VSSML17 L3. Clusters and Anomaly Detection

Valencian Summer School in Machine Learning
3rd edition
September 14-15, 2017

BigML, Inc 2
Clusters
Finding Similarities
Poul Petersen
CIO, BigML, Inc

BigML, Inc 3Clusters
What is Clustering?
• An unsupervised learning technique
• No labels necessary
• Useful for finding similar instances
• Smart sampling/labelling
• Finds “self-similar" groups of instances
• Customer: groups with similar behavior
• Medical: patients with similar diagnostic measurements
• Defines each group by a “centroid”
• Geometric center of the group
• Represents the “average” member
• Number of centroids (k) can be specified or determined

Cluster Centroids
date customer account auth class zip amount
Mon Bob 3421 pin clothes 46140 135
Tue Bob 3421 sign food 46140 401
Tue Alice 2456 pin food 12222 234
Wed Sally 6788 pin gas 26339 94
Wed Bob 3421 pin tech 21350 2459
Wed Bob 3421 pin gas 46140 83
Thr Sally 6788 sign food 26339 51

Cluster Centroids
auth = pin
amount ~ $100
Same:
date: Mon != Wed
customer: Sally != Bob
account: 6788 != 3421
class: clothes != gas
zip: 26339 != 46140
Different:
date = Wed (2 out of 3)
customer = Bob
account = 3421
auth = pin
class = gas
zip = 46140
amount = $104
Centroid:
similar

Use Cases
• Customer segmentation
• Which customers are similar?
• How many natural groups are there?
• Item discovery
• What other items are similar to this one?
• Similarity
• What other instances share a speciﬁc property?
• Recommender (almost)
• If you like this item, what other items might you like?
• Active learning
• Labelling unlabelled data efﬁciently

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%

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%

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*.

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

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

Clusters Demo #1

Human Expert
Cluster into 3 groups…

Human Expert

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

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

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

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

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

K-Means Algorithm
K=3

K-Means Algorithm
K=3
Repeat until centroids stop moving

Features Matter
Metal Other
Wood

Convergence
Convergence guaranteed

but not necessarily unique

Starting points important (K++)

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

Scaling Matters
price
number of bedrooms
d = 160,000
d = 1

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”?

Distance to Missing?
• Nonsense! Try replacing missing values with:
• Maximum
• Mean
• Median
• Minimum
• Zero
• Ignore instances with missing values

Distance to Categorical?
• Define special distance function: For two instances 𝑥 and 𝑦

and the categorical field 𝑎:
• if 𝑥 𝑎
＝
𝑦 𝑎 then 
(𝑥,𝑦)distance＝0
(or field scaling value)  
else  
(𝑥,𝑦)distance＝1
Approach: similar to “k-prototypes”

Distance to Categorical?
animal favorite toy toy color
cat ball red
cat ball green
d=0 d=0 d=1
cat laser red
dog squeaky red
d=1 d=1 d=0
D = 1
Then compute Euclidean distance between vectors
D = √2
Note: the centroid is assigned the most common
category of the member instances

Text Vectors
1
Cosine Similarity
0
-1
"hippo" "safari" "zebra" ….
1 0 1 …
1 1 0 …
0 1 1 …
Text Field #1
Text Field #2
Features(thousands)
• Cosine
Similarity

• cos() between two vectors
• 1 if collinear, 0 if orthogonal
• only positive vectors: 0
≤
CS
≤
1
• Cosine
Distance＝1－Cosine
Similarity

• CD(TF1,
TF2)
=
0.5

Finding K: G-Means

Finding K: G-Means
Let K=2
Keep 1, Split 1
New K=3

Finding K: G-Means
Let K=3
Keep 1, Split 2
New K=5

Finding K: G-Means
Let K=5
K=5

Clusters Demo #2

Summary
• Cluster Purpose
• Unsupervised technique for finding self-similar groups
of instances
• Number of centroids (k) can be inputed or computed
• Outputs list of centroids
• Configuration:
• Algorithm: K-means / G-means
• Cluster Parameter: k or critical value
• Default missing / Summary fields / Scales / Weights
• Model Clusters
• Centroid / Batchcentroids

BigML, Inc 2
Anomaly Detection
Finding the Unusual
Poul Petersen
CIO, BigML, Inc

BigML, Inc 3Anomaly Detection
What is Anomaly Detection?
• An unsupervised learning technique
• No labels necessary
• Useful for finding unusual instances
• Filtering, finding mistakes, 1-class classifiers
• Finds instances that do not match
• Customer: big or small spender for profile
• Medical: healthy patient despite indicative diagnostics
• Defines each unusual instance by an “anomaly score”
• in BigML: 0＝normal,
1＝unusual, and 0.7
≫
0.6
﹥0.5

• Standard deviation, distributions, etc

Clusters

Clusters
similar

Anomaly Detection

Anomaly Detection
anomaly
• Amount $2,459 is higher than all other transactions
• It is the only transaction
• In zip 21350
• for the purchase class "tech"

Use Cases
• Unusual instance discovery - "exploration"
• Intrusion Detection - "looking for unusual usage patterns"
• Fraud - "looking for unusual behavior"
• Identify Incorrect Data - "looking for mistakes"
• Remove Outliers - "improve model quality"
• Model Competence / Input Data Drift

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

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

Anomaly Demo #1

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

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

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

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.

Univariate Approach
measurement
frequency
outliersoutliers
• Available in BigML API

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

Multivariate Matters

Human Expert
Most Unusual?

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

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

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

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

length/width > 5
smooth?
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
TrueFalse
TrueFalse TrueFalse
FalseTrue
TrueFalse
Random Splits

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)

Isolation Forest Scoring
D = 3
D = 6
D = 2
S=0.45
Map avg depth
to ﬁnal score
f1 f2 f3
i1 red cat ball
i2 red cat ball
i3 red cat box
i4 blue dog pen
For the instance, i2
Find the depth in each tree

Model Competence
• A low anomaly score means the loan is similar to the
modeled loans.
• A high anomaly score means you should 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

Anomaly Demo #2

1-Class Classiﬁer?
• You place an advertisement in a local newspaper
• You collect demographic information about all responders
• Now you want to market in a new locality with direct letters
• To optimize mailing costs, need to predict who will respond
• But, can not distinguish not interested from didn’t see the ad
• Train an anomaly detector on the 1-class data
• Pick the households with the lowest scores for mailing:
• If a household has a low anomaly score, then they are
“similar” to enough of your positive responders and
therefore may respond as well
• If an individual has a high anomaly score, then they are
dissimilar from all previous responders and therefore are
less likely to respond.

Summary
• Anomaly detection is the process of finding unusual instances
• Some techniques and how they work:
• Univariate: standard deviation
• Benford’s law
• Isolation Forest
• Applications
• Filtering to improve models
• Finding mistakes, fraud, and intruders
• Knowing when to retrain a model (competence)
• 1-class classifiers
• In general… unsupervised learning techniques:
• Require more finesse and interpretation
• Are more commonly part of a multistep workflow

VSSML17 L3. Clusters and Anomaly Detection

VSSML17 L3. Clusters and Anomaly Detection

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