Description Usage Arguments Details Value Author(s) References See Also Examples

Applies mode-wise projection pursuit to tensorial data with respect to the chosen measure of interestingness.

1 | ```
tPP(x, nl = "pow3", eps = 1e-6, maxiter = 100)
``` |

`x` |
Numeric array of an order at least three. It is assumed that the last dimension corresponds to the sampling units. |

`nl` |
The chosen measure of interestingness/objective function. Current choices include |

`eps` |
The convergence tolerance of the iterative algortihm. |

`maxiter` |
The maximum number of iterations. |

The observed tensors (arrays) *X* of size *p_1 x p_2 x ... x p_r* measured on *N* units are standardized from each mode and then projected mode-wise onto the directions that maximize the *L_2*-norm of the vector of the values *E[G(u_k^T X X^T u_k)] - E[G(c^2)]*, where *G* is the chosen objective function and *c^2* obeys the chi-squared distribution with *q* degress of freedom. Currently the function allows the choices *G(x) = x^2* (`pow3`

) and *G(x) = x √{x}* (`skew`

), which correspond roughly to the maximization of kurtosis and skewness, respectively. The algorithm is the multilinear extension of FastICA, where the names of the objective functions also come from.

A list with class 'tbss', inheriting from class 'bss', containing the following components:

`S ` |
Array of the same size as x containing the estimated components. |

`W ` |
List containing all the unmixing matrices. |

`iter ` |
The numbers of iteration used per mode. |

`Xmu ` |
The data location. |

`datatype` |
Character string with value "iid". Relevant for |

Joni Virta

Nordhausen, K. and Virta, J. (2018), Tensorial projection pursuit, Manuscript in preparation.

Hyvarinen, A. (1999) Fast and robust fixed-point algorithms for independent component analysis, IEEE transactions on Neural Networks 10.3: 626-634.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
n <- 1000
S <- t(cbind(rexp(n)-1,
rnorm(n),
runif(n, -sqrt(3), sqrt(3)),
rt(n,5)*sqrt(0.6),
(rchisq(n,1)-1)/sqrt(2),
(rchisq(n,2)-2)/sqrt(4)))
dim(S) <- c(3, 2, n)
A1 <- matrix(rnorm(9), 3, 3)
A2 <- matrix(rnorm(4), 2, 2)
X <- tensorTransform(S, A1, 1)
X <- tensorTransform(X, A2, 2)
tpp <- tPP(X)
MD(tpp$W[[1]], A1)
MD(tpp$W[[2]], A2)
tMD(tpp$W, list(A1, A2))
``` |

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