evclust (version 2.0.3)

nnevclus: NN-EVCLUS algorithm

Description

nnevclus computes a credal partition from a dissimilarity matrix using the NN-EVCLUS algorithm.

Usage

nnevclus(
  x,
  k = n - 1,
  D = NULL,
  J = NULL,
  c,
  type = "simple",
  n_H,
  ntrials = 1,
  d0 = quantile(D, 0.9),
  fhat = NULL,
  lambda = 0,
  y = NULL,
  Is = NULL,
  nu = 0,
  ML = NULL,
  CL = NULL,
  xi = 0,
  tr = FALSE,
  options = c(1, 1000, 1e-04, 10),
  param0 = list(U0 = NULL, V0 = NULL, W0 = NULL, beta0 = NULL)
)

Value

The output credal partition (an object of class "credpart"). In addition to the usual attributes, the output credal partition has the following attributes:

Kmat

The matrix of degrees of conflict. Same size as D.

D

The normalized dissimilarity matrix.

trace

Trace of the algorithm (Stress function vs iterations).

J

The matrix of indices.

param

The network parameters as a list with components U, V, W and beta.

Arguments

x

nxp matrix of p attributes observed for n objects.

k

Number of distances to compute for each object (default: n-1).

D

nxn or nxk dissimilarity matrix (optional). If absent, the Euclidean distance is computed.

J

nxk matrix of indices. D[i,j] is the distance between objects i and J[i,j]. (Used only if D is supplied and ncol(D)<n.)

c

Number of clusters

type

Type of focal sets ("simple": empty set, singletons and Omega; "full": all \(2^c\) subsets of \(\Omega\); "pairs": \(\emptyset\), singletons, \(\Omega\), and all or selected pairs).

n_H

Number of hidden units (if one hidden layer), or a two-dimensional vector of numbers of hidden units (if two hidden layers).

ntrials

Number of runs of the optimization algorithm (set to 1 if param0 is supplied).

d0

Parameter used for matrix normalization. The normalized distance corresponding to d0 is 0.95.

fhat

Vector of outputs from a one-class SVM for novelty detection (optional)

lambda

Regularization coefficient (default: 0)

y

Optional vector of class labels for a subset of the training set (for semi-supervised learning).

Is

Vector of indices corresponding to y (for semi-supervised learning).

nu

Coefficient of the supervised error term (default: 0).

ML

Optional nbML*2 matrix of must-link constraints (for constrained clustering). Each row of ML contains the indices of objects that belong to the same class.

CL

Optional nbCL*2 matrix of cannot-link constraints (for constrained clustering). Each row of CL contains the indices of objects that belong to different classes.

xi

Coefficient of the constrained clustering loss (default: 0).

tr

If TRUE, a trace of the stress function is returned.

options

Parameters of the optimization algorithm (see harris).

param0

Optional list of initial network parameters (see details).

Author

Thierry Denoeux.

Details

This is a neural network version of kevclus. The neural net has one or two layers of ReLU units and a softmax output layer (see Denoeux, 2020). The weight matrices are denoted by U, V and W for a two-hidden-layer network, or V and W for a one-hidden-layer network. The inputs are a feature vector x, an optional distance matrix D, and an optional vector of one-class SVM outputs fhat, which is used for novelty detection. Part of the output belief mass is transfered to the empty set based on beta[1]+beta[2]*fhat, where beta is an additional parameter vector. The network can be trained in fully unsupervised mode, in semi-supervised mode (with class labels for a subset of the learning instances), or with pairwise constraints. The output is a credal partition (a "credpart" object), with a specific field containing the network parameters (U, V, W, beta).

References

T. Denoeux. NN-EVCLUS: Neural Network-based Evidential Clustering. Information Sciences, Vol. 572, Pages 297-330, 2021.

See Also

nnevclus_mb, predict.credpart, kevclus, kcevclus, harris

Examples

if (FALSE) {
## Example with one hidden layer and no novelty detection
data(fourclass)
x<-scale(fourclass[,1:2])
y<-fourclass[,3]
clus<-nnevclus(x,c=4,n_H=c(5,5),type='pairs') # One hidden layer
plot(clus,x,mfrow=c(2,2))

## Example with two hidden layers and novelty detection
library(kernlab)
data(fourclass)
x<-scale(fourclass[,1:2])
y<-fourclass[,3]
x<-data.frame(x)
svmfit<-ksvm(~.,data=x,type="one-svc",kernel="rbfdot",nu=0.2,kpar=list(sigma=0.2))
fhat<-predict(svmfit,newdata=x,type="decision")
clus<-nnevclus(x,k=200,c=4,n_H=c(5,5),type='pairs',fhat=fhat)
plot(clus,x,mfrow=c(2,2))

## Example with semi-supervised learning
data<-bananas(400)
x<-scale(data$x)
y<-data$y
Is<-sample(400, 50)  # Indices of labeled instances
plot(x,col=y,pch=y)
points(x[Is,],pch=16)
svmfit<-ksvm(~.,data=x,type="one-svc",kernel="rbfdot",nu=0.2,kpar=list(sigma=0.2))
fhat<-predict(svmfit,newdata=x,type="decision")
clus<-nnevclus(x,k=100,c=2,n_H=10,type='full',fhat=fhat,Is=Is,y=y[Is],nu=0.5)
plot(clus,x)

## Example with pairwise constraints
data<-bananas(400)
x<-scale(data$x)
y<-data$y
const<-create_MLCL(y,500)
clus<-nnevclus(x,k=100,c=2,n_H=10,type='full',fhat=fhat,ML=const$ML,CL=const$CL,
rho=0.5)
plot(clus,x)

## Example with pairwise constraints and PCCA
data(iris)
x<-scale(as.matrix(iris[,1:4]))
y<-as.integer(iris[,5])
const<-create_MLCL(y,100)
res.pcca<-pcca(x,3,const$ML,const$CL,beta=1)
plot(res.pcca$z,pch=y,col=y)
clus<-nnevclus(x=x,D=res.pcca$D,c=3,n_H=10,type='full',ML=const$ML,CL=const$CL,rho=0.5)
plot(clus,x[,3:4])
}