genTriangles {TFunHDDC} | R Documentation |
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:
X1(t)=U+(0.6−U)H1(t)+ϵ1(t)
X2(t)=U+(0.5−U)H1(t)+ϵ1(t)
Contaminated X1(t)=sin(t)+(0.6−U)H1(t)+ϵ2(t)
Contaminated
X2(t)=sin(t)+(0.5−U)H1(t)+ϵ2(t)
Group 2:
X1(t)=U+(0.6−U)H2(t)+ϵ1(t)
X2(t)=U+(0.5−U)H2(t)+ϵ1(t)
Group 3:
X1(t)=U+(0.5−U)H1(t)+ϵ1(t)
X2(t)=U+(0.6−U)H2(t)+ϵ1(t)
Contaminated X1(t)=sin(t)+(0.5−U)H1(t)+ϵ3(t)
Contaminated X2(t)=sin(t)+(0.6−U)H2(t)+ϵ3(t)
Group 4:
X1(t)=U+(0.5−U)H2(t)+ϵ1(t)
X2(t)=U+(0.6−U)H1(t)+ϵ1(t).
Here t∈[1,21]
, H1(t)=(6−∣t−7∣)+
, and H2(t)=(6−∣t−15∣)+
, with (⋅)+
representing the positive part. U∼U(0,0.1)
, and ϵ1(t)∼N(0,0.5)
, ϵ2(t)∼N(0,2)
, ϵ3(t)∼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)
[Package
TFunHDDC version 1.0.1
Index]