FeatureDistance

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`FeatureDistance`

[Experimental]

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FeatureDistance[example₁,example₂,extractor]

gives the distance between example₁ and example₂ in the feature space defined by extractor.

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FeatureDistance[extractor]

represents an operator form of FeatureDistance that can be applied to a pair of examples.

Details and Options

FeatureDistance can be used on many types of data, including numerical, textual, sounds, and images, as well as combinations of these.
The extractor is typically a FeatureExtractorFunction object as generated by FeatureExtraction.
FeatureDistance[extractor][ex₁,ex₂] is equivalent to FeatureDistance[ex₁,ex₂,extractor].
The following options can be given:
DistanceFunction Automatic the distance to use in the feature space
The option DistanceFunction can be any distance or dissimilarity function or a function f defining a distance between two values.
For numeric feature vectors, the default setting is DistanceFunctionEuclideanDistance.

Examples

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Basic Examples (1)Summary of the most common use cases

Construct a dataset of dog images:

In[1]:=1

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https://wolfram.com/xid/0n4lbm4u8j2-j1wja

Train an extractor function from this dataset:

In[2]:=2

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https://wolfram.com/xid/0n4lbm4u8j2-tgbyra

Out[2]=2

Compute the distance in the feature space between two images using FeatureDistance:

In[3]:=3

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https://wolfram.com/xid/0n4lbm4u8j2-vorwy8

Out[3]=3

Generate an operator form of FeatureDistance:

In[4]:=4

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https://wolfram.com/xid/0n4lbm4u8j2-yn5hu5

Out[4]=4

This operator form can be used to compute distances:

In[5]:=5

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https://wolfram.com/xid/0n4lbm4u8j2-k0bv8h

Out[5]=5

Compute the distance matrix of the dataset using this feature distance:

In[6]:=6

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https://wolfram.com/xid/0n4lbm4u8j2-mbpe22

In[7]:=7

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https://wolfram.com/xid/0n4lbm4u8j2-g3kjo7

Out[7]=7

Find the dog that maximizes its distance from the others in the feature space:

In[8]:=8

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https://wolfram.com/xid/0n4lbm4u8j2-s9mh8g

Out[8]=8

Options (1)Common values & functionality for each option

DistanceFunction (1)

Train a feature extractor to compute term frequency-inverse document frequency vectors from texts:

In[1]:=1

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https://wolfram.com/xid/0n4lbm4u8j2-z78xih

Out[1]=1

Construct a feature distance for this feature extractor:

In[2]:=2

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https://wolfram.com/xid/0n4lbm4u8j2-0o3p11

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0n4lbm4u8j2-ilk6s8

Out[3]=3

The distance function EuclideanDistance has been chosen. Use the option DistanceFunction to chose CosineDistance instead:

In[4]:=4

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https://wolfram.com/xid/0n4lbm4u8j2-ojw8jn

Out[4]=4

In[5]:=5

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https://wolfram.com/xid/0n4lbm4u8j2-xztmwj

Out[5]=5

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