diamondback.models package¶
Submodules¶
diamondback.models.DiversityModel module¶
Description
A diversity model realizes the selection and retention of a state as a finite collection of observations extracted from an incident signal, to maximize a minimum distance between any members of a state, according to a specified classification or distance metric.
\[d_{k} = \min(\ d_{u,v}\ )\quad\quad u, v \in [\ 0,\ M\ ),\ u \neq v\]\[d_{k} \geq d_{n}\qquad \longrightarrow\qquad d_{n} = d_{k}\]A diversity model is an opportunistic unsupervised learning model which typically improves condition and numerical accuracy and reduces storage relative to alternative approaches including generalized linear inverse.
A factory is defined to facilitate construction of an instance, defining a state array of a specified order. A stationary dimension is inferred through observation. An instance, classification, and order are specified.
Classification is in ( ‘Chebyshev’, ‘Euclidean’, ‘Geometric’, ‘Manhattan’ ).
‘Chebyshev’ distance is an L-infinity norm, a maximum absolute differencein any dimension.\[d_{u,v} = \max(\ |\ \vec{x_{u}} - \vec{x_{v}}\ |\ )\]
‘Euclidean’ distance is an L-2 norm, a square root of a sum of squareddifferences in each dimension.\[d_{u,v} = \matrix{\sum_{i=0}^{N}(\ |\ \vec{x_{u,i}} - \vec{x_{v,i}}\ )^2|}^{0.5}\]
‘Geometric’ distance is a ordered root of a product of absolute differencesin each dimension.\[d_{u,v} = \prod_{i=0}^{N}{(\ |\ \vec{x_{u,i}} - \vec{x_{v,i}}\ |\ )}^{\frac{1}{N}}\]
‘Manhattan’ distance is an L-1 norm, a sum of absolute differences in eachdimension.\[d_{u,v} = \sum_{i=0}^{N}{\ (\ |\ \vec{x_{u}} - \vec{x_{v}}\ |\ )\ }\]
Example
from diamondback import DiversityModel # Create an instance from a Factory with constraints. obj = DiversityModel.Factory.instance( typ = DiversityModel, classification = 'Euclidean', order = 4 ) # Model an incident signal and extract a state. x = numpy.random.rand( 2, 32 ) y = obj.model( x ) s = obj.s
License
© 2018 - 2021 Larry Turner, Schneider Electric Industries SAS. All rights reserved.
Author
Larry Turner, Schneider Electric, Analytics & AI, 2018-02-08.
Definition
- class diamondback.models.DiversityModel.DiversityModel(distance: Callable[[Any, Any], Any], order: int)[source]¶
Bases:
diamondback.interfaces.IClear.IClear
,diamondback.interfaces.IS.IS
,diamondback.interfaces.IEqual.IEqual
Diversity model.
Initialize.
Arguments :
distance : Callable[ [ Any, Any ], Any ].
order : int.
- model(x: Union[List, numpy.ndarray]) → numpy.ndarray[source]¶
Models an incident signal and produces a reference signal.
Arguments :
x : Union[ List, numpy.ndarray ] - incident signal.
Returns :
y : numpy.ndarray - diversity.
diamondback.models.PrincipalComponentModel module¶
Description
A principal component model analyzes an incident signal to define transformation matrices which consume an incident signal to produce a reference signal, normalized and ordered to define orthogonal axes of descending variance.
A principal component model is a supervised learning model which analyzes an incident signal representing a training set to learn a mean vector, standard deviation vector, and a collection of eigenvectors associated with an incident signal.
\[\vec{\mu_{i}} = \matrix{\ \frac{\sum_{n=0}^{N}\vec{x_{i,n}}}{N}}\]\[\vec{\sigma_{i}} = \matrix{\ \frac{\sum_{n=0}^{N}(\ \vec{x_{i,n}} - \vec{\mu_{i}}\ )^{2}}{N}}^{0.5}\]\[\Lambda_{n} = eig\matrix{\ cov\matrix{\ \matrix{\frac{\ X_{n}^{T} - \vec{\mu}\ }{\vec{\sigma}}\ }\ }^{T}\ }^{T}\]An incident signal which is not a part of an inital training set is transformed without modifying a principal component model, by translation, normalization, and rotation to produce a reference signal which is a candidate for dimension reduction, in which higher order dimensions are discarded, reducing the order of the reference signal, while preserving significant and often sufficient information.
\[Y_{n} = \Lambda_{n} \ \matrix{\frac{\ X_{n}^{T} - \vec{\mu}\ }{\vec{\sigma}}\ }^{T}\]Principal component analysis and dimension reduction has application in clustering, classification, pattern recognition, and visualization.
Example
from diamondback import PrincipalComponentModel # Create an instance. obj = PrincipalComponentModel( ) # Model an incident signal and extract eigenvalue, standard deviation, means, and rotation arrays. x = numpy.random.rand( 3, 32 ) y = obj.model( x ) e, s, u, v = obj.e, obj.s, obj.u, obj.v
License
© 2018 - 2021 Larry Turner, Schneider Electric Industries SAS. All rights reserved.
Author
Larry Turner, Schneider Electric, Analytics & AI, 2019-01-25.
Definition
- class diamondback.models.PrincipalComponentModel.PrincipalComponentModel[source]¶
Bases:
diamondback.interfaces.IClear.IClear
,diamondback.interfaces.IS.IS
,diamondback.interfaces.IEqual.IEqual
Principal component model.
Initialize.
- property e¶
numpy.ndarray - eigenvalues.
- Type
e
- property u¶
numpy.ndarray.
- Type
mean
- property v¶
numpy.ndarray
- Type
rotation
- model(x: Union[List, numpy.ndarray]) → numpy.ndarray[source]¶
Models an incident signal and produces a reference signal.
Arguments :
x : Union[ List, numpy.ndarray ] - incident signal.
Returns :
y : numpy.ndarray - reference signal.