Brazilian Summer School in Machine Learning 2016 Day 1 - Lecture 3: Clusters and Anomaly Detection Lecturer: Poul Petersen (BigML)

1. D E C E M B E R 8 - 9 , 2 0 1 6

2. BigML, Inc 2
Poul Petersen
CIO, BigML, Inc.
Cluster AnalysisFinding Similarities

3. BigML, Inc 3Clusters
Trees vs Clusters
Trees/LR (Supervised Learning)
Provide: labeled data
Learning Task: be able to predict label
Clusters (Unsupervised Learning)
Provide: unlabeled data
Learning Task: group data by similarity

4. BigML, Inc 4Clusters
Trees vs Clusters
sepal
length
sepal
width
petal
length
petal
width
species
5,1 3,5 1,4 0,2 setosa
5,7 2,6 3,5 1,0 versicolor
6,7 2,5 5,8 1,8 virginica
… … … … …
sepal
length
sepal
width
petal
length
petal
width
5,1 3,5 1,4 0,2
5,7 2,6 3,5 1,0
6,7 2,5 5,8 1,8
… … … …
Inputs “X” Label “Y”
Learning Task:
Find function “f” such that:
f(X)≈Y
Learning Task:
Find “k” clusters such that
the data in each cluster is self
similar

5. BigML, Inc 5Clusters
Use Cases
• Customer segmentation
• Item discovery
• Similarity
• Recommender
• Active learning

6. BigML, Inc 6Clusters
Customer Segmentation
GOAL: Cluster the users by usage
statistics. Identify clusters with a
higher percentage of high LTV users.
Since they have similar usage
patterns, the remaining users in
these clusters may be good
candidates for up-sell.
• Dataset of mobile game users.
• Data for each user consists of usage
statistics and a LTV based on in-game
purchases
• Assumption: Usage correlates to LTV
0%
3%
1%

7. BigML, Inc 7Clusters
Item Discovery
GOAL: Cluster the whiskies by flavor
profile to discover whiskies that have
similar taste.
• Dataset of 86 whiskies
• Each whiskey scored on a scale from
0 to 4 for each of 12 possible flavor
characteristics.
Smoky
Fruity

8. BigML, Inc 8
Clustering Demo #1

9. BigML, Inc 9Clusters
Similarity
GOAL: Cluster the loans by
application profile to rank loan
quality by percentage of trouble
loans in population
• Dataset of Lending Club Loans
• Mark any loan that is currently or has
even been late as “trouble”
0%
3%
7%
1%

10. BigML, Inc 10Clusters
Active Learning
GOAL:
Rather than sample randomly, use clustering to group
patients by similarity and then test a sample from each
cluster to label the data.
• Dataset of diagnostic measurements
of 768 patients.
• Want to test each patient for diabetes
and label the dataset to build a model
but the test is expensive*.

11. BigML, Inc 11Clusters
Active Learning
*For a more realistic example of high cost, imagine a dataset
with a billion transactions, each one needing to be labelled as
fraud/not-fraud. Or a million images which need to be labeled as
cat/not-cat.
2323

12. BigML, Inc 12Clusters
Human Expert
Cluster into 3 groups…

13. BigML, Inc 13Clusters
Human Expert

14. BigML, Inc 14Clusters
Human Expert
• Jesa used prior knowledge to select possible
features that separated the objects.
• “round”, “skinny”, “edges”, “hard”, etc
• Items were then clustered based on the chosen
features
• Separation quality was then tested to ensure:
• met criteria of K=3
• groups were sufficiently “distant”
• no crossover

15. BigML, Inc 15Clusters
Human Expert
• Length/Width
• greater than 1 => “skinny”
• equal to 1 => “round”
• less than 1 => invert
• Number of Surfaces
• distinct surfaces require “edges” which have corners
• easier to count
Create features that capture these object differences

16. BigML, Inc 16Clusters
Clustering Features
Object Length / Width Num Surfaces
penny 1 3
dime 1 3
knob 1 4
eraser 2,75 6
box 1 6
block 1,6 6
screw 8 3
battery 5 3
key 4,25 3
bead 1 2

17. BigML, Inc 17Clusters
Plot by Features
Num
Surfaces
Length / Width
box block eraser
knob
penny
dime
bead
key battery screw
K-Means Key Insight:
We can find clusters using distances
in n-dimensional feature space
K=3

18. BigML, Inc 18Clusters
Plot by Features
Num
Surfaces
Length / Width
box block eraser
knob
penny
dime
bead
key battery screw
K-Means
Find “best” (minimum distance)
circles that include all points

19. BigML, Inc 19Clusters
K-Means Algorithm
K=3

20. BigML, Inc 20Clusters
K-Means Algorithm
K=3

21. BigML, Inc 21Clusters
Features Matter
Metal Other
Wood

22. BigML, Inc 22Clusters
Convergence
Convergence guaranteed
but not necessarily unique
Starting points important (K++)

23. BigML, Inc 23Clusters
Starting Points
• Random points or instances in n-dimensional space
• Chose points “farthest” away from each other
• but this is sensitive to outliers
• k++
• the first center is chosen randomly from instances
• each subsequent center is chosen from the
remaining instances with probability proportional to
its squared distance from the point's closest existing
cluster center

24. BigML, Inc 24Clusters
Scaling Matters
price
number of bedrooms
d = 160,000
d = 1

25. BigML, Inc 25Clusters
Other Tricks
• What is the distance to a “missing value”?
• What is the distance between categorical values?
• What is the distance between text features?
• Does it have to be Euclidean distance?
• Unknown “K”?

26. BigML, Inc 26Clusters
Distance to Missing?
• Nonsense! Try replacing missing values with:
• Maximum
• Mean
• Median
• Minimum
• Zero
• Ignore instances with missing values

27. BigML, Inc 27Clusters
Distance to Categorical?
• Special distance function
• if xA == xB then
x distance = 0 (or scaling value)
else
x distance = 1
• Assign centroid the most common category of the
member instances
Approach: similar to “k-prototypes”

28. BigML, Inc 28Clusters
Distance to Categorical?
feature_1 feature_2 feature_3
instance_1 red cat ball
instance_2 red cat ball
instance_3 red cat box
instance_4 blue dog fridge
D = 0
D = 1
D = sqrt(3)
Compute Euclidean distance between discrete vectors

29. BigML, Inc 29Clusters
Text Vectors
1
Cosine Similarity
0
-1
"hippo" "safari" "zebra" ….
3 0 1 …
2 4 0 …
0 5 7 …
Text Field #1
Text Field #2
Cosine Distance = 1 - Cosine Similarity
CD(TF1, TF2) = 0.575736
Features(thousands)

30. BigML, Inc 30Clusters
Finding K: G-Means

31. BigML, Inc 31Clusters
Finding K: G-Means

32. BigML, Inc 32Clusters
Finding K: G-Means
Let K=2
Keep 1, Split 1
New K=3

33. BigML, Inc 33Clusters
Finding K: G-Means
Let K=3
Keep 1, Split 2
New K=5

34. BigML, Inc 34Clusters
Finding K: G-Means
Let K=5
K=5

35. BigML, Inc 35
Clustering Demo #2

36. BigML, Inc 36
Poul Petersen
CIO, BigML, Inc.
Anomaly DetectionFinding the Unusual

37. BigML, Inc 37Anomaly Detection
Clusters vs Anomalies
Clusters (Unsupervised Learning)
Provide: unlabeled data
Learning Task: group data by similarity
Anomalies (Unsupervised Learning)
Provide: unlabeled data
Learning Task: Rank data by dissimilarity

38. BigML, Inc 38Anomaly Detection
Clusters vs Anomalies
sepal
length
sepal
width
petal
length
petal
width
5,1 3,5 1,4 0,2
5,7 2,6 3,5 1,0
6,7 2,5 5,8 1,8
… … … …
Learning Task:
Find “k” clusters such that the data
in each cluster is self similar
sepal
length
sepal
width
petal
length
petal
width
5,1 3,5 1,4 0,2
5,7 2,6 3,5 1,0
6,7 2,5 5,8 1,8
… … … …
Learning Task:
Assign value from 0 (similar) to 1
(dissimilar) to each instance.

39. BigML, Inc 39Anomaly Detection
Use Cases
• Unusual instance discovery
• Intrusion Detection
• Fraud
• Identify Incorrect Data
• Remove Outliers
• Model Competence / Input Data Drift

40. BigML, Inc 40Anomaly Detection
Removing Outliers
• Models need to generalize
• Outliers negatively impact generalization
GOAL: Use anomaly detector to identify most anomalous
points and then remove them before modeling.
DATASET FILTERED
DATASET
ANOMALY
DETECTOR
CLEAN
MODEL

41. BigML, Inc 41Anomaly Detection
Diabetes Anomalies
DIABETES
SOURCE
DIABETES
DATASET
TRAIN SET
TEST SET
ALL
MODEL
CLEAN
DATASET
FILTER
ALL
MODEL
ALL
EVALUATION
CLEAN
EVALUATION
COMPARE
EVALUATIONS
ANAOMALY
DETECTOR

42. BigML, Inc 42
Anomaly Demo #1

43. BigML, Inc 43Anomaly Detection
Intrusion Detection
GOAL: Identify unusual command line behavior per user and
across all users that might indicate an intrusion.
• Dataset of command line history for users
• Data for each user consists of commands,
flags, working directories, etc.
• Assumption: Users typically issue the same
flag patterns and work in certain directories
Per User Per Dir All User All Dir

44. BigML, Inc 44Anomaly Detection
Fraud
• Dataset of credit card transactions
• Additional user profile information
GOAL: Cluster users by profile and use multiple anomaly
scores to detect transactions that are anomalous on multiple
levels.
Card Level User Level Similar User Level

45. BigML, Inc 45Anomaly Detection
Model Competence
• After putting a model it into production, data that is being
predicted can become statistically different than the
training data.
• Train an anomaly detector at the same time as the model.
GOAL: For every prediction, compute an anomaly score. If the
anomaly score is high, then the model may not be competent
and should not be trusted.
Prediction T T
Confidence 86 % 84 %
Anomaly Score 0,5367 0,7124
Competent? Y N
At Prediction TimeAt Training Time
DATASET
MODEL
ANOMALY
DETECTOR

46. BigML, Inc 46Anomaly Detection
Univariate Approach
• Single variable: heights, test scores, etc
• Assume the value is distributed “normally”
• Compute standard deviation
• a measure of how “spread out” the numbers are
• the square root of the variance (The average of the
squared differences from the Mean.)
• Depending on the number of instances, choose a
“multiple” of standard deviations to indicate an anomaly.
A multiple of 3 for 1000 instances removes ~ 3 outliers.

47. BigML, Inc 47Anomaly Detection
Univariate Approach
measurement
frequency
outliersoutliers
• Available in BigML API

48. BigML, Inc 48Anomaly Detection
Benford’s Law
• In real-life numeric sets the small digits occur disproportionately often as
leading significant digits.
• Applications include:
• accounting records
• electricity bills
• street addresses
• stock prices
• population numbers
• death rates
• lengths of rivers
• Available in BigML API

49. BigML, Inc 49Anomaly Detection
Multivariate Matters

50. BigML, Inc 50Anomaly Detection
Multivariate Matters

51. BigML, Inc 51Anomaly Detection
Human Expert
Most Unusual?

52. BigML, Inc 52Anomaly Detection
Human Expert
“Round”“Skinny” “Corners”
“Skinny”
but not “smooth”
No
“Corners”
Not
“Round”
Key Insight
The “most unusual” object
is different in some way from
every partition of the features.
Most unusual

53. BigML, Inc 53Anomaly Detection
Human Expert
• Human used prior knowledge to select possible
features that separated the objects.
• “round”, “skinny”, “smooth”, “corners”
• Items were then separated based on the chosen
features
• Each cluster was then examined to see which
object fit the least well in its cluster and did not fit
any other cluster

54. BigML, Inc 54Anomaly Detection
Human Expert
• Length/Width
• greater than 1 => “skinny”
• equal to 1 => “round”
• less than 1 => invert
• Number of Surfaces
• distinct surfaces require “edges” which have corners
• easier to count
• Smooth - true or false
Create features that capture these object differences

55. BigML, Inc 55Anomaly Detection
Anomaly Features
Object Length / Width Num Surfaces Smooth
penny 1 3 TRUE
dime 1 3 TRUE
knob 1 4 TRUE
eraser 2,75 6 TRUE
box 1 6 TRUE
block 1,6 6 TRUE
screw 8 3 FALSE
battery 5 3 TRUE
key 4,25 3 FALSE
bead 1 2 TRUE

56. BigML, Inc 56Anomaly Detection
Random Splits
smooth = True
length/width > 5
box
blockeraser
knob
penny
dime
bead
key
battery
screw
num surfaces = 6
length/width =1
length/width < 2
Know that “splits” matter - don’t know the order

57. BigML, Inc 57Anomaly Detection
Isolation Forest
Grow a random decision tree until
each instance is in its own leaf
“easy” to isolate
“hard” to isolate
Depth
Now repeat the process several times and
use average Depth to compute anomaly
score: 0 (similar) -> 1 (dissimilar)

58. BigML, Inc 58Anomaly Detection
Isolation Forest Scoring
f_1 f_2 f_3
i_1 red cat ball
i_2 red cat ball
i_3 red cat box
i_4 blue dog pen
D = 3
D = 6
D = 2
Score

59. BigML, Inc 59Anomaly Detection
Model Competence
• A low anomaly score means the loan is similar to the
modeled loans.
• A high anomaly score means you can not trust the
model.
Prediction T T
Confidence
86 % 84 %
Anomaly
Score
0,5367 0,7124
Competent? Y N
OPEN LOANS
PREDICTION
ANOMALY
SCORE
CLOSED LOAN
MODEL
CLOSED LOAN
ANOMALY DETECTOR

60. BigML, Inc 60
Anomaly Demo #2