An overview of the algorithms, and an introduction to how these can be used to solve Root Cause Analysis problems

1. Analy&cs for Time-series Data
An Overview Of SAX And Matrix Profile
Supreet Oberoi
VP, IoT and Big Data Applica&ons

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Safe Harbor Statement
The following is intended to outline our general product direc&on. It is intended for
informa&on purposes only, and may not be incorporated into any contract. It is not a
commitment to deliver any material, code, or func&onality, and should not be relied upon
in making purchasing decisions. The development, release, and &ming of any features or
func&onality described for Oracle’s products remains at the sole discre&on of Oracle.
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Commercializa&on Credits
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Professor Eamonn Keogh
University of California at Riverside
Marius Trufas
Oracle Corpora&on
Vlad Pertovici
Oracle Corpora&on
CrisAan Toma
Oracle Corpora&on

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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
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Sampling of Oracle’s IoT Use cases
Manufacturing
Shop floor equipment
monitoring
Predic&ve Analy&cs
for machine failures
Integra&on with MES
and ERP
Manufacturing
Real-&me filtering
and processing of
Valve events
Proac&ve parts
replacement
Integra&on with CRM
and Service Ticke&ng
system
Inventory Monitoring
Monitoring humidity,
temperature of smart
Freezers
Monitoring load for
inventory levels
Integra&on with
Mobile App,
Inventory systems
Asset Tracking
Tracking of assets in
conference center
and warehouses
Track u&liza&on,
dispatch/returns
Integra&on with ERP
for orders & invoicing

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Connect Analyze Integrate
Oracle IoT Cloud Applica&ons
Internet of Things Cloud
Enterprise (Placorm)
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Learn
Connected
Worker
Enhance worker safety
through monitoring of
workers and
environment
Monitor shipments,
fleet vehicles, driver
behavior and costs
Manufacturing
equipment & produc&on
line monitoring &
prognos&cs
ProducAon
Monitoring
Monitor assets, their
health, u&liza&on &
availability
Asset
Monitoring
Service Monitoring
for Connected
Assets
Automate asset
monitoring and customer
service to enhance
customer experience
Fleet
Monitoring

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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

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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

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Let’s Visualize What This Means (click for Video)
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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!
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Why is Root-case Analysis Challenging To Solve? (2/2)
• Oscilloscope-like techniques does not help in detec&ng anomalies
– There may be security issues with allowing access to raw data
– Similarity search, anomaly detec&on and other mining techniques are not available
– Trends may be microscopic or macroscopic – detec&on by eye not possible
• UX: Need to navigate large data-sets of &me-series data
– Render large data sets
– Show query results in human-response &me
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Introduc&on to SAX – Symbolic Aggregate Approxima&on
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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)

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Introduc&on to SAX – Symbolic Aggregate Approxima&on
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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

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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.

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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
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i
ii cqCQD
1
2
,

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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
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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
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Now, Let’s Look At Another Way To Analyze Time Series
Matrix Profile is a data structure that annotates a *me series
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• The matrix profile record the distance of a sequence to its nearest neighbor in Euclidean distance
• For example, the sequence star&ng at 921 has its nearest neighbor at a distance of 177

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Compu&ng a Matrix Profile
Step 1: Using a sliding window, compute distance to neighboring windows
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• 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

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Compu&ng a Matrix Profile
Step 2: Using min(), build vector of sequence to its nearest neighbor
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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

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Matrix Profile Gives Us Addi&on Insights For Free
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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

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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
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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
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When To Use SAX And Matrix Profile
If you are dealing with “short” pakerns, the Euclidean distance (matrix
profile) is what you need.
If you are dealing with “long” pakerns, some summary method
(including SAX based bitmaps) is what you need
Euclidean distance
(matrix profile)
SAX fingerprints

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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

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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
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