class LocallyLinearEmbedding (part of the Efficient Dimensionality Reduction Toolkit) used to embed data using Locally Linear Embedding algorithm described in
Saul, L. K., Ave, P., Park, F., & Roweis, S. T. (2001). An Introduction to Locally Linear Embedding. Available from, 290(5500), 2323-2326. Retrieved from: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.123.7319&rep=rep1&type=pdf
The process of finding nearest neighbors is parallel and involves Fibonacci Heap and Euclidean distance.
Linear reconstruction step runs in parallel for objects and involves LAPACK routine DPOSV for solving a system of linear equations.
The eigenproblem stated in the algorithm is solved with LAPACK routine DSYEVR or with ARPACK DSAUPD/DSEUPD routines if available.
Due to computation speed, ARPACK is being used with small regularization of weight matrix and Cholesky factorization is used internally for Lanzcos iterations (in case of only LAPACK is available) and SUPERLU library for fast solving sparse equations stated by ARPACK is being used if available.
This class also have capability of selecting k automatically in range between "k" and "max_k" in case if "auto_k" is true. This is being done using ternary search of minima of the mean reconstruction error. The reconstruction error is considered to have only one global minimum in this mode.
It is optimized with alignment formulation as described in
Zhao, D. (2006). Formulating LLE using alignment technique. Pattern Recognition, 39(11), 2233-2235. Retrieved from http://linkinghub.elsevier.com/retrieve/pii/S0031320306002160
To use this converter with static interfaces please refer it by sg('create_converter','lle',k);
Definition at line 67 of file LocallyLinearEmbedding.h.
Public Member Functions | |
CLocallyLinearEmbedding () | |
virtual | ~CLocallyLinearEmbedding () |
virtual CFeatures * | apply (CFeatures *features) |
void | set_k (int32_t k) |
int32_t | get_k () const |
void | set_max_k (int32_t max_k) |
int32_t | get_max_k () const |
void | set_auto_k (bool auto_k) |
bool | get_auto_k () const |
void | set_reconstruction_shift (float64_t reconstruction_shift) |
float64_t | get_reconstruction_shift () const |
void | set_nullspace_shift (float64_t nullspace_shift) |
float64_t | get_nullspace_shift () const |
void | set_use_arpack (bool use_arpack) |
bool | get_use_arpack () const |
virtual const char * | get_name () 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) |
CDistance * | get_distance () const |
void | set_kernel (CKernel *kernel) |
CKernel * | get_kernel () const |
virtual CSGObject * | shallow_copy () const |
virtual CSGObject * | deep_copy () const |
virtual bool | is_generic (EPrimitiveType *generic) const |
template<class T > | |
void | set_generic () |
void | unset_generic () |
virtual void | print_serializable (const char *prefix="") |
virtual bool | save_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=VERSION_PARAMETER) |
virtual bool | load_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=VERSION_PARAMETER) |
DynArray< TParameter * > * | load_file_parameters (const SGParamInfo *param_info, int32_t file_version, CSerializableFile *file, const char *prefix="") |
DynArray< TParameter * > * | load_all_file_parameters (int32_t file_version, int32_t current_version, CSerializableFile *file, const char *prefix="") |
void | map_parameters (DynArray< TParameter * > *param_base, int32_t &base_version, DynArray< const SGParamInfo * > *target_param_infos) |
void | set_global_io (SGIO *io) |
SGIO * | get_global_io () |
void | set_global_parallel (Parallel *parallel) |
Parallel * | get_global_parallel () |
void | set_global_version (Version *version) |
Version * | get_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_parameter_dictionary (CMap< TParameter *, CSGObject * > &dict) |
Public Attributes | |
SGIO * | io |
Parallel * | parallel |
Version * | version |
Parameter * | m_parameters |
Parameter * | m_model_selection_parameters |
ParameterMap * | m_parameter_map |
uint32_t | m_hash |
Protected Member Functions | |
void | init () |
HELPERS. | |
virtual SGMatrix< float64_t > | construct_weight_matrix (CDenseFeatures< float64_t > *simple_features, float64_t *W_matrix, SGMatrix< int32_t > neighborhood_matrix) |
virtual SGMatrix< float64_t > | construct_embedding (SGMatrix< float64_t > matrix, int dimension) |
virtual SGMatrix< int32_t > | get_neighborhood_matrix (SGMatrix< float64_t > distance_matrix, int32_t k) |
int32_t | estimate_k (CDenseFeatures< float64_t > *simple_features, SGMatrix< int32_t > neighborhood_matrix) |
float64_t | compute_reconstruction_error (int32_t k, int dim, int N, float64_t *feature_matrix, float64_t *z_matrix, float64_t *covariance_matrix, float64_t *resid_vector, float64_t *id_vector, SGMatrix< int32_t > neighborhood_matrix) |
virtual TParameter * | migrate (DynArray< TParameter * > *param_base, const SGParamInfo *target) |
virtual void | one_to_one_migration_prepare (DynArray< TParameter * > *param_base, const SGParamInfo *target, TParameter *&replacement, TParameter *&to_migrate, char *old_name=NULL) |
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) |
virtual bool | update_parameter_hash () |
Static Protected Member Functions | |
static void * | run_linearreconstruction_thread (void *p) |
THREADS. | |
Protected Attributes | |
int32_t | m_k |
FIELDS. | |
int32_t | m_max_k |
float64_t | m_reconstruction_shift |
float64_t | m_nullspace_shift |
bool | m_use_arpack |
bool | m_auto_k |
int32_t | m_target_dim |
CDistance * | m_distance |
CKernel * | m_kernel |
constructor
Definition at line 95 of file LocallyLinearEmbedding.cpp.
~CLocallyLinearEmbedding | ( | ) | [virtual] |
destructor
Definition at line 127 of file LocallyLinearEmbedding.cpp.
apply preprocessor to features
features |
Implements CEmbeddingConverter.
Reimplemented in CKernelLocallyLinearEmbedding.
Definition at line 198 of file LocallyLinearEmbedding.cpp.
void build_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.
dict | dictionary of parameters to be built. |
Definition at line 1201 of file SGObject.cpp.
float64_t compute_reconstruction_error | ( | int32_t | k, | |
int | dim, | |||
int | N, | |||
float64_t * | feature_matrix, | |||
float64_t * | z_matrix, | |||
float64_t * | covariance_matrix, | |||
float64_t * | resid_vector, | |||
float64_t * | id_vector, | |||
SGMatrix< int32_t > | neighborhood_matrix | |||
) | [protected] |
computes reconstruction error using subset of given features
k | ||
dim | ||
N | ||
feature_matrix | ||
z_matrix | ||
covariance_matrix | ||
resid_vector | ||
id_vector | ||
neighborhood_matrix |
Definition at line 298 of file LocallyLinearEmbedding.cpp.
SGMatrix< float64_t > construct_embedding | ( | SGMatrix< float64_t > | matrix, | |
int | dimension | |||
) | [protected, virtual] |
constructs embedding
matrix | computed weight matrix | |
dimension | dimension of embedding |
Definition at line 419 of file LocallyLinearEmbedding.cpp.
SGMatrix< float64_t > construct_weight_matrix | ( | CDenseFeatures< float64_t > * | simple_features, | |
float64_t * | W_matrix, | |||
SGMatrix< int32_t > | neighborhood_matrix | |||
) | [protected, virtual] |
constructs weight matrix
simple_features | features to be used | |
W_matrix | weight matrix | |
neighborhood_matrix | matrix containing neighbor idxs |
Reimplemented in CHessianLocallyLinearEmbedding, and CLocalTangentSpaceAlignment.
Definition at line 342 of file LocallyLinearEmbedding.cpp.
virtual CSGObject* deep_copy | ( | ) | const [virtual, inherited] |
A deep copy. All the instance variables will also be copied.
Definition at line 131 of file SGObject.h.
CDenseFeatures< float64_t > * embed | ( | CFeatures * | features | ) | [virtual, inherited] |
embed given features, acts the same as apply, but returns DenseFeatures
features | features to embed |
Definition at line 35 of file EmbeddingConverter.cpp.
int32_t estimate_k | ( | CDenseFeatures< float64_t > * | simple_features, | |
SGMatrix< int32_t > | neighborhood_matrix | |||
) | [protected] |
estimates k using ternary search
simple_features | simple features to use | |
neighborhood_matrix | matrix containing indexes of neighbors for every vector |
Definition at line 261 of file LocallyLinearEmbedding.cpp.
bool get_auto_k | ( | ) | const |
getter for auto_k parameter
Definition at line 158 of file LocallyLinearEmbedding.cpp.
CDistance * get_distance | ( | ) | const [inherited] |
SGIO * get_global_io | ( | ) | [inherited] |
Parallel * get_global_parallel | ( | ) | [inherited] |
Version * get_global_version | ( | ) | [inherited] |
int32_t get_k | ( | ) | const |
CKernel * get_kernel | ( | ) | const [inherited] |
int32_t get_max_k | ( | ) | const |
getter for max_k parameter
Definition at line 148 of file LocallyLinearEmbedding.cpp.
SGStringList< char > get_modelsel_names | ( | ) | [inherited] |
Definition at line 1108 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
param_name | name of the parameter |
Definition at line 1132 of file SGObject.cpp.
index_t get_modsel_param_index | ( | const char * | param_name | ) | [inherited] |
Returns index of model selection parameter with provided index
param_name | name of model selection parameter |
Definition at line 1145 of file SGObject.cpp.
const char * get_name | ( | ) | const [virtual] |
get name
Reimplemented from CEmbeddingConverter.
Reimplemented in CHessianLocallyLinearEmbedding, CKernelLocallyLinearEmbedding, CKernelLocalTangentSpaceAlignment, CLinearLocalTangentSpaceAlignment, CLocalTangentSpaceAlignment, and CNeighborhoodPreservingEmbedding.
Definition at line 193 of file LocallyLinearEmbedding.cpp.
SGMatrix< int32_t > get_neighborhood_matrix | ( | SGMatrix< float64_t > | distance_matrix, | |
int32_t | k | |||
) | [protected, virtual] |
constructs neighborhood matrix by distance
distance_matrix | distance matrix to be used | |
k | number of neighbors |
Reimplemented in CKernelLocallyLinearEmbedding.
Definition at line 566 of file LocallyLinearEmbedding.cpp.
float64_t get_nullspace_shift | ( | ) | const |
getter for nullspace shift parameter
Definition at line 168 of file LocallyLinearEmbedding.cpp.
float64_t get_reconstruction_shift | ( | ) | const |
getter for reconstruction shift parameter
Definition at line 178 of file LocallyLinearEmbedding.cpp.
int32_t get_target_dim | ( | ) | const [inherited] |
getter for target dimension
Definition at line 46 of file EmbeddingConverter.cpp.
bool get_use_arpack | ( | ) | const |
getter for use arpack parameter
Definition at line 188 of file LocallyLinearEmbedding.cpp.
void init | ( | ) | [protected] |
HELPERS.
default init
Reimplemented from CEmbeddingConverter.
Definition at line 111 of file LocallyLinearEmbedding.cpp.
bool is_generic | ( | EPrimitiveType * | generic | ) | const [virtual, inherited] |
If the SGSerializable is a class template then TRUE will be returned and GENERIC is set to the type of the generic.
generic | set to the type of the generic if returning TRUE |
Definition at line 278 of file SGObject.cpp.
DynArray< TParameter * > * load_all_file_parameters | ( | int32_t | file_version, | |
int32_t | current_version, | |||
CSerializableFile * | file, | |||
const char * | prefix = "" | |||
) | [inherited] |
maps all parameters of this instance to the provided file version and loads all parameter data from the file into an array, which is sorted (basically calls load_file_parameter(...) for all parameters and puts all results into a sorted array)
file_version | parameter version of the file | |
current_version | version from which mapping begins (you want to use VERSION_PARAMETER for this in most cases) | |
file | file to load from | |
prefix | prefix for members |
Definition at line 679 of file SGObject.cpp.
DynArray< TParameter * > * load_file_parameters | ( | const SGParamInfo * | param_info, | |
int32_t | file_version, | |||
CSerializableFile * | file, | |||
const char * | prefix = "" | |||
) | [inherited] |
loads some specified parameters from a file with a specified version The provided parameter info has a version which is recursively mapped until the file parameter version is reached. Note that there may be possibly multiple parameters in the mapping, therefore, a set of TParameter instances is returned
param_info | information of parameter | |
file_version | parameter version of the file, must be <= provided parameter version | |
file | file to load from | |
prefix | prefix for members |
Definition at line 523 of file SGObject.cpp.
bool load_serializable | ( | CSerializableFile * | file, | |
const char * | prefix = "" , |
|||
int32_t | param_version = VERSION_PARAMETER | |||
) | [virtual, inherited] |
Load this object from file. If it will fail (returning FALSE) then this object will contain inconsistent data and should not be used!
file | where to load from | |
prefix | prefix for members | |
param_version | (optional) a parameter version different to (this is mainly for testing, better do not use) |
Reimplemented in CModelSelectionParameters.
Definition at line 354 of file SGObject.cpp.
void load_serializable_post | ( | ) | throw (ShogunException) [protected, virtual, inherited] |
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.
ShogunException | Will be thrown if an error occurres. |
Reimplemented in CLinearHMM, CAlphabet, CANOVAKernel, CCircularKernel, CExponentialKernel, CGaussianKernel, CInverseMultiQuadricKernel, CKernel, CWeightedDegreePositionStringKernel, and CList.
Definition at line 1033 of file SGObject.cpp.
void load_serializable_pre | ( | ) | throw (ShogunException) [protected, virtual, inherited] |
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.
ShogunException | Will be thrown if an error occurres. |
Definition at line 1028 of file SGObject.cpp.
void map_parameters | ( | DynArray< TParameter * > * | param_base, | |
int32_t & | base_version, | |||
DynArray< const SGParamInfo * > * | target_param_infos | |||
) | [inherited] |
Takes a set of TParameter instances (base) with a certain version and a set of target parameter infos and recursively maps the base level wise to the current version using CSGObject::migrate(...). The base is replaced. After this call, the base version containing parameters should be of same version/type as the initial target parameter infos. Note for this to work, the migrate methods and all the internal parameter mappings have to match
param_base | set of TParameter instances that are mapped to the provided target parameter infos | |
base_version | version of the parameter base | |
target_param_infos | set of SGParamInfo instances that specify the target parameter base |
Definition at line 717 of file SGObject.cpp.
TParameter * migrate | ( | DynArray< TParameter * > * | param_base, | |
const SGParamInfo * | target | |||
) | [protected, virtual, inherited] |
creates a new TParameter instance, which contains migrated data from the version that is provided. The provided parameter data base is used for migration, this base is a collection of all parameter data of the previous version. Migration is done FROM the data in param_base TO the provided param info Migration is always one version step. Method has to be implemented in subclasses, if no match is found, base method has to be called.
If there is an element in the param_base which equals the target, a copy of the element is returned. This represents the case when nothing has changed and therefore, the migrate method is not overloaded in a subclass
param_base | set of TParameter instances to use for migration | |
target | parameter info for the resulting TParameter |
Definition at line 923 of file SGObject.cpp.
void one_to_one_migration_prepare | ( | DynArray< TParameter * > * | param_base, | |
const SGParamInfo * | target, | |||
TParameter *& | replacement, | |||
TParameter *& | to_migrate, | |||
char * | old_name = NULL | |||
) | [protected, virtual, inherited] |
This method prepares everything for a one-to-one parameter migration. One to one here means that only ONE element of the parameter base is needed for the migration (the one with the same name as the target). Data is allocated for the target (in the type as provided in the target SGParamInfo), and a corresponding new TParameter instance is written to replacement. The to_migrate pointer points to the single needed TParameter instance needed for migration. If a name change happened, the old name may be specified by old_name. In addition, the m_delete_data flag of to_migrate is set to true. So if you want to migrate data, the only thing to do after this call is converting the data in the m_parameter fields. If unsure how to use - have a look into an example for this. (base_migration_type_conversion.cpp for example)
param_base | set of TParameter instances to use for migration | |
target | parameter info for the resulting TParameter | |
replacement | (used as output) here the TParameter instance which is returned by migration is created into | |
to_migrate | the only source that is used for migration | |
old_name | with this parameter, a name change may be specified |
Definition at line 864 of file SGObject.cpp.
void print_modsel_params | ( | ) | [inherited] |
prints all parameter registered for model selection and their type
Definition at line 1084 of file SGObject.cpp.
void print_serializable | ( | const char * | prefix = "" |
) | [virtual, inherited] |
prints registered parameters out
prefix | prefix for members |
Definition at line 290 of file SGObject.cpp.
void * run_linearreconstruction_thread | ( | void * | p | ) | [static, protected] |
THREADS.
runs linear reconstruction thread
p | thread params |
Reimplemented in CKernelLocallyLinearEmbedding.
Definition at line 473 of file LocallyLinearEmbedding.cpp.
bool save_serializable | ( | CSerializableFile * | file, | |
const char * | prefix = "" , |
|||
int32_t | param_version = VERSION_PARAMETER | |||
) | [virtual, inherited] |
Save this object to file.
file | where to save the object; will be closed during returning if PREFIX is an empty string. | |
prefix | prefix for members | |
param_version | (optional) a parameter version different to (this is mainly for testing, better do not use) |
Reimplemented in CModelSelectionParameters.
Definition at line 296 of file SGObject.cpp.
void save_serializable_post | ( | ) | throw (ShogunException) [protected, virtual, inherited] |
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.
ShogunException | Will be thrown if an error occurres. |
Reimplemented in CKernel.
Definition at line 1043 of file SGObject.cpp.
void save_serializable_pre | ( | ) | throw (ShogunException) [protected, virtual, inherited] |
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.
ShogunException | Will be thrown if an error occurres. |
Reimplemented in CKernel.
Definition at line 1038 of file SGObject.cpp.
void set_auto_k | ( | bool | auto_k | ) |
setter for auto_k parameter
auto_k | auto_k value |
Definition at line 153 of file LocallyLinearEmbedding.cpp.
void set_distance | ( | CDistance * | distance | ) | [inherited] |
setter for distance
distance | distance to set |
Definition at line 51 of file EmbeddingConverter.cpp.
void set_generic< floatmax_t > | ( | ) | [inherited] |
set generic type to T
void set_global_io | ( | SGIO * | io | ) | [inherited] |
void set_global_parallel | ( | Parallel * | parallel | ) | [inherited] |
set the parallel object
parallel | parallel object to use |
Definition at line 230 of file SGObject.cpp.
void set_global_version | ( | Version * | version | ) | [inherited] |
set the version object
version | version object to use |
Definition at line 265 of file SGObject.cpp.
void set_k | ( | int32_t | k | ) |
setter for k parameter
k | k value |
Definition at line 131 of file LocallyLinearEmbedding.cpp.
void set_kernel | ( | CKernel * | kernel | ) | [inherited] |
setter for kernel
kernel | kernel to set |
Definition at line 64 of file EmbeddingConverter.cpp.
void set_max_k | ( | int32_t | max_k | ) |
setter for max_k parameter
max_k | max_k value |
Definition at line 142 of file LocallyLinearEmbedding.cpp.
void set_nullspace_shift | ( | float64_t | nullspace_shift | ) |
setter for nullspace shift parameter
nullspace_shift | nullsapce shift value |
Definition at line 163 of file LocallyLinearEmbedding.cpp.
void set_reconstruction_shift | ( | float64_t | reconstruction_shift | ) |
setter for reconstruction shift parameter
reconstruction_shift | reconstruction shift value |
Definition at line 173 of file LocallyLinearEmbedding.cpp.
void set_target_dim | ( | int32_t | dim | ) | [inherited] |
setter for target dimension
dim | target dimension |
Definition at line 40 of file EmbeddingConverter.cpp.
void set_use_arpack | ( | bool | use_arpack | ) |
setter for use arpack parameter
use_arpack | use arpack value |
Definition at line 183 of file LocallyLinearEmbedding.cpp.
virtual CSGObject* shallow_copy | ( | ) | const [virtual, inherited] |
A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.
Reimplemented in CGaussianKernel.
Definition at line 122 of file SGObject.h.
void unset_generic | ( | ) | [inherited] |
unset generic type
this has to be called in classes specializing a template class
Definition at line 285 of file SGObject.cpp.
bool update_parameter_hash | ( | ) | [protected, virtual, inherited] |
Updates the hash of current parameter combination.
Definition at line 237 of file SGObject.cpp.
io
Definition at line 462 of file SGObject.h.
bool m_auto_k [protected] |
whether use automatic k or not
Definition at line 216 of file LocallyLinearEmbedding.h.
CDistance* m_distance [protected, inherited] |
distance to be used
Definition at line 97 of file EmbeddingConverter.h.
uint32_t m_hash [inherited] |
Hash of parameter values
Definition at line 480 of file SGObject.h.
int32_t m_k [protected] |
kernel to be used
Definition at line 100 of file EmbeddingConverter.h.
int32_t m_max_k [protected] |
maximum number of neighbors
Definition at line 204 of file LocallyLinearEmbedding.h.
Parameter* m_model_selection_parameters [inherited] |
model selection parameters
Definition at line 474 of file SGObject.h.
float64_t m_nullspace_shift [protected] |
regularization shift of nullspace finding step
Definition at line 210 of file LocallyLinearEmbedding.h.
ParameterMap* m_parameter_map [inherited] |
map for different parameter versions
Definition at line 477 of file SGObject.h.
Parameter* m_parameters [inherited] |
parameters
Definition at line 471 of file SGObject.h.
float64_t m_reconstruction_shift [protected] |
regularization shift of reconstruction step
Definition at line 207 of file LocallyLinearEmbedding.h.
int32_t m_target_dim [protected, inherited] |
target dim of dimensionality reduction preprocessor
Definition at line 94 of file EmbeddingConverter.h.
bool m_use_arpack [protected] |
whether use arpack or not
Definition at line 213 of file LocallyLinearEmbedding.h.
parallel
Definition at line 465 of file SGObject.h.
version
Definition at line 468 of file SGObject.h.