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 results, and provides a set of methods to access its properties.

Properties¶

Let M be an instance of Isomap, n be the number of observations, and d be the output dimension.

outdim(M)¶: Get the output dimension d, i.e the dimension of the subspace.

projection(M)¶: Get the projection matrix (of size (d, n)). Each column of the projection matrix corresponds to an observation in projected subspace.

neighbors(M)¶: The number of nearest neighbors used for approximating local coordinate structure.

ccomponent(M)¶: The observations index array of the largest connected component of the distance matrix.

Data Transformation¶

One can use the transform method to perform Isomap over a given dataset.

transform(Isomap, X; ...)¶

Perform Isomap over the data given in a matrix X. Each column of X is an observation.

This method returns an instance of Isomap.

Keyword arguments:

name	description	default
k	The number of nearest neighbors for determining local coordinate structure.	`12`
d	Output dimension.	`2`

Example:

using ManifoldLearning

# suppose X is a data matrix, with each observation in a column
# apply Isomap transformation to the dataset
Y = transform(Isomap, X; k = 12, d = 2)

References

[1]	Tenenbaum, 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. http://isomap.stanford.edu/