Description Usage Arguments Value Author(s) References Examples

The `ALS.CPC`

function implement
ALS algorithm based on the update formula

*\bold{D_{k+1}} = R_{\bold{D_k}} (-β^{m_k} \ α \ grad(Φ (\bold{D}_k)))*

until convergence (i.e. *|Φ(\bold{D}_k)-Φ (\bold{D}_{k+1})| ≤ ε*)
and return the orthogonal matrix
*\bold{D}_r*, *r* is the smallest nonnegative integer *k* such that
*|Φ(\bold{D}_k)-Φ (\bold{D}_{k+1})| ≤ ε*.

1 |

`alpha` |
positive real number. |

`beta` |
real number belong to (0,1). |

`sigma` |
real number belong to (0,1). |

`epsilon` |
small positive constant controlling error term. |

`G` |
number of groups in common principal components analysis. |

`nval` |
a numeric vector containing the positive integers of sample sizes minus one in each group. |

`D` |
an initial square orthogonal matrix of order |

`S` |
a list of length |

An orthogonal matrix such that minimize *Φ(\bold{D})*.

Dariush Najarzadeh

Absil, P. A., Mahony, R., & Sepulchre, R. (2009). Optimization algorithms on matrix manifolds. Princeton University Press.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
nval<-numeric(3)
nval[[1]]<-49
nval[[2]]<-49
nval[[3]]<-49
S<-vector("list",length=3)
setosa<-iris[1:50,1:4]; names(setosa)<-NULL
versicolor<-iris[51:100,1:4]; names(versicolor)<-NULL
virginica<-iris[101:150,1:4]; names(virginica)<-NULL
S[[1]]<-as.matrix(var(versicolor))
S[[2]]<-as.matrix(var(virginica))
S[[3]]<-as.matrix(var(setosa))
D<-diag(4)
ALS.CPC(10,0.5,0.4,1e-5,G=3,nval,D,S)
``` |

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