ClusterWithMeanCurve: Cluster Curves

In sysbioTurin/connector: Fitting and clustering of longitudinal data

Cluster Curves

Description

Visualizes the plots regarding the fitted and clustered data by exploiting the FCM.

Usage

ClusterWithMeanCurve(
  clusterdata,
  feature,
  title = "",
  labels = c("", ""),
  save = FALSE,
  path = NULL
)

Arguments

clusterdata	The list obtained from extrapolating the most probable clustering from the StabilityAnalysis function output. (see StabilityAnalysis and MostProbableClustering.Extrapolation).
feature	The column name reported in the AnnotationFile containing the feature to be investigated.
title	The string containing the plot title.
labels	The vector containing the axis names.
save	If TRUE then the following objects are saved: (i) the mean curves plot, (ii) the plots of each cluster showing the correspondive mean curve and the samples belonging to the cluster, (iii) one plot storing all the clustering plots, and (iv) the tables reporting the M, S, R and fDB indexes considering the 0, 1 and 2 derivatives.
path	The folder path where the plots will be saved. If it is missing, the plots are saved in the current working directory.

Details

We define the following indexes for obtaining a cluster separation measure:

• S_k:

  S_k = \sqrt{\frac{1}{G_k} \sum_{i=1}^{G_k} D_q^2(\hat{g}_i, \bar{g}^k);}

  with G_k the number of curves in the k-th cluster;

• M_hk: the distance between centroids (mean-curves) of h-th and k-th cluster

  M_{hk} = D_q(\bar{g}^h, \bar{g}^k);

• R_hk: a measure of how good the clustering is,

  R_{hk} = \frac{S_h + S_k}{M_{hk}};

• fDB_q: functional Davies-Bouldin index, the cluster separation measure

  fDB_q = \frac{1}{G} \sum_{k=1}^G \max_{h \neq k} { R_{hk} }.

Where the proximities measures choosen is defined as follow

D_q(f,g) = \sqrt( \integral | f^{(q)}(s)-g^{(q)}(s) |^2 ds ), d=0,1,2

with f and g are two curves and f^(q) and g^(q) are their q-th derivatives. Note that for q=0, the equation becomes the distance induced by the classical L^2-norm.

Value

ClusterWithMeanCurve returns a list with three objects:

• PlotsCluster:a list storing the growth curves plots partitioned according to the cluster membership;

• PlotMeanCurve:the cluster mean curves plot;

• spline.plots:a list of N plots, where N is the number of samples, showing: (i) in blue the sample curve, (ii) in red the cubic spline estimated from the FCM, (iii) in black the correspondive cluster mean curve, and finally (iv) the grey area represents the confidence interval.

Author(s)

Cordero Francesca, Pernice Simone, Sirovich Roberta

See Also

MostProbableClustering.Extrapolation, StabilityAnalysis, Spline.plots.

sysbioTurin/connector documentation built on April 9, 2024, 12:10 p.m.