R: Quality Criteria for dimensionality reduction.

quality,dimRedResult-method {dimRed} | R Documentation

## Quality Criteria for dimensionality reduction.

### Description

A collection of functions to compute quality measures on `dimRedResult` objects.

### Usage

    ## S4 method for signature 'dimRedResult'
    quality(.data, .method = dimRedQualityList(),
      .mute = character(0), ...)

    dimRedQualityList()

### Arguments

`.data` | object of class `dimRedResult`
`.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 `pars = list(...)`

### Value

a number

### Methods (by class)

- `dimRedResult`: Calculate a quality index from a dimRedResult object.

### Implemented methods

Method must be one of `"Q_local", "Q_global", "mean_R_NX", "total_correlation", "cophenetic_correlation", "distance_correlation", "reconstruction_rmse"`

### Rank based criteria

`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.

### Correlation based criteria

`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 error

`reconstruction_rmse` calculates the root mean squared error of the reconstrucion. `object` requires an inverse function.

### Author(s)

Guido Kraemer

### References

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

### See Also

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`, `reconstruction_error,dimRedResult-method`, `reconstruction_rmse,dimRedResult-method`, `total_correlation,dimRedResult-method`

### Examples

    ## Not run:
    embed_methods <- dimRedMethodList()
    quality_methods <- dimRedQualityList()
    scurve <- loadDataSet("3D S Curve", n = 500)

    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)

[Package dimRed version 0.1.0 Index]