genTriangles {TFunHDDC}

genTriangles

Description

Generate contaminated triangle data. Groups 1, 2, 3, and 4 are separable over the two dimensions of functional data. Groups 5 and 6 contain the contaminated curves of groups 1 and 3 respectively.

Usage

genTriangles()

Details

Group 1:

X_1(t) = U + (0.6 - U)H_1(t) + \epsilon_1(t)

X_2(t) = U + (0.5 - U)H_1(t) + \epsilon_1(t)

Contaminated X_1(t) = \sin(t) + (0.6 - U)H_1(t) + \epsilon_2(t)

Contaminated X_2(t) = \sin(t) + (0.5 - U)H_1(t) + \epsilon_2(t)

Group 2:

X_1(t) = U + (0.6 - U)H_2(t) + \epsilon_1(t)

X_2(t) = U + (0.5 - U)H_2(t) + \epsilon_1(t)

Group 3:

X_1(t) = U + (0.5 - U)H_1(t) + \epsilon_1(t)

X_2(t) = U + (0.6 - U)H_2(t) + \epsilon_1(t)

Contaminated X_1(t) = \sin(t) + (0.5 - U)H_1(t) + \epsilon_3(t)

Contaminated X_2(t) = \sin(t) + (0.6 - U)H_2(t) + \epsilon_3(t)

Group 4:

X_1(t) = U + (0.5 - U)H_2(t) + \epsilon_1(t)

X_2(t) = U + (0.6 - U)H_1(t) + \epsilon_1(t). Here t\in [1,21], H_1(t) = (6-\vert t-7\vert)_+, and H_2(t) = (6-\vert t-15\vert)_+, with (\cdot)_+ representing the positive part. U \sim \mathcal{U}(0, 0.1), and \epsilon_1(t)\sim N(0, 0.5), \epsilon_2(t)\sim N(0, 2), \epsilon_3(t) \sim Cauchy(0, 4) are mutually independent white noises and independent of U. We simulate 100 curves for each group, groups 1 and 3 consisting of 80 ordinary curves and 20 contaminated curves. Curves are smoothed using a 25 cubic B-spline basis.

Value

fd

List of functional data objects representing the two dimensions of triangle data.

groupd

Group classification for each curve

Author(s)

Cristina Anton and Iain Smith

References

- C.Bouveyron and J.Jacques (2011), Model-based Clustering of Time Series in Group-specific Functional Subspaces, Advances in Data Analysis and Classification, vol. 5 (4), pp. 281-300, <doi:10.1007/s11634-011-0095-6>

- Schmutz A, Jacques J, Bouveyron C, et al (2020) Clustering multivariate functional data in group-specific functional subspaces. Comput Stat 35:1101-1131

- Cristina Anton, Iain Smith Model-based clustering of functional data via mixtures of t distributions. Advances in Data Analysis and Classification (to appear).

See Also

plotTriangles

Examples

# Multivariate Contaminated Triangles
conTrig <- genTriangles()
cls = conTrig$groupd
plotTriangles(conTrig)