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Modular toolkit for Data Processing MDP
Package mdp :: Package utils :: Class QuadraticForm
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Class QuadraticForm

Define an inhomogeneous quadratic form as 1/2 x'Hx + f'x + c . This class implements the quadratic form analysis methods presented in:

Berkes, P. and Wiskott, L. (2006). On the analysis and interpretation of inhomogeneous quadratic forms as receptive fields. Neural Computation, 18(8): 1868-1895.

Instance Methods [hide private]
 
__init__(self, H, f=None, c=None, dtype='d')
The quadratic form is defined as 1/2 x'Hx + f'x + c . 'dtype' specifies the numerical type of the internal structures.
 
_eig_sort(self, x)
 
_maximize(self, norm, tol=0.0001, x0=None, factor=None)
 
apply(self, x)
Apply the quadratic form to the input vectors. Return 1/2 x'Hx + f'x + c .
 
get_extrema(self, norm, tol=0.0001)
Find the input vectors xmax and xmin with norm 'nrm' that maximize or minimize the quadratic form.
 
get_invariances(self, xstar)
Compute invariances of the quadratic form at extremum 'xstar'. Outputs:

Inherited from unreachable.newobject: __long__, __native__, __nonzero__, __unicode__, next

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self, H, f=None, c=None, dtype='d')
(Constructor)

 
The quadratic form is defined as 1/2 x'Hx + f'x + c . 'dtype' specifies the numerical type of the internal structures.
Overrides: object.__init__

_eig_sort(self, x)

 

_maximize(self, norm, tol=0.0001, x0=None, factor=None)

 

apply(self, x)

 
Apply the quadratic form to the input vectors. Return 1/2 x'Hx + f'x + c .

get_extrema(self, norm, tol=0.0001)

 

Find the input vectors xmax and xmin with norm 'nrm' that maximize or minimize the quadratic form.

tol: norm error tolerance

get_invariances(self, xstar)

 

Compute invariances of the quadratic form at extremum 'xstar'. Outputs:

w -- w[:,i] is the direction of the i-th invariance nu -- nu[i] second derivative on the sphere in the direction w[:,i]

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Modular toolkit for Data Processing MDP
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