Hessian Eigenmaps
The Hessian Eigenmaps (Hessian LLE, HLLE) method adapts the weights in LLE
to minimize the Hessian operator. Like LLE
, it requires careful setting of the nearest neighbor parameter. The main advantage of Hessian LLE is the only method designed for non-convex data sets [1].
This package defines a HLLE
type to represent a Hessian LLE results, and provides a set of methods to access its properties.
ManifoldLearning.HLLE
— TypeHLLE{NN <: AbstractNearestNeighbors, T <: Real} <: NonlinearDimensionalityReduction
The HLLE
type represents a Hessian eigenmaps model constructed for T
type data with a help of the NN
nearest neighbor algorithm.
StatsAPI.fit
— Methodfit(HLLE, data; k=12, maxoutdim=2, nntype=BruteForce)
Fit a Hessian eigenmaps model to data
.
Arguments
data
: a matrix of observations. Each column ofdata
is an observation.
Keyword arguments
k
: a number of nearest neighbors for construction of local subspace representationmaxoutdim
: a dimension of the reduced space.nntype
: a nearest neighbor construction class (derived fromAbstractNearestNeighbors
)
Examples
M = fit(HLLE, rand(3,100)) # construct Hessian eigenmaps model
R = predict(M) # perform dimensionality reduction
StatsAPI.predict
— Methodpredict(R::HLLE)
Transforms the data fitted to the Hessian eigenmaps model R
into a reduced space representation.
References
- 1Donoho, D. and Grimes, C. "Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data", Proc. Natl. Acad. Sci. USA. 2003 May 13; 100(10): 5591–5596. DOI:10.1073/pnas.1031596100