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Understanding Feature Space
in Machine Learning
Alice Zheng
Director of Data Science, Dato
RainyData Datoinc
#datapopupseattle
UNSTRUCTURED
Data Science POP-UP in Seattle
www.dominodatalab.com
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Produced by Domino Data Lab
Domino’s enterprise data science platform is used
by leading analytical organizations to increase
productivity, enable collaboration, and publish
models into production faster.
Understanding Feature Space
in Machine Learning
Alice Zheng, Dato
October, 2015
3
‹#›
My journey so far
Applied+machine+learning+
(Data+science)
Build+ML+tools
Shortage+of+experts+
and+good+tools.
‹#›
Why machine learning?
Model data.
Make predictions.
Build intelligent
applications.
‹#›
The machine learning pipeline
I+fell+in+love+the+instant+I+laid+
my+eyes+on+that+puppy.+His+
big+eyes+and+playful+tail,+his+
soft+furry+paws,+…
Raw+data
Features
Models
Predictions
Deploy+in+
production
‹#›
Three things to know about ML
• Feature = numeric representation of raw data
• Model = mathematical “summary” of features
• Making something that works = choose the right model
and features, given data and task
Feature = Numeric representation of raw data
‹#›
Representing natural text
It#is#a#puppy#and#it#is#
extremely#cute.
What’s+important?+
Phrases?+Specific+
words?+Ordering?+
Subject,+object,+verb?
Classify:++
puppy+or+not?
Raw+Text
{“it”:2,++
+“is”:2,++
+“a”:1,++
+“puppy”:1,++
+“and”:1,+
+“extremely”:1,+
+“cute”:1+}
Bag+of+Words
‹#›
Representing natural text
It#is#a#puppy#and#it#is#
extremely#cute.
Classify:++
puppy+or+not?
Raw+Text Bag+of+Words
it 2
they 0
I 0
am 0
how 0
puppy 1
and 1
cat 0
aardvark 0
cute 1
extremely 1
… …
Sparse+vector+
representation
‹#›
Representing images
Image+source:+“Recognizing+and+learning+object+categories,”++
Li+Fei[Fei,+Rob+Fergus,+Anthony+Torralba,+ICCV+2005—2009.
Raw+image:++
millions+of+RGB+triplets,+
one+for+each+pixel
Classify:++
person+or+animal?
Raw+Image Bag+of+Visual+Words
‹#›
Representing images
Classify:++
person+or+animal?
Raw+Image Deep+learning+features
3.29+
[15+
[5.24+
48.3+
1.36+
47.1+
[1.92
36.5+
2.83+
95.4+
[19+
[89+
5.09+
37.8
Dense+vector+
representation
‹#›
Feature space in machine learning
• Raw data ! high dimensional vectors
• Collection of data points ! point cloud in feature space
• Feature engineering = creating features of the appropriate
granularity for the task
Visualizing Feature Space
Crudely speaking, mathematicians fall into two categories:
the algebraists, who find it easiest to reduce all problems
to sets of numbers and variables, and the geometers, who
understand the world through shapes.



-- Masha Gessen, “Perfect Rigor”
‹#›
Visualizing bag-of-words
puppy
cute
1
1
I+have+a+puppy+and+
it+is+extremely+cute
I#have#a#puppy#and#
it#is#extremely#cute
it 1
they 0
I 1
am 0
how 0
puppy 1
and 1
cat 0
aardvark 0
zebra 0
cute 1
extremely 1
… …
‹#›
Visualizing bag-of-words
puppy
cute
1
1
1
extremely
I+have+a+puppy+and++
it+is+extremely+cute
I+have+an+extremely++
cute+cat
I+have+a+cute++
puppy
‹#›
Document point cloud
word+1
word+2
Model = Mathematical “summary” of features
‹#›
What is a summary?
• Data ! point cloud in feature space
• Model = a geometric shape that best “fits” the point cloud
‹#›
Classification model
Feature+2
Feature+1
Decide+between+two+classes
‹#›
Clustering model
Feature+2
Feature+1
Group+data+points+tightly
‹#›
Regression model
Target
Feature
Fit+the+target+values
Visualizing Feature Engineering

‹#›
When does bag-of-words fail?
puppy
cat
2
1
1
have
I+have+a+puppy
I+have+a+cat
I+have+a+kitten
Task:+find+a+surface+that+separates++
documents+about+dogs+vs.+cats
Problem:+the+word+“have”+adds+fluff++
instead+of+information
I+have+a+dog+
and+I+have+a+pen
1
‹#›
Improving on bag-of-words
• Idea: “normalize” word counts so that popular words are
discounted
• Term frequency (tf) = Number of times a terms appears in a
document
• Inverse document frequency of word (idf) =
• N = total number of documents
• Tf-idf count = tf x idf
‹#›
From BOW to tf-idf
puppy
cat
2
1
1
have
I+have+a+puppy
I+have+a+cat
I+have+a+kitten
idf(puppy)+=+log+4+
idf(cat)+=+log+4+
idf(have)+=+log+1+=+0
I+have+a+dog+
and+I+have+a+pen
1
‹#›
From BOW to tf-idf
puppy
cat1
have
tfidf(puppy)+=+log+4+
tfidf(cat)+=+log+4+
tfidf(have)+=+0
I+have+a+dog+
and+I+have+a+pen,+
I+have+a+kitten
1
log+4
log+4
I+have+a+cat
I+have+a+puppy
Decision+surface
Tf[idf+flattens+
uninformative+
dimensions+in+the+
BOW+point+cloud
‹#›
That’s not all, folks!
• Geometry is the key to understanding feature space and
machine learning
• Many other fun topics:
- Feature normalization
- Feature transformations
- Model regularization
• Dato is hiring! jobs@dato.com
@RainyData,+@DatoInc
#datapopupseattle
@datapopup
#datapopupseattle
#datapopupseattle
Thank You To Our Sponsors

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