Description Usage Arguments Details Value References

Given a set of training data, this function builds the HDRDA classifier from Ramey, Stein, and Young (2017). Specially designed for small-sample, high-dimensional data, the HDRDA classifier incorporates dimension reduction and covariance-matrix shrinkage to enable a computationally efficient classifier.

For a given `rda_high_dim`

object, we predict the class of each observation
(row) of the the matrix given in `newdata`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
rda_high_dim(x, ...)
## Default S3 method:
rda_high_dim(
x,
y,
lambda = 1,
gamma = 0,
shrinkage_type = c("ridge", "convex"),
prior = NULL,
tol = 1e-06,
...
)
## S3 method for class 'formula'
rda_high_dim(formula, data, ...)
## S3 method for class 'rda_high_dim'
predict(
object,
newdata,
projected = FALSE,
type = c("class", "prob", "score"),
...
)
``` |

`x` |
Matrix or data frame containing the training data. The rows are the sample observations, and the columns are the features. Only complete data are retained. |

`...` |
additional arguments (not currently used). |

`y` |
vector of class labels for each training observation |

`lambda` |
the HDRDA pooling parameter. Must be between 0 and 1, inclusively. |

`gamma` |
a numeric values used for the shrinkage parameter. |

`shrinkage_type` |
the type of covariance-matrix shrinkage to apply. By
default, a ridge-like shrinkage is applied. If |

`prior` |
vector with prior probabilities for each class. If |

`tol` |
a threshold for determining nonzero eigenvalues. |

`formula` |
A formula of the form |

`data` |
data frame from which variables specified in |

`object` |
Object of type |

`newdata` |
Matrix or data frame of observations to predict. Each row corresponds to a new observation. |

`projected` |
logical indicating whether |

`type` |
Prediction type: either |

The HDRDA classifier utilizes a covariance-matrix estimator that is a convex
combination of the covariance-matrix estimators used in the Linear
Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA)
classifiers. For each of the `K`

classes given in `y`

,
*(k = 1, …, K)*, we first define this convex combination as

*\hat{Σ}_k(λ) = (1 - λ) \hat{Σ}_k
+ λ \hat{Σ},*

where *λ \in [0, 1]* is the *pooling* parameter. We then
calculate the covariance-matrix estimator

*\tilde{Σ}_k = α_k \hat{Σ}_k(λ) + γ I_p,*

where *I_p* is the *p \times p* identity matrix. The matrix
*\tilde{Σ}_k* is substituted into the HDRDA classifier. See Ramey et
al. (2017) for more details.

The matrix of training observations are given in `x`

. The rows of
`x`

contain the sample observations, and the columns contain the features
for each training observation. The vector of class labels given in `y`

are coerced to a `factor`

. The length of `y`

should match the number
of rows in `x`

.

The vector `prior`

contains the *a priori* class membership for
each class. If `prior`

is `NULL`

(default), the class membership
probabilities are estimated as the sample proportion of observations
belonging to each class. Otherwise, `prior`

should be a vector with the
same length as the number of classes in `y`

. The `prior`

probabilities should be nonnegative and sum to one. The order of the prior
probabilities is assumed to match the levels of `factor(y)`

.

`rda_high_dim`

object that contains the trained HDRDA classifier

list with predicted class and discriminant scores for each of the K classes

Ramey, J. A., Stein, C. K., and Young, D. M. (2017), "High-Dimensional Regularized Discriminant Analysis." https://arxiv.org/abs/1602.01182.

Friedman, J. H. (1989), "Regularized Discriminant Analysis," Journal of American Statistical Association, 84, 405, 165-175. http://www.jstor.org/stable/2289860 (Requires full-text access).

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