CLaplacianEigenmaps Class Reference

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Detailed Description

the class LaplacianEigenmaps used to preprocess data using Laplacian Eigenmaps algorithm as described in:

Belkin, M., & Niyogi, P. (2002). Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering. Science, 14, 585-591. MIT Press. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.19.9400&rep=rep1&type=pdf

Note that the algorithm is very sensitive to the heat distribution coefficient and number of neighbors in the nearest neighbor graph. No connectivity check is provided, so the preprocessor will not produce reasonable embeddings if the k value makes a graph that is not connected.

This implementation is not parallel due to performance issues. Generalized eigenproblem is the bottleneck for this algorithm.

Solving of generalized eigenproblem involves LAPACK DSYGVX routine and requires extra memory for right-hand side matrix storage. If ARPACK is available then DSAUPD/DSEUPD is used with no extra memory usage.

Definition at line 47 of file LaplacianEigenmaps.h.

Inheritance diagram for CLaplacianEigenmaps:

List of all members.

Public Member Functions
	CLaplacianEigenmaps ()
virtual	~CLaplacianEigenmaps ()
virtual CFeatures *	apply (CFeatures *features)
virtual CSimpleFeatures < float64_t > *	embed_distance (CDistance *distance, CFeatures *features=NULL)
void	set_k (int32_t k)
int32_t	get_k () const
void	set_tau (float64_t tau)
float64_t	get_tau () const
virtual const char *	get_name () const
Protected Member Functions
void	init ()
virtual CSimpleFeatures < float64_t > *	construct_embedding (CFeatures *features, SGMatrix< float64_t > W_matrix)
Protected Attributes
int32_t	m_k
float64_t	m_tau

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Constructor & Destructor Documentation

CLaplacianEigenmaps

(

)

constructor

Definition at line 24 of file LaplacianEigenmaps.cpp.

~CLaplacianEigenmaps

(

)

[virtual]

destructor

Definition at line 39 of file LaplacianEigenmaps.cpp.

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Member Function Documentation

CFeatures * apply

(

CFeatures *

features

)

[virtual]

apply to features

Parameters:

	features	to embed
	embedding	features

Implements CEmbeddingConverter.

Definition at line 69 of file LaplacianEigenmaps.cpp.

CSimpleFeatures< float64_t > * construct_embedding	(	CFeatures *	features,
		SGMatrix< float64_t >	W_matrix
	)			[protected, virtual]

construct embedding

Parameters:

	features	features
	W_matrix	W matrix to be used

Reimplemented in CLocalityPreservingProjections.

Definition at line 160 of file LaplacianEigenmaps.cpp.

CSimpleFeatures< float64_t > * embed_distance	(	CDistance *	distance,
		CFeatures *	features = NULL
	)			[virtual]

embed distance

Parameters:

	distance	to use for embedding
	embedding	features

Definition at line 88 of file LaplacianEigenmaps.cpp.

int32_t get_k

(

)

const

getter for K parameter

Returns:

k value

Definition at line 49 of file LaplacianEigenmaps.cpp.

const char * get_name

(

)

const [virtual]

get name

Reimplemented from CEmbeddingConverter.

Reimplemented in CLocalityPreservingProjections.

Definition at line 64 of file LaplacianEigenmaps.cpp.

float64_t get_tau

(

)

const

getter for TAU parameter

Returns:

tau value

Definition at line 59 of file LaplacianEigenmaps.cpp.

void init

(

)

[protected]

init

Reimplemented from CEmbeddingConverter.

Definition at line 33 of file LaplacianEigenmaps.cpp.

void set_k

(

int32_t

k

)

setter for K parameter

Parameters:

k

k value

Definition at line 43 of file LaplacianEigenmaps.cpp.

void set_tau

(

float64_t

tau

)

setter for TAU parameter

Parameters:

tau

tau value

Definition at line 54 of file LaplacianEigenmaps.cpp.

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Member Data Documentation

int32_t m_k [protected]

number of neighbors

Definition at line 107 of file LaplacianEigenmaps.h.

float64_t m_tau [protected]

tau parameter of heat distribution

Definition at line 110 of file LaplacianEigenmaps.h.

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The documentation for this class was generated from the following files:

• LaplacianEigenmaps.h
• LaplacianEigenmaps.cpp