dot-diss_d0_d1_L2: Dissimilarity Index for Multidimensional Curves

In funMoDisco: Motif Discovery in Functional Data

Dissimilarity Index for Multidimensional Curves

Description

Computes a Sobolev-type dissimilarity index for multidimensional curves based on a weighted combination of L2 norms of the function and its derivative. The distance is normalized on a common support, allowing for a comparison between curves considering both their levels and variations.

Usage

.diss_d0_d1_L2(y, v, w, alpha, transform_y = FALSE, transform_v = FALSE)

Arguments

y	A list of two matrices: y[[1]]: Values of the curve at points in the domain (y(x)). y[[2]]: Values of the derivative of the curve at the same points (y'(x)). Each matrix should have d columns, where d is the dimensionality of the curves.
v	A list of two matrices: v[[1]]: Values of the reference curve at points in the domain (v(x)). v[[2]]: Values of the derivative of the reference curve at the same points (v'(x)). Each matrix should have d columns, where d is the dimensionality of the curves.
w	A numeric vector of weights for the dissimilarity index in different dimensions. Each weight should be greater than 0.
alpha	A numeric value (between 0 and 1) that specifies the weight coefficient between the L2 norm of the function (d0.L2) and the L2 norm of the derivative (d1.L2): alpha = 0: Only the levels (d0.L2) are considered. alpha = 1: Only the derivative information (d1.L2) is considered. Values between 0 and 1 provide a mixture of both.
transform_y	A logical value indicating whether to normalize y to the range [0, 1] before applying the distance computation. Default is FALSE.
transform_v	A logical value indicating whether to normalize v to the range [0, 1] before applying the distance computation. Default is FALSE.

Details

The dissimilarity index is calculated based on the following Sobolev-type distance:

D = (1 - \alpha) \cdot d0.L2 + \alpha \cdot d1.L2

where:

• d0.L2: L2 distance considering only the levels of the curves.

• d1.L2: L2 distance considering only the derivatives of the curves.

The function normalizes the inputs based on the specified flags to ensure that all features are comparable.

Value

A numeric value representing the dissimilarity index between the curves defined by y and v.

funMoDisco documentation built on April 16, 2025, 1:10 a.m.