Quality Criteria for dimensionality reduction.
A collection of functions to compute quality measures on
dimRedResult objects.
## S4 method for signature 'dimRedResult' quality(.data, .method = dimRedQualityList(), .mute = character(0), ...) dimRedQualityList()
.data |
object of class |
.method |
character vector naming one of the methods |
.mute |
what output from the embedding method should be muted. |
... |
the pameters, internally passed as a list to the
quality method as |
a number
dimRedResult: Calculate a quality index from a dimRedResult object.
Method must be one of "Q_local", "Q_global",
"mean_R_NX", "total_correlation",
"cophenetic_correlation", "distance_correlation",
"reconstruction_rmse"
Q_local, Q_global, and mean_R_nx are
quality criteria based on the Co-ranking matrix. Q_local
and Q_global determine the local/global quality of the
embedding, while mean_R_nx determines the quality of the
overall embedding. They are parameter free and return a single
number. The object must include the original data. The number
returns is in the range [0, 1], higher values mean a better
local/global embedding.
total_correlation calculates the sum of the mean squared
correlations of the original axes with the axes in reduced
dimensions, because some methods do not care about correlations
with axes, there is an option to rotate data in reduced space to
maximize this criterium. The number may be greater than one if more
dimensions are summed up.
cophenetic_correlation calculate the correlation between the
lower triangles of distance matrices, the correlation and distance
methods may be specified. The result is in range [-1, 1].
distance_correlation measures the independes of samples by
calculating the correlation of distances. For details see
dcor.
reconstruction_rmse calculates the root mean squared error
of the reconstrucion. object requires an inverse function.
Guido Kraemer
Lueks, W., Mokbel, B., Biehl, M., Hammer, B., 2011. How to Evaluate Dimensionality Reduction? - Improving the Co-ranking Matrix. arXiv:1110.3917 [cs].
Szekely, G.J., Rizzo, M.L., Bakirov, N.K., 2007. Measuring and testing dependence by correlation of distances. Ann. Statist. 35, 2769-2794. doi:10.1214/009053607000000505
Lee, J.A., Peluffo-Ordonez, D.H., Verleysen, M., 2015. Multi-scale similarities in stochastic neighbour embedding: Reducing dimensionality while preserving both local and global structure. Neurocomputing, 169, 246-261. doi:10.1016/j.neucom.2014.12.095
Other Quality scores for dimensionality reduction: AUC_lnK_R_NX,dimRedResult-method,
LCMC,dimRedResult-method,
Q_NX,dimRedResult-method,
Q_global,dimRedResult-method,
Q_local,dimRedResult-method,
R_NX,dimRedResult-method,
cophenetic_correlation,dimRedResult-method,
distance_correlation,dimRedResult-method,
mean_R_NX,dimRedResult-method,
plot_R_NX,
reconstruction_error,dimRedResult-method,
reconstruction_rmse,dimRedResult-method,
total_correlation,dimRedResult-method
## Not run:
embed_methods <- dimRedMethodList()
quality_methods <- dimRedQualityList()
scurve <- loadDataSet("Iris")
quality_results <- matrix(NA, length(embed_methods), length(quality_methods),
dimnames = list(embed_methods, quality_methods))
embedded_data <- list()
for (e in embed_methods) {
message("embedding: ", e)
embedded_data[[e]] <- embed(scurve, e, .mute = c("message", "output"))
for (q in quality_methods) {
message(" quality: ", q)
quality_results[e, q] <- tryCatch(
quality(embedded_data[[e]], q),
error = function (e) NA
)
}
}
print(quality_results)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.