# Isomap

Isomap is a method for low-dimensional embedding. Isomap is used for computing a quasi-isometric, low-dimensional embedding of a set of high-dimensional data points[1].

This package defines a Isomap type to represent a Isomap calculation results, and provides a set of methods to access its properties.

ManifoldLearning.IsomapType
Isomap{NN <: AbstractNearestNeighbors} <: AbstractDimensionalityReduction

The Isomap type represents an isometric mapping model constructed with a help of the NN nearest neighbor algorithm.

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StatsBase.fitMethod
fit(Isomap, data; k=12, maxoutdim=2, nntype=BruteForce)

Fit an isometric mapping model to data.

Arguments

• data: a matrix of observations. Each column of data is an observation.

Keyword arguments

• k: a number of nearest neighbors for construction of local subspace representation
• maxoutdim: a dimension of the reduced space.
• nntype: a nearest neighbor construction class (derived from AbstractNearestNeighbors)

Examples

M = fit(Isomap, rand(3,100)) # construct Isomap model
R = transform(M)             # perform dimensionality reduction
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MultivariateStats.transformMethod
transform(R::Isomap, X::AbstractVecOrMat)

Returns a transformed out-of-sample data X given the Isomap model R into a reduced space representation.

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## References

• 1Tenenbaum, J. B., de Silva, V. and Langford, J. C. "A Global Geometric Framework for Nonlinear Dimensionality Reduction". Science 290 (5500): 2319-2323, 22 December 2000.