the normaliza&on step to compute devia&on in linear &me • Mueen’s Algorithm for Similarity Search (MASS) O(nlogn) – Does not depend on query length (m) – free of “curse of dimensionality” – Use convolu&ons to mul&ply two polynomials – Use Fast Fourier Transform to reduce doubling of the vector size 22
- 23. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | It Also Claims To Provide Addi&onal Benefits • Parameter free – no need to set window, alphabet size • Domain agnosAc – no need for prior data sets for training to detect anomalies • Space efficient – linear in &me-series length with constant overhead • Near real-Ame anomaly detecAon with approximate distance computa&on (STAMP) • Lower false-posiAve rate as no similarity threshold needs to be provided • Big Data friendly – can be easily parallelized Review Matrix Profile tutorials (page 57-60) to review benchmark results 23
- 25. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | 25 Root Cause Analysis: Let’s Revisit This Again… Gather Data Develop Hypothesis Detect Problem Matrix Profile Validate Hypothesis SAX Review Historical Related Problems SAX Continually Monitor for Future Problems Matrix Profile Develop Model SAX
- 26. Copyright © 2017, Oracle and/or its affiliates. All rights reserved. | References • About Oracle IoT • hkps://www.oracle.com/solu&ons/internet-of-things/ • About SAX • hkp://www.cs.ucr.edu/~eamonn/SAX.htm (Introduc&on to SAX) • hkp://www.cs.ucr.edu/~eamonn/kais_2000.pdf (Introduc&on to PAA) • About Matrix Profile • hkp://www.cs.ucr.edu/~eamonn/Matrix_Profile_Tutorial_Part1.pdf • hkp://www.cs.ucr.edu/~eamonn/Matrix_Profile_Tutorial_Part2.pdf • About MASS algorithm for similarity search • hkp://www.cs.unm.edu/~mueen/FastestSimilaritySearch.html 26