MainModule

This is the main unit containing the PosDefManifoldML module.

dependencies

The main module does not contain functions.

types

MLmodel

As typical in machine learning packages, a type is created (a struct in Julia) to specify a ML model. Supertype

abstract type MLmodel end

is the abstract type for all machine learning models. Supertype

abstract type PDmodel<:MLmodel end

is the abstract type for all machine learning models acting on the positive definite (PD) manifold (for example, see MDM). Supertype

abstract type TSmodel<:MLmodel end

is the abstract type for all machine learning models acting on the tangent space (for example, see ENLR).

IntVector

In all concerned functions class labels are given as a vector of integers, of type

IntVector=Vector{Int}

Class labels are natural numbers in $[1,...,z]$, where $z$ is the number of classes.

Tips & Tricks

working with metrics

In order to work with metrics for the manifold of positive definite matrices, make sure you install the PosDefManifold package.

the ℍVector type

Check this documentation on typecasting matrices.

notation & nomenclature

Throughout the code of this package the following notation is followed:

• scalars and vectors are denoted using lower-case letters, e.g., y,
• matrices using upper case letters, e.g., X
• sets (vectors) of matrices using bold upper-case letters, e.g., 𝐗.

The following nomenclature is used consistently:

• 𝐏Tr: a training set of positive definite matrices
• 𝐏Te: a testing set of positive definite matrices
• 𝐏: a generic set of positive definite matrices.
• w: a weights vector of non-negative real numbers
• yTr: a training set class labels vector of positive integer numbers (1, 2,...)
• yTe: a testing set class labels vector of positive integer numbers
• y: a generic class labels vector of positive integer numbers.
• z: number of classes of a ML model
• k: number of matrices in a set

In the examples, bold upper-case letters are replaced by upper case letters in order to allow reading in the REPL.

acronyms

• MDM: minimum distance to mean
• ENLR: Elastic-Net Logistic Regression
• SVM: Support-Vector Machine
• cv: cross-validation