Radviz: Project Multidimensional Data in 2D Space

Description

An implementation of the radviz projection in R. It enables the visualization of multidimensional data while maintaining the relation to the original dimensions. This package provides functions to create and plot radviz projections, and a number of summary plots that enable comparison and analysis. For reference see Hoffman *et al.* (1999) (doi:10.1145/331770.331775) for original implementation, see Di Caro *et al* (2012) (doi:10.1007/978-3-642-13672-6_13), for the original method for dimensional anchor arrangements, see Demsar *et al.* (2007) (doi:10.1016/j.jbi.2007.03.010) for the original Freeviz implementation.

Radviz uses Dimensional Anchors and the spring paradigm to project a multidimensional space in 2D. This allows for the quick visualization of large and complex datasets.

Author(s)

Maintainer: Yann Abraham yann.abraham@gmail.com

Authors:

• Nicolas Sauwen nicolas.sauwen@openanalytics.eu

See Also

Useful links:

• https://github.com/yannabraham/Radviz

• Report bugs at https://github.com/yannabraham/Radviz/issues

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
plot(rv,anchors.only=FALSE)

Computation of weighted version of the Davies-Bouldin index. This index serves as a measure of clustering quality of a 2D projection result with known class labels

Description

Computation of weighted version of the Davies-Bouldin index. This index serves as a measure of clustering quality of a 2D projection result with known class labels

Usage

DB_weightedIdx(x, className = NULL)

Arguments

Details

If className is left NULL (the default) the function expects a single extra column on top of the data columns (used to define springs) and the standard Radviz columns.

Value

weighted DB index value

Author(s)

Nicolas Sauwen

Defunct Functions

Description

These functions are Defunct in this release of Radviz, they will be marked as Defunct and removed in a future version.

Usage

do.density(x, ...)

do.hex(x, ...)

## S3 method for class 'radviz'
identify(x, ...)

Filtering out anchors with low contributions to the projection

Description

Filtering out anchors with low contributions to the projection

Usage

anchor.filter(x, lim = 0)

Arguments

Details

When anchor.filter is a number and type is not Radviz, any springs whose length is lower than this number will be filtered out of the visualization. This has no effect on the projection itself.

Value

a radviz object as produced by do.radviz

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
plot(rv,anchors.only=FALSE)
new.S <- do.optimFreeviz(x = iris[,das], classes = iris$Species)
new.rv <- do.radviz(iris,new.S)
plot(new.rv,anchors.only=FALSE)
plot(anchor.filter(new.rv,0.2))

A Plotting Function for the Radviz Object

Description

Plots the Dimensional Anchors and projected data points in a 2D space.

Usage

bubbleRadviz(
  x,
  main = NULL,
  group = NULL,
  color = NULL,
  size = c(3, 16),
  label.color = NULL,
  label.size = NULL,
  bubble.color,
  bubble.fg,
  bubble.size,
  scale,
  decreasing,
  add
)

Arguments

Details

This function allows for the projection of clusters in Radviz (for example results of the SPADE algorithm), where the cluster size is derived from the number of events that fall into a specific cluster. If color is not specified the grouping variable is used.

Value

the internal ggplot2 object plus added layers, allowing for extra geoms to be added

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
bubbleRadviz(rv, group='Species')

Plots the Dimensional Anchors and density lines for projected data points in a 2D space.

Description

Plots the Dimensional Anchors and density lines for projected data points in a 2D space.

Usage

## S3 method for class 'radviz'
contour(
  x,
  ...,
  main = NULL,
  color = NULL,
  size = 0.5,
  label.color = NULL,
  label.size = NULL,
  contour.color,
  contour.size,
  point.color,
  point.shape,
  point.size,
  n,
  drawlabels,
  drawpoints,
  add
)

Arguments

Value

the internal ggplot2 object plus added layers, allowing for extra geoms to be added

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
contour(rv,color='Species')

Compute the Cosine Similarity between the Columns of a Data Set

Description

Given a dataset, compute the cosine similarity between to columns for use in optimization of Dimensional Anchors

Usage

cosine(mat)

Arguments

Details

implementation by ekstroem (see StackOverflow for details)

Value

A symmetrical matrix with as many rows as there are columns in input

Author(s)

Yann Abraham

David Ruau

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
mat <- iris[,das]
sim.mat <- cosine(mat)
ncol(mat)
dim(sim.mat)

Perform L-Normalization on a Vector

Description

Standardizes all values in a vector to the unit vector ([0,1]) using local min and max

Usage

do.L(v, fun = range, na.rm = T)

Arguments

Details

This is an alternative to performing a L normalization over the full matrix. if the minimum and the maximum values returned after applying fun are the same, do.L will return 0.

Value

A vector of values of the same length as x, scaled to the unit vector.

Author(s)

Yann Abraham

Examples

data(iris)
mat <- iris[,c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')]
scaled <- apply(mat,2,do.L)
summary(scaled) # all values are between [0,1]

scaled2 <- apply(mat,2,do.L,fun=function(x) quantile(x,c(0.025,0.975)))
summary(scaled2) # all values are between [0,1]

plot(scaled,scaled2,
     col=rep(seq(1,ncol(scaled)),each=nrow(scaled)),
     pch=16)
legend('topleft',legend=dimnames(scaled)[[2]],col=seq(1,ncol(scaled)),pch=16,bty='n')

Optimize the Dimensional Anchors Position using the Freeviz algorithm

Description

Allows to compute the best arrangement of Dimensional Anchors so that visualization efficiency (i.e. separation between classes) is maximized. The Freeviz algorithm is implemented in C++ for optimal computational efficiency.

Usage

do.optimFreeviz(
  x,
  classes,
  attractG = 1,
  repelG = 1,
  law = 0,
  steps = 10,
  springs = NULL,
  multilevel = FALSE,
  nClusters = 5000,
  minTreeLevels = 3,
  subsetting = FALSE,
  minSamples = 1000,
  print = TRUE
)

Arguments

Details

Freeviz is an optimization method that finds the linear projection that best separates instances of different classes, based on a physical metaphor. Observations are considered as physical particles, that exert forces onto each other. Attractive forces occur between observations of the same class, and repulsive forces between observations of different classes, with the force strength depending on the distance between observations. The goal of Freeviz is to find the projection with minimal potential energy. For more details, see the original Freeviz paper: doi:10.1016/j.jbi.2007.03.010

Value

A matrix with 2 columns (x and y coordinates of dimensional anchors) and 1 line per dimensional anchor (so called springs).

Author(s)

Nicolas Sauwen

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
plot(rv,anchors.only=FALSE)
new.S <- do.optimFreeviz(x = iris[,das], classes = iris$Species)
new.rv <- do.radviz(iris,new.S)
plot(new.rv,anchors.only=FALSE)

Optimize the Dimensional Anchors Position using the Graphviz algorithm

Description

Allows to compute the best arrangement of Dimensional Anchors so that visualization efficiency (i.e. maintaining graph structure) is optimized. The Graphviz algorithm is implemented in C++ for optimal computational efficiency.

Usage

do.optimGraphviz(
  x,
  graph,
  attractG = 1,
  repelG = 1,
  law = 0,
  steps = 10,
  springs = NULL,
  weight = "weight"
)

Arguments

Details

Graphviz is a variant of Freeviz (do.optimFreeviz, applicable to a dataset for which a graph structure (i.e. igraph object) is available. Attractive forces are defined between connected nodes in the graph, and repulsive forces between all non-connected nodes. To better maintain the original graph structure after projection, spring constants between connected nodes are proportional to their edge weights. Graphviz can be used as an alternative to Freeviz when class labels are not available.

Value

A matrix with 2 columns (x and y coordinates of dimensional anchors) and 1 line per dimensional anchor (so called springs).

Author(s)

Nicolas Sauwen

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)

plot(rv,anchors.only=FALSE)

## compute distance matrix
d.iris <- dist(iris[,das])

## define a kNN matrix
n.iris <- as.matrix(d.iris)
n.iris <- apply(n.iris,1,function(x,k=12) {
  x[order(x)>(k+1)] <- 0
  return(x)
})
diag(n.iris) <- 0

## compute weights for kNN matrix
w.iris <- n.iris
w.iris <- exp(-w.iris^2/(2*median(w.iris[w.iris!=0])^2))
w.iris[n.iris==0] <- 0

## create graph
library(igraph)
g.iris <- graph.adjacency(w.iris,mode='undirected',weight=TRUE,diag=FALSE)

V(g.iris)$Species <- as.character(iris[,'Species'])
V(g.iris)$color <- as.numeric(iris[,'Species'])

plot(g.iris,
     vertex.label=NA)

## project using Radviz
new.S <- do.optimGraphviz(iris[,das],
                          g.iris)

grv <- do.radviz(iris[,das],
                new.S,
                graph=g.iris)

library(ggplot2)
plot(grv)+
  geom_point(aes(color=iris[,'Species']))

Optimize the Dimensional Anchors Position for Radviz projection using a Genetic Algorithm

Description

Allows to compute the best arrangement of Dimensional Anchors so that visualization efficiency is maximized.

Usage

do.optimRadviz(
  springs,
  similarity,
  iter = 100,
  n = 1000,
  top = round(n * 0.1),
  lambda = 0.01,
  nlast = 5,
  optim = "in.da"
)

do.optim(
  springs,
  similarity,
  iter = 100,
  n = 1000,
  top = round(n * 0.1),
  lambda = 0.01,
  nlast = 5,
  optim = "in.da"
)

Arguments

Details

The first generation is a random sampling of all Dimensional Anchors. For every generation afterwards, only the best solutions (as specified by top) are kept; the solutions are normalized around the unit circle (ie c(1,2,3,4) is equivalent to c(4,1,2,3) for Radviz projection) before the next generation is created. The next generation consists of

• all unique best solutions from the previous generation (after circular normalization)

• a permutation of all previous solutions.

Briefly, for every Dimensional Anchor position the previous generation is sampled to give a mixture of identical and slightly shifted (mutated) solutions. The algorithm will stop when the maximum number of iterations (as defined by iter) is reached, or when a number of generations (defined by nlast) as not improved over the best solution by more than a given threshold (specified by lambda).

Value

a list containing 3 sets of values:

• perfs the list of the best performances by generation

• best the best performing arrangement by generation

• last the top performing arrangements of the last generation

do.optim

do.optim is being deprecated, please use do.optimRadviz.

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
plot(rv,anchors.only=FALSE)
sim.mat <- cosine(iris[,das])
in.da(S,sim.mat) # the starting value
new <- do.optimRadviz(S,sim.mat,iter=10,n=100)
new.S <- make.S(get.optim(new))
new.rv <- do.radviz(iris,new.S)
plot(new.rv,anchors.only=FALSE)

Projects a Matrix or a Data Frame to a 2D space defined by Dimensional Anchors

Description

do.radviz will return a projection of a multidimensional dataset onto a 2D space defined by dimensional anchors that have been projected on the unit circle using make.S

Usage

do.radviz(
  x,
  springs,
  trans = do.L,
  scaling = 1,
  label.color = "orangered4",
  label.size = NA,
  type = NULL,
  graph = NULL
)

Arguments

Details

The function expects that at least some of the column names in x will be matched by all row names in springs. The scaling factor can be used to increase the distance between points, making it useful in situations where all points are pulled together either because of similar values or large number of channels. The scaling is applied **after** the transformation by trans. The scaling idea is taken from [Artur & Minghim 2019](https://doi.org/10.1016/j.cag.2019.08.015).

Value

an object of class radviz with the following slots:

• proj: a ggplot2 object with a single geom_text layer corresponding to springs. the data slot of the ggplot2 corresponds to the input parameter x with the following extra columns:

  • rx and ry the X and Y coordinates of the radviz projection of x over springs

  • rvalid an index of points corresponding to an invalid projection (any rx or ry is NA)

• springs: the matrix containing the spring coordinates.

• type: character string specifying the method used for obtaining the springs.

• trans: the function used to transform the data.

• graphEdges: when the input graph is provided (for a Graphviz analysis), this slot will contain a dataframe with the graph edges

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
summary(rv)
data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
iris0 <- rbind(iris,c(rep(0,length(das)),NA))
S <- make.S(das)
rv0 <- do.radviz(iris0,S)

sum(!is.valid(rv0)) # should be 1

# to find which points where invalid in the data
which(!is.valid(rv0))

# to review the original data points
rv1 <- subset(rv0,is.valid(rv0))

summary(rv1)

Get the Result of the Optimization Operation

Description

Once the order of anchors has been optimized using do.optimRadviz this function can be used to recover the optimized anchors or any intermediate step

Usage

get.optim(opt, n = NULL)

Arguments

Value

a character vector of the anchor names, ordered as in the n^th^ step of the optimization

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
sim.mat <- cosine(iris[,das])
in.da(S,sim.mat) # the starting value
new <- do.optimRadviz(S,sim.mat,iter=10,n=100)
get.optim(new) # the optimal order
get.optim(new,2) # the second step of the optimization

A hexplot function for Radviz objects

Description

Plots the Dimensional Anchors and a hexplot-based density representation of projected data points in a 2D space.

Usage

hexplot(
  x,
  main = NULL,
  nbins = 30,
  color = NULL,
  label.color = NULL,
  label.size = NULL,
  mincnt,
  style
)

Arguments

Value

the internal ggplot2 object plus added layers, allowing for extra geoms to be added

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
hexplot(rv,color='Sepal.Length')

Optimization functions for Dimensional Anchors in Radviz

Description

Visual efficiency of Radviz plots depends heavily on the correct arrangement of Dimensional Anchors. These functions implement the optimization strategies described in Di Caro et al 2012

Usage

in.da(springs, similarity)
rv.da(springs, similarity)

Arguments

Details

Following the recommendation of Di Caro *et al.* we used a cosine function to calculate the similarity between Dimensional Anchors (see cosine for details). The in.da function implements the independent similarity measure, where the value increases as the Radviz projection improves. The rv.da function implements the radviz-dependent similarity measure, where the value decreases as the Radviz projection improves.

Value

A measure of the efficiency of the Radviz projection of the similarity matrix onto a set of springs

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
mat <- iris[,das]
sim.mat <- cosine(mat)
in.da(S,sim.mat)
rv.da(S,sim.mat)

Test if the object is a Radviz object

Description

The function will return TRUE if the object is a Radviz object

Usage

is.radviz(x)

Arguments

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
is.radviz(rv) # should be true

Identify the valid projections from a Radviz object

Description

The function will return a vector as long as the data in x where points that could not be projected are TRUE

Usage

is.valid(x)

Arguments

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
iris0 <- rbind(iris,c(rep(0,length(das)),NA))
S <- make.S(das)
rv0 <- do.radviz(iris0,S)

sum(!is.valid(rv0)) # should be 1

# to find which points where invalid in the data
which(!is.valid(rv0))

# to review the original data points
rv1 <- subset(rv0,is.valid(rv0))

summary(rv1)

Define Dimensional Anchors around the Unit Circle

Description

make.S will return [x,y] coordinates for n dimensional anchors equally spaced around the unit circle

Usage

make.S(x)

Arguments

Details

If x is a vector or a list, values will be used to set the row names of the matrix.

Value

A matrix with 2 columns (x and y coordinates of dimensional anchors) and 1 line per dimensional anchor (so called springs). If x is a vector, the row names of the matrix will be set to the syntactically correct version of values in the vector (through a call to make.names). Please note that some functions expect to match column names of data to row names of the spring matrix.

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
make.S(length(das)) # without row names
make.S(das) # with row names
make.S(list(c('Sepal.Length','Sepal.Width'),c('Petal.Length','Petal.Width')))

A Plotting Function for the Radviz Object

Description

Plots the Dimensional Anchors and projected data points in a 2D space.

Usage

## S3 method for class 'radviz'
plot(
  x,
  main = NULL,
  anchors.only = TRUE,
  anchors.filter = NULL,
  label.color = NULL,
  label.size = NULL,
  point.color,
  point.shape,
  point.size,
  add,
  ...
)

Arguments

Details

by default the plot function only shows the anchors. Extra geoms are required to display the data. When anchors.filter is a number and type is not Radviz, any springs whose length is lower than this number will be filtered out of the visualization. This has no effect on the projection itself. Please note that this parameter is being superseded by the anchor.filter function.

Value

the internal ggplot2 object, allowing for extra geoms to be added

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
plot(rv)
plot(rv,anchors.only=FALSE)

library(ggplot2)
## should look the same as before
plot(rv)+geom_point()
plot(rv)+geom_point(aes(color=Species))

Rotate Dimensional Anchors around the Unit Circle

Description

recenter will rotate the order of the dimensional anchors around the circle, to put a channel of reference to the top of the display.

Usage

recenter(springs, newc)

Arguments

Value

a spring object with rotated labels

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
iris.S <- make.S(das)
iris.S
recenter(iris.S,'Petal.Length')

Rescaling of projected data for plotting

Description

Rescaling of projected data for plotting

Usage

rescalePlot(x, fraction = 0.9)

Arguments

Details

A different rescaling is used here for plotting the projected data as compared to do.radviz. Only feature-wise rescaling is applied to the original data (through do.L), in accordance with the rescaling used in do.optimFreeviz and do.optimGraphviz. The projected data is then rescaled based on amplitude, to cover a pre-specified fraction of the unit circle. For Freeviz and Graphviz objects, the rescaling will issue a warning if some points extend beyond the some anchors: in that case only the direction of the anchor can be interpreted but not the magnitude represented by the anchor's position.

Value

a radviz object as produced by do.radviz

Author(s)

Nicolas Sauwen

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
library(ggplot2)
plot(rv)+geom_point(aes(color=Species))
new.rv <- rescalePlot(rv)
plot(new.rv)+geom_point(aes(color=Species))

A smoothScatter function for Radviz objects

Description

Plots the Dimensional Anchors and a smoothed color density representation of projected data points in a 2D space.

Usage

smoothRadviz(
  x,
  main = NULL,
  color = "dodgerblue4",
  nbin = 200,
  label.color = NULL,
  label.size = NULL,
  smooth.color,
  max.dens,
  transformation,
  nrpoints,
  ncols,
  bandwidth
)

Arguments

Value

the internal ggplot2 object plus added layers, allowing for extra geoms to be added

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
smoothRadviz(rv)

Subsetting a Radviz projection

Description

Subsetting a Radviz projection

Usage

## S3 method for class 'radviz'
subset(x, i = TRUE, ...)

Arguments

Value

a new Radviz object containing only rows specified in i

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
# subset rv
srv <- subset(rv,iris$Species=='setosa')
summary(srv)
sum(iris$Species=='setosa') # 50 objects in srv corresponding to setosa values

Radviz Object Summary, head, print, dim and springs Methods

Description

Provides a summary for Radviz objects

Usage

## S3 method for class 'radviz'
summary(object, ..., n = 6)

## S3 method for class 'radviz'
head(x, n = 6, ...)

## S3 method for class 'radviz'
dim(x)

## S3 method for class 'radviz'
print(x, ...)

springs(x)

Arguments

Details

dim returns the number of points and the number of dimensions used for the projection. print returns invisibly the data, including the projected coordinates

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)

summary(rv)
head(rv)
dim(rv)
print(rv)

Text annotations for for the Radviz Plots

Description

Text draws the strings given in the vector labels at the coordinates given by the radviz projection

Usage

## S3 method for class 'radviz'
text(
  x,
  ...,
  main = NULL,
  labels = NULL,
  size = FALSE,
  label.color = NULL,
  label.size = NULL,
  adj,
  pos,
  offset,
  vfont,
  cex,
  col,
  font,
  add
)

Arguments

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
text(rv,labels='Species')

Complete ggplot2 theme for Radviz projections

Description

A complete Radviz theme based on 'ggplot2::theme_light'

Usage

theme_radviz(
  base_size = 11,
  base_family = "",
  base_line_size = base_size/22,
  base_rect_size = base_size/22
)

Arguments

Details

on top of 'ggplot2::theme_light' this theme removes axis title, text and ticks, as well as the reference grid. See theme for details.

Value

a complete ggplot2 theme

Author(s)

Yann Abraham

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
plot(rv,main='Iris projection')
plot(rv,main='Iris projection')+
  theme_radviz(base_size=16)

Method to compute optimal ratio between repulsive and attractive forces for Freeviz.

Description

Method to compute optimal ratio between repulsive and attractive forces for Freeviz.

Usage

tuneForceRatio(
  x,
  classes,
  law = 0,
  steps = 10,
  springs = NULL,
  multilevel = TRUE,
  print = TRUE
)

Arguments

Details

Running Freeviz, it is hard to know what weights to specify for the attractive and repulsive forces to optimize the projection result. This function runs an iterative procedure to find the optimal force ratio. First, a logarithmic grid search is performed, followed by 1D optimization on the refined interval. This approach is less prone to getting stuck in a suboptimal local optimum, and requires less Freeviz evaluations than direct 1D optimization

Value

Value of the optimal force ratio (attractive force in the nominator)

Author(s)

Nicolas Sauwen

Examples

data(iris)
das <- c('Sepal.Length','Sepal.Width','Petal.Length','Petal.Width')
S <- make.S(das)
rv <- do.radviz(iris,S)
plot(rv,anchors.only=FALSE)
forceRatio <- tuneForceRatio(x = iris[,das], classes = iris$Species)
new.S <- do.optimFreeviz(x = iris[,das], classes = iris$Species, attractG = forceRatio, repelG = 1)
new.rv <- do.radviz(iris,new.S)
plot(new.rv,anchors.only=FALSE)