Detailed Description

ZeroMeanCenterKernelNormalizer centers the kernel in feature space.

After centering, each feature must have zero mean. The centered kernel matrix can be expressed in terms of the non-centered version.

Denoting the mapping from input space to feature space by $\phi:\mathcal{X}\rightarrow\mathcal{F}$ , the centered square kernel matrix $K_c$ (with dimensionality $ M $ )

can be expressed in terms of the original matrix $K$ as follows:

$\begin{eqnarray*} k({\bf x}_i,{\bf x}_j)_c & = & \left(\phi({\bf x}_i) - \frac{1}{m} \sum_{p=1}^M \phi({\bf x}_p)\right) \cdot \left(\phi({\bf x}_j) - \frac{1}{M} \sum_{q=1}^M \phi({\bf x}_q)\right) \\ & = & K_{ij} - \frac{1}{M} \sum_{p=1}^M K_{pj} - \frac{1}{M} \sum_{q=1}^M K_{iq} + \frac{1}{M^2} \sum_{p=1}^M \sum_{q=1}^M K_{pq} \\ & = & (K - 1_M K - K 1_M + 1_M K 1_M)_{ij} \end{eqnarray*}$

Additionally, let $K^{t}$ be the $L \times M$ test matrix describing the similarity between a $ L $ test instances with $M$ training instances

(defined by a $ M x M $ kernel matrix $ K$ ), the centered testing set kernel matrix is given by

$K_{c}^t = (K - 1'_M K - K^{t} 1_M + 1'_M K 1_M)$

Definition at line 41 of file ZeroMeanCenterKernelNormalizer.h.

Inheritance diagram for CZeroMeanCenterKernelNormalizer:

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Public Member Functions
	CZeroMeanCenterKernelNormalizer ()
virtual	~CZeroMeanCenterKernelNormalizer ()
virtual bool	init (CKernel *k)
virtual float64_t	normalize (float64_t value, int32_t idx_lhs, int32_t idx_rhs)
virtual float64_t	normalize_lhs (float64_t value, int32_t idx_lhs)
virtual float64_t	normalize_rhs (float64_t value, int32_t idx_rhs)
bool	alloc_and_compute_row_means (CKernel k, float64_t &v, int32_t num_lhs, int32_t num_rhs)
virtual const char *	get_name () const
Public Member Functions inherited from CKernelNormalizer
	CKernelNormalizer ()
virtual	~CKernelNormalizer ()
virtual void	register_params ()
ENormalizerType	get_normalizer_type ()
void	set_normalizer_type (ENormalizerType type)
Public Member Functions inherited from CSGObject
	CSGObject ()
	CSGObject (const CSGObject &orig)
virtual	~CSGObject ()
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="")
virtual bool	load_serializable (CSerializableFile file, const char prefix="")
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 ()
SGVector< char * >	get_modelsel_names ()
char *	get_modsel_param_descr (const char *param_name)
index_t	get_modsel_param_index (const char *param_name)

Protected Attributes
float64_t *	ktrain_row_means
int32_t	num_ktrain
float64_t *	ktest_row_means
int32_t	num_ktest
float64_t	ktrain_mean
Protected Attributes inherited from CKernelNormalizer
ENormalizerType	m_type

Additional Inherited Members
Public Attributes inherited from CSGObject
SGIO *	io
Parallel *	parallel
Version *	version
Parameter *	m_parameters
Parameter *	m_model_selection_parameters
Protected Member Functions inherited from CSGObject
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)