 | Cloud Class |
Inheritance HierarchyNamespace: Novacta.Analytics.Advanced
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.0.0
SyntaxThe Cloud type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | Cloud(DoubleMatrix) |
Initializes a new instance of the Cloud class that
contains points whose coordinates
are taken with respect to
the standard basis. To each point is assigned a weight equal to
the reciprocal of the
number of points.
|
| Cloud(DoubleMatrix, DoubleMatrix) |
Initializes a new instance of the Cloud class that
contains points having the specified weights and whose coordinates
are taken with respect to
the standard basis.
|
| Cloud(DoubleMatrix, DoubleMatrix, Basis) |
Initializes a new instance of the Cloud class
that contains points having the specified weights and whose
coordinates are taken with respect to the given basis.
|
| Cloud(DoubleMatrix, DoubleMatrix, Basis, Boolean) |
Initializes a new instance of the Cloud class
that contains points having the specified weights and whose
coordinates are taken with respect to the given basis, with
coordinates and weights eventually copied before instantiation.
|
Properties| Name | Description | |
|---|---|---|
 | Basis |
Gets the basis of the cloud.
|
| Coordinates |
Gets the coordinates of the cloud points.
|
| Covariance |
Gets the covariance matrix of the
active variables in the Cloud.
|
| Mean |
Gets the mean coordinates of the Cloud
with respect to its Basis.
|
| Variance |
Gets the variance of the points
represented in the Cloud.
|
| Weights |
Gets the weights of the cloud points.
|
Methods| Name | Description | |
|---|---|---|
| Center |
Returns a modified Cloud having zero mean
coordinates.
|
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) |
| GetHashCode | Serves as the default hash function. (Inherited from Object.) |
| GetPrincipalProjections |
Gets the principal projections of this instance.
|
| GetType | Gets the Type of the current instance. (Inherited from Object.) |
| GetVariances(DoubleMatrix) |
Computes the variances of the specified supplementary variables.
|
| GetVariances(ReadOnlyDoubleMatrix) |
Computes the variances of the specified supplementary variables.
|
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) |
| Rebase |
Returns a Cloud representing the same points
of this instance, using coordinates referred to the
specified basis.
|
| Standardize |
Returns a standardized Cloud.
|
| ToString | Returns a string that represents the current object. (Inherited from Object.) |
RemarksPoints and variables
Let us consider 
points 
in
, and assume that a weighting scheme has
been imposed to them to control their contributions to the
statistical characteristics of their ensemble: that is, a
relative weight 
is assigned to
point 
, with 
.
Such set of weighted points can thus
be represented
by means of the pair 
,
referred to as a
weighted multidimensional structure
where
is the 
matrix whose 
-th
row is 
, and 
is
the weighting scheme expressed as a sequence:
Given a basis 
of 
, a
structure
can be represented by a
cloud, say 
, which
can be formally defined as the
triplet 
, where
is the coordinates matrix w.r.t. 
of the points
in 
, i.e., its 
-th row,
, represents the coordinates
of point 
.
Given a Cloud instance representing
, you can inspect
its Basis, 
,
the Coordinates
of the points 
, and
their Weights, 
.
The mean point of 
is the vector 
whose 
coordinates are given by:
Such coordinates are returned by method Mean.
The variance of 
,
say 
, is returned by
method Variance
and defined as follows:
where
is
the distance
induced by basis 
.
The columns of 
represent
the active variables
observed at the 
points w.r.t. basis
. The covariance matrix of such variables
can be defined
as follows
where
Such matrix can be inspected by calling method
Covariance.
A variable which is not active is said supplementary. Supplementary variables have as many rows as the number of points in the cloud, while the number of columns is the number of supplementary variables. Their variances can be computed, which means that the weighting scheme of the cloud will be applied.
Cloud modifications
A cloud can be re-based, so that the cloud coordinates are updated to be referable to a new basis. Clouds can also be centered so as to have zero mean coordinates, or standardized by subtracting to each variable its mean and then dividing the difference by its standard deviation.
See Also