nnevclus_mb {evclust}

NN-EVCLUS algorithm (minibatch version)

Description

nnevclus_mb computes a credal partition from a dissimilarity matrix using the NN-EVCLUS algorithm. Training is done using mini-batch gradient descent with the RMSprop optimization algorithm.

Usage

nnevclus_mb(
  x,
  foncD = function(x) as.matrix(dist(x)),
  c,
  type = "simple",
  n_H,
  nbatch = 10,
  alpha0 = 0.9,
  fhat = NULL,
  lambda = 0,
  y = NULL,
  Is = NULL,
  nu = 0,
  disp = TRUE,
  options = list(Niter = 1000, epsi = 0.001, rho = 0.9, delta = 1e-08, Dtmax = 100, print
    = 5),
  param0 = list(V0 = NULL, W0 = NULL, beta0 = NULL)
)

Arguments

x

nxp matrix of p attributes observed for n objects.

foncD

A function to compute distances.

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

Size or the hidden layer.

nbatch

Number of mini-batches.

alpha0

Order of the quantile to normalize distances. Parameter d0 is set to the alpha0-quantile of distances. Default: 0.9.

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).

disp

If TRUE, intermediate results are displayed.

options

Parameters of the optimization algorithm (Niter: maximum number of iterations; epsi, rho, delta: parameters of RMSprop; Dtmax: the algorithm stops when the loss has not decreased in the last Dtmax iterations; print: number of iterations between two displays).

param0

Optional list of initial network parameters (see details).

#'

Details

This is a neural network version of kevclus. The neural net has one layer of ReLU units and a softmax output layer (see Denoeux, 2020). The network is trained in mini-batch mode using the RMSprop algorithm. 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 or in semi-supervised mode (with class labels for a subset of the learning instances). The output is a credal partition (a "credpart" object), with a specific field containing the network parameters (U, V, W, beta).

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.

trace

Trace of the algorithm (values of the loss function).

param

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

Author(s)

Thierry Denoeux.

References

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

See Also

nnevclus, predict.credpart, kevclus, kcevclus, harris

Examples

## Not run: 
## Unsupervised learning
data(fourclass)
x<-scale(fourclass[,1:2])
y<-fourclass[,3]
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_mb(x,foncD=function(x) as.matrix(dist(x)),c=4,type='pairs',
n_H=10,nbatch=10,alpha0=0.9,fhat=fhat)
plot(clus,x)
## semi-supervised learning
Is<-sample(400,100)
clus<-nnevclus_mb(x,foncD=function(x) as.matrix(dist(x)),c=4,type='pairs',
n_H=10,nbatch=10,alpha0=0.9,fhat=fhat,lambda=0, y=y[Is],Is=Is,nu=0.5)
plot(clus,x)

## End(Not run)