SHOGUN  4.1.0
CIsomap Class Reference

## Detailed Description

The Isomap class is used to embed data using Isomap algorithm as described in:

Silva, V. D., & Tenenbaum, J. B. (2003). Global versus local methods in nonlinear dimensionality reduction. Advances in Neural Information Processing Systems 15, 15(Figure 2), 721-728. MIT Press. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.9.3407&rep=rep1&type=pdf

The Isomap algorithm can be considered as a modification of the classic Multidimensional Scaling algorithm. The algorithm itself consists of the following steps:

• For each feature vector $$x\in X$$ find its $$k$$ nearest neighbours and construct the sparse neighbourhood graph.
• Compute the squared distances matrix $$D$$ such as $$D\{i,j\} = d^2(x_i,x_j)$$.
• Relax distances with shortest (so-called geodesic) distances on the sparse neighbourhood graph (e.g. with Dijkstra's algorithm).
• Center the matrix $$D$$ with subtracting row mean, column mean and adding to the grand mean. Multiply $$D$$ element-wise with $$-0.5$$.
• Compute embedding with the $$t$$ eigenvectors that correspond to the largest eigenvalues of the matrix $$D$$; normalize these vectors dividing each eigenvector by the square root of its corresponding eigenvalue. Form the final embedding with eigenvectors as rows and projected feature vectors as columns.

It is possible to apply preprocessor to specified distance using apply_to_distance.

Uses implementation from the Tapkee library.

To use this converter with static interfaces please refer it by sg('create_converter','isomap',k);

Definition at line 59 of file Isomap.h.

Inheritance diagram for CIsomap:
[legend]

## Public Member Functions

CIsomap ()

virtual ~CIsomap ()

const char * get_name () const

void set_k (int32_t k)

int32_t get_k () const

virtual CDenseFeatures
< float64_t > *
embed_distance (CDistance *distance)

virtual CFeaturesapply (CFeatures *features)

SGVector< float64_tget_eigenvalues () const

void set_landmark_number (int32_t num)

int32_t get_landmark_number () const

void set_landmark (bool landmark)

bool get_landmark () const

virtual CDenseFeatures
< float64_t > *
embed (CFeatures *features)

void set_target_dim (int32_t dim)

int32_t get_target_dim () const

void set_distance (CDistance *distance)

CDistanceget_distance () const

void set_kernel (CKernel *kernel)

CKernelget_kernel () const

virtual CSGObjectshallow_copy () const

virtual CSGObjectdeep_copy () const

virtual bool is_generic (EPrimitiveType *generic) const

template<class T >
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

void unset_generic ()

virtual void print_serializable (const char *prefix="")

virtual bool save_serializable (CSerializableFile *file, const char *prefix="")

virtual bool load_serializable (CSerializableFile *file, const char *prefix="")

void set_global_io (SGIO *io)

SGIOget_global_io ()

void set_global_parallel (Parallel *parallel)

Parallelget_global_parallel ()

void set_global_version (Version *version)

Versionget_global_version ()

SGStringList< char > get_modelsel_names ()

void print_modsel_params ()

char * get_modsel_param_descr (const char *param_name)

index_t get_modsel_param_index (const char *param_name)

void build_gradient_parameter_dictionary (CMap< TParameter *, CSGObject * > *dict)

virtual void update_parameter_hash ()

virtual bool parameter_hash_changed ()

virtual bool equals (CSGObject *other, float64_t accuracy=0.0, bool tolerant=false)

virtual CSGObjectclone ()

## Public Attributes

SGIOio

Parallelparallel

Versionversion

Parameterm_parameters

Parameterm_model_selection_parameters

uint32_t m_hash

## Protected Member Functions

virtual void init ()
HELPERS. More...

virtual void load_serializable_pre () throw (ShogunException)

virtual void load_serializable_post () throw (ShogunException)

virtual void save_serializable_pre () throw (ShogunException)

virtual void save_serializable_post () throw (ShogunException)

## Protected Attributes

int32_t m_k
FIELDS. More...

SGVector< float64_tm_eigenvalues
FIELDS. More...

bool m_landmark

int32_t m_landmark_number

int32_t m_target_dim

CDistancem_distance

CKernelm_kernel

## Constructor & Destructor Documentation

 CIsomap ( )

Definition at line 19 of file Isomap.cpp.

 ~CIsomap ( )
virtual

Definition at line 31 of file Isomap.cpp.

## Member Function Documentation

 CFeatures * apply ( CFeatures * features )
virtualinherited

apply preprocessor to feature matrix, changes feature matrix to the one having target dimensionality

Parameters
 features features which feature matrix should be processed
Returns
new feature matrix

Implements CEmbeddingConverter.

Definition at line 103 of file MultidimensionalScaling.cpp.

 void build_gradient_parameter_dictionary ( CMap< TParameter *, CSGObject * > * dict )
inherited

Builds a dictionary of all parameters in SGObject as well of those of SGObjects that are parameters of this object. Dictionary maps parameters to the objects that own them.

Parameters
 dict dictionary of parameters to be built.

Definition at line 597 of file SGObject.cpp.

 CSGObject * clone ( )
virtualinherited

Creates a clone of the current object. This is done via recursively traversing all parameters, which corresponds to a deep copy. Calling equals on the cloned object always returns true although none of the memory of both objects overlaps.

Returns
an identical copy of the given object, which is disjoint in memory. NULL if the clone fails. Note that the returned object is SG_REF'ed

Definition at line 714 of file SGObject.cpp.

 CSGObject * deep_copy ( ) const
virtualinherited

A deep copy. All the instance variables will also be copied.

Definition at line 198 of file SGObject.cpp.

 CDenseFeatures< float64_t > * embed ( CFeatures * features )
virtualinherited

embed given features, acts the same as apply, but returns DenseFeatures

Parameters
 features features to embed
Returns
embedding simple features

Definition at line 35 of file EmbeddingConverter.cpp.

 CDenseFeatures< float64_t > * embed_distance ( CDistance * distance )
virtual

embed distance

Reimplemented from CMultidimensionalScaling.

Definition at line 51 of file Isomap.cpp.

 bool equals ( CSGObject * other, float64_t accuracy = 0.0, bool tolerant = false )
virtualinherited

Recursively compares the current SGObject to another one. Compares all registered numerical parameters, recursion upon complex (SGObject) parameters. Does not compare pointers!

May be overwritten but please do with care! Should not be necessary in most cases.

Parameters
 other object to compare with accuracy accuracy to use for comparison (optional) tolerant allows linient check on float equality (within accuracy)
Returns
true if all parameters were equal, false if not

Definition at line 618 of file SGObject.cpp.

 CDistance * get_distance ( ) const
inherited

getter for distance

Returns
distance

Definition at line 58 of file EmbeddingConverter.cpp.

 SGVector< float64_t > get_eigenvalues ( ) const
inherited

get last embedding eigenvectors

Returns
vector with last eigenvalues

Definition at line 48 of file MultidimensionalScaling.cpp.

 SGIO * get_global_io ( )
inherited

get the io object

Returns
io object

Definition at line 235 of file SGObject.cpp.

 Parallel * get_global_parallel ( )
inherited

get the parallel object

Returns
parallel object

Definition at line 277 of file SGObject.cpp.

 Version * get_global_version ( )
inherited

get the version object

Returns
version object

Definition at line 290 of file SGObject.cpp.

 int32_t get_k ( ) const

getter for k parameter

Returns
k value

Definition at line 41 of file Isomap.cpp.

 CKernel * get_kernel ( ) const
inherited

getter for kernel

Returns
kernel

Definition at line 71 of file EmbeddingConverter.cpp.

 bool get_landmark ( ) const
inherited

getter for landmark parameter

Returns
true if landmark embedding is used

Definition at line 71 of file MultidimensionalScaling.cpp.

 int32_t get_landmark_number ( ) const
inherited

get number of landmarks

Returns
current number of landmarks

Definition at line 61 of file MultidimensionalScaling.cpp.

 SGStringList< char > get_modelsel_names ( )
inherited
Returns
vector of names of all parameters which are registered for model selection

Definition at line 498 of file SGObject.cpp.

 char * get_modsel_param_descr ( const char * param_name )
inherited

Returns description of a given parameter string, if it exists. SG_ERROR otherwise

Parameters
 param_name name of the parameter
Returns
description of the parameter

Definition at line 522 of file SGObject.cpp.

 index_t get_modsel_param_index ( const char * param_name )
inherited

Returns index of model selection parameter with provided index

Parameters
 param_name name of model selection parameter
Returns
index of model selection parameter with provided name, -1 if there is no such

Definition at line 535 of file SGObject.cpp.

 const char * get_name ( ) const
virtual

get name

Reimplemented from CEmbeddingConverter.

Definition at line 46 of file Isomap.cpp.

 int32_t get_target_dim ( ) const
inherited

getter for target dimension

Returns
target dimension

Definition at line 46 of file EmbeddingConverter.cpp.

 void init ( )
protectedvirtual

HELPERS.

default init

Reimplemented from CMultidimensionalScaling.

Definition at line 26 of file Isomap.cpp.

 bool is_generic ( EPrimitiveType * generic ) const
virtualinherited

If the SGSerializable is a class template then TRUE will be returned and GENERIC is set to the type of the generic.

Parameters
 generic set to the type of the generic if returning TRUE
Returns
TRUE if a class template.

Definition at line 296 of file SGObject.cpp.

 bool load_serializable ( CSerializableFile * file, const char * prefix = "" )
virtualinherited

Load this object from file. If it will fail (returning FALSE) then this object will contain inconsistent data and should not be used!

Parameters
 file where to load from prefix prefix for members
Returns
TRUE if done, otherwise FALSE

Definition at line 369 of file SGObject.cpp.

 void load_serializable_post ( ) throw ( ShogunException )
protectedvirtualinherited

Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_POST is called.

Exceptions
 ShogunException will be thrown if an error occurs.

Definition at line 426 of file SGObject.cpp.

 void load_serializable_pre ( ) throw ( ShogunException )
protectedvirtualinherited

Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_PRE is called.

Exceptions
 ShogunException will be thrown if an error occurs.

Definition at line 421 of file SGObject.cpp.

 bool parameter_hash_changed ( )
virtualinherited
Returns
whether parameter combination has changed since last update

Definition at line 262 of file SGObject.cpp.

 void print_modsel_params ( )
inherited

prints all parameter registered for model selection and their type

Definition at line 474 of file SGObject.cpp.

 void print_serializable ( const char * prefix = "" )
virtualinherited

prints registered parameters out

Parameters
 prefix prefix for members

Definition at line 308 of file SGObject.cpp.

 bool save_serializable ( CSerializableFile * file, const char * prefix = "" )
virtualinherited

Save this object to file.

Parameters
 file where to save the object; will be closed during returning if PREFIX is an empty string. prefix prefix for members
Returns
TRUE if done, otherwise FALSE

Definition at line 314 of file SGObject.cpp.

 void save_serializable_post ( ) throw ( ShogunException )
protectedvirtualinherited

Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_POST is called.

Exceptions
 ShogunException will be thrown if an error occurs.

Reimplemented in CKernel.

Definition at line 436 of file SGObject.cpp.

 void save_serializable_pre ( ) throw ( ShogunException )
protectedvirtualinherited

Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_PRE is called.

Exceptions
 ShogunException will be thrown if an error occurs.

Definition at line 431 of file SGObject.cpp.

 void set_distance ( CDistance * distance )
inherited

setter for distance

Parameters
 distance distance to set

Definition at line 51 of file EmbeddingConverter.cpp.

 void set_generic ( )
inherited

Definition at line 41 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 46 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 51 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 56 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 61 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 66 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 71 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 76 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 81 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 86 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 91 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 96 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 101 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 106 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 111 of file SGObject.cpp.

 void set_generic ( )
inherited

set generic type to T

 void set_global_io ( SGIO * io )
inherited

set the io object

Parameters
 io io object to use

Definition at line 228 of file SGObject.cpp.

 void set_global_parallel ( Parallel * parallel )
inherited

set the parallel object

Parameters
 parallel parallel object to use

Definition at line 241 of file SGObject.cpp.

 void set_global_version ( Version * version )
inherited

set the version object

Parameters
 version version object to use

Definition at line 283 of file SGObject.cpp.

 void set_k ( int32_t k )

setter for k parameter

Parameters
 k value

Definition at line 35 of file Isomap.cpp.

 void set_kernel ( CKernel * kernel )
inherited

setter for kernel

Parameters
 kernel kernel to set

Definition at line 64 of file EmbeddingConverter.cpp.

 void set_landmark ( bool landmark )
inherited

setter for landmark parameter

Parameters
 landmark true if landmark embedding should be used

Definition at line 66 of file MultidimensionalScaling.cpp.

 void set_landmark_number ( int32_t num )
inherited

set number of landmarks should be lesser than number of examples and greater than 3 for consistent embedding as triangulation is used

Parameters
 num number of landmark to be set

Definition at line 53 of file MultidimensionalScaling.cpp.

 void set_target_dim ( int32_t dim )
inherited

setter for target dimension

Parameters
 dim target dimension

Definition at line 40 of file EmbeddingConverter.cpp.

 CSGObject * shallow_copy ( ) const
virtualinherited

A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.

Reimplemented in CGaussianKernel.

Definition at line 192 of file SGObject.cpp.

 void unset_generic ( )
inherited

unset generic type

this has to be called in classes specializing a template class

Definition at line 303 of file SGObject.cpp.

 void update_parameter_hash ( )
virtualinherited

Updates the hash of current parameter combination

Definition at line 248 of file SGObject.cpp.

## Member Data Documentation

 SGIO* io
inherited

io

Definition at line 369 of file SGObject.h.

 CDistance* m_distance
protectedinherited

distance to be used

Definition at line 99 of file EmbeddingConverter.h.

 SGVector m_eigenvalues
protectedinherited

FIELDS.

last embedding eigenvalues

Definition at line 124 of file MultidimensionalScaling.h.

inherited

parameters wrt which we can compute gradients

Definition at line 384 of file SGObject.h.

 uint32_t m_hash
inherited

Hash of parameter values

Definition at line 387 of file SGObject.h.

 int32_t m_k
protected

FIELDS.

k, number of neighbors for K-Isomap

Definition at line 95 of file Isomap.h.

 CKernel* m_kernel
protectedinherited

kernel to be used

Definition at line 102 of file EmbeddingConverter.h.

 bool m_landmark
protectedinherited

use landmark approximation?

Definition at line 127 of file MultidimensionalScaling.h.

 int32_t m_landmark_number
protectedinherited

number of landmarks

Definition at line 130 of file MultidimensionalScaling.h.

 Parameter* m_model_selection_parameters
inherited

model selection parameters

Definition at line 381 of file SGObject.h.

 Parameter* m_parameters
inherited

parameters

Definition at line 378 of file SGObject.h.

 int32_t m_target_dim
protectedinherited

target dim of dimensionality reduction preprocessor

Definition at line 96 of file EmbeddingConverter.h.

 Parallel* parallel
inherited

parallel

Definition at line 372 of file SGObject.h.

 Version* version
inherited

version

Definition at line 375 of file SGObject.h.

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

SHOGUN Machine Learning Toolbox - Documentation