We assume that both K and R are known. A range of values of lambda is usually considered - value that results in the lowest BIC is selected.

1 2 | ```
matrixBC.BIC(x, k, r, lambda, alpha = 0.2, beta = 0.2, nstart = 20,
Sigma.init = NULL, Delta.init = NULL)
``` |

`x` |
Data matrix; samples are rows and columns are features. Cannot contain missing values. |

`k` |
The number of row clusters, i.e., the number of clusters for the observations. |

`r` |
The number of column clusters, i.e., the number of clusters for the features. |

`lambda` |
A range of values of tuning parameters to be considered. All values must be non-negative. |

`alpha` |
Non-negative regularization parameter for the graphical lasso to estimate the covariance matrix of the samples. lambda=0 means no regularization. |

`beta` |
Non-negative regularization parameter for the graphical lasso to estimate the covariance matrix of the features. lambda=0 means no regularization. |

`nstart` |
The number of random initialization sets used in the kmeans function. The default is 20. |

`Sigma.init` |
Starting values for the covariance matrix of the observations. The default value is NULL – the graphical lasso as described in Friedman, Hastie, and Tibshirani (2007) is performed to estimate the covariance matrix of the observations. |

`Delta.init` |
Starting values for the covariance matrix of the features. The default value is NULL – the graphical lasso as described in Friedman, Hastie, and Tibshirani (2007) is performed to estimate the covariance matrix of the features. |

This implements the tuning parameter selection for MVN biclustering using BIC criterion as described in Section 5.2 in Tan and Witten (2014) 'Sparse biclustering of transposable data'. The BIC criterion is BIC = np x log(RSS) + np log(q) where RSS is the usual residual sum of squares, and q is the number of non-zero bicluster mean in the output of matrixBC. We select the value of lambda that leads to the smallest BIC.

The data is centered to have mean 0 in this function.

`lambda` |
Value of lambda that results in lowest BIC. |

`BIC` |
BIC values for a range of tuning parameters considered. |

`nonzeromus` |
Number of nonzero bicluster means for a range of tuning parameters considered. |

Kean Ming Tan and Daniela Witten

KM Tan and D Witten (2014) Sparse biclustering of transposable data. *Journal of Computational and Graphical Statistics* 23(4):985-1008.

`matrixBC`

1 2 3 4 5 | ```
########### Create data matrix
#x <- matrix(rnorm(20*30),nrow=20,ncol=30)
########### Perform sparseBC.BIC to select lambda
#lambda<-matrixBC.BIC(x,k=2,r=2,lambda=c(0,10,20,30,40),alpha=0.2,beta=0.2)$lambda
``` |

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