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FeatureDistance[example1,example2,extractor]

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

FeatureDistance[extractor]

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

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
DistanceFunction  
Applications  
Properties & Relations  
Neat Examples  
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FeatureDistance

FeatureDistance[example1,example2,extractor]

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

FeatureDistance[extractor]

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

Details and Options

Examples

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Basic Examples  (1)

Train a FeatureExtractorFunction on a simple dataset of pairs to use with FeatureDistance:

Wolfram Language code: fe = FeatureExtraction[{{1.4, "A"}, {1.5, "A"}, {2.3, "B"}, {5.4, "B"}}]

Compute the distance between two pairs using the trained feature extractor:

Wolfram Language code: FeatureDistance[{1.8, "A"}, {4.5, "B"}, fe]

Scope  (1)

Train a FeatureDistance function on a list of colors:

Wolfram Language code: list = ColorData["AlpineColors"] /@ Range[0, 1, 0.1]
Wolfram Language code: fe = FeatureExtraction[list]
Wolfram Language code: fd = FeatureDistance[fe]

Compute the distance between new colors using the trained distance function:

Wolfram Language code: fd[Yellow, Orange]

Find the color closest to Red under this distance metric:

Wolfram Language code: Nearest[list, Red, 1, DistanceFunction -> fd]

Options  (1)

DistanceFunction  (1)

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

Wolfram Language code: fe = FeatureExtraction[{"the cat is grey", "my cat is fast", "this dog is scary", "the big dog"}, "TFIDF"]

Construct a feature distance for this feature extractor:

Wolfram Language code: fd1 = FeatureDistance[fe]
Wolfram Language code: fd1["the cat is grey", "the big dog"]

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

Wolfram Language code: fd2 = FeatureDistance[fe, DistanceFunction -> CosineDistance]
Wolfram Language code: fd2["the cat is grey", "the big dog"]

Applications  (1)

Construct a dataset of dog images:

Wolfram Language code: dataset = {[image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image]};

Train an extractor function from this dataset:

Wolfram Language code: fe = FeatureExtraction[dataset]

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

Wolfram Language code: FeatureDistance[[image], [image], fe]

Compare to EuclideanDistance between the extracted features:

Wolfram Language code: EuclideanDistance@@fe[{[image], [image]}]

Generate an operator form of FeatureDistance:

Wolfram Language code: fd = FeatureDistance[fe]

This operator form can be used to compute distances:

Wolfram Language code: fd[[image], [image]]

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

Wolfram Language code: dm = DistanceMatrix[dataset, DistanceFunction -> fd];
Wolfram Language code: dm // MatrixPlot

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

Wolfram Language code: dataset[[Ordering[Mean[dm], -1]]]

Properties & Relations  (1)

FeatureNearest can be used to find close examples in feature space:

Wolfram Language code: lines = ExampleData[{"Text", "OriginOfSpecies"}, "Lines"]; fe = FeatureExtraction[ExampleData[{"Text", "OriginOfSpecies"}, "Lines"], {"LowerCasedText", "TFIDF", "DimensionReducedVector"}]; FeatureNearest[ExampleData[{"Text", "OriginOfSpecies"}, "Lines"], "domesticated pigeons", FeatureExtractor -> fe]//Short//AbsoluteTiming

This is usually faster than using Nearest with custom DistanceFunction:

Wolfram Language code: fd = FeatureDistance[fe]; Nearest[lines, "domesticated pigeons", 1, DistanceFunction -> fd]//Short//AbsoluteTiming

Neat Examples  (1)

Generate a NearestNeighborGraph of handwritten digits:

Wolfram Language code: mnist = ExampleData[{"MachineLearning", "MNIST"}, "Data"]; fe = FeatureExtraction[Keys[mnist]]; fd = FeatureDistance[fe]

Sample a number of different digits:

Wolfram Language code: digits = Catenate@GroupBy[mnist, Values -> Keys, RandomSample[#, 2]&]

Compute the graph:

Wolfram Language code: NearestNeighborGraph[digits, DistanceFunction -> fd, VertexLabels -> Automatic]
Wolfram Research (2016), FeatureDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/FeatureDistance.html.

Text

Wolfram Research (2016), FeatureDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/FeatureDistance.html.

CMS

Wolfram Language. 2016. "FeatureDistance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FeatureDistance.html.

APA

Wolfram Language. (2016). FeatureDistance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FeatureDistance.html

BibTeX

@misc{reference.wolfram_2026_featuredistance, author="Wolfram Research", title="{FeatureDistance}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/FeatureDistance.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_featuredistance, organization={Wolfram Research}, title={FeatureDistance}, year={2016}, url={https://reference.wolfram.com/language/ref/FeatureDistance.html}, note=[Accessed: 13-June-2026]}