System

CentralFeature

CentralFeature[{x1,x2,}]

gives the central feature of the elements .

CentralFeature[{x1v1,x2v2,}]

gives the vi corresponding to the central feature .

CentralFeature[data]

gives the central feature for several different forms of data.

Details and Options

  • CentralFeature is a location measure. It gives a point in the data with the minimum total distance to every other point.
  • CentralFeature finds the element that minimizes the sum of distances for the unweighted case and for the weighted case.
  • The data data has the following forms and interpretations:
  • {data1,data2,}list of data of different formats including numerical, geospatial, textual, visual, dates and times, as well as combinations of these
    {data1,data2,}{v1,v2,}data with indices {v1,v2,}
    {data1,data2,}Automatictake the vi to be successive integers i
    GeoPosition[]array of geodetic positions
    WeightedData[]data with weights
  • The following option can be given:
  • DistanceFunctionAutomaticthe distance metric to use
  • The setting for DistanceFunction can be any distance or dissimilarity function or a function f defining a distance between two points.
  • By default, the following distance functions are used for different types of elements:
  • EuclideanDistancenumeric data
    ImageDistanceimages
    JaccardDissimilarityBoolean data
    EditDistancetext and nominal sequences
    Abs[DateDifference[#1,#2]]&dates and times
    ColorDistancecolors
    GeoDistancegeospatial data
    Boole[SameQ[#1,#2]]&nominal data
    HammingDistancenominal vector data
    WarpingDistancenumerical sequences
  • All images are first conformed using ConformImages when the option DistanceFunction is Automatic.
  • By default, when data elements are mixed-type vectors, distances are computed independently for each type and combined using Norm.

Examples

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Basic Examples  (2)

Find the central feature in a list of vectors:

In[1]:=
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Out[1]=

Find the central feature in a list of vectors with given weights:

In[1]:=
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Out[1]=

Scope  (9)

Options  (2)

Applications  (4)

Properties & Relations  (5)

See Also

Mean  Median  TrimmedMean  WinsorizedMean  BiweightLocation  SpatialMedian  GraphCenter  DistanceMatrix

Introduced in 2017
(11.1)