In jlmelville/uwot: The Uniform Manifold Approximation and Projection (UMAP) Method for Dimensionality Reduction

The default approach of UMAP is that all your data is numeric and will be treated as one block using the Euclidean distance metric. To use a different metric, set the metric parameter, e.g. metric = "cosine".

Treating the data as one block may not always be appropriate. uwot now supports a highly experimental approach to mixed data types. It is not based on any deep understanding of topology and sets, so consider it subject to change, breakage or completely disappearing.

To use different metrics for different parts of a data frame, pass a list to the metric parameter. The name of each item is the metric to use and the value is a vector containing the names of the columns (or their integer id, but I strongly recommend names) to apply that metric to, e.g.:

metric = list("euclidean" = c("A1", "A2"), "cosine" = c("B1", "B2", "B3"))

this will treat columns A1 and A2 as one block of data, and generate neighbor data using the Euclidean distance, while a different set of neighbors will be generated with columns B1, B2 and B3, using the cosine distance. This will create two different simplicial sets. The final set used for optimization is the intersection of these two sets. This is exactly the same process that is used when carrying out supervised UMAP (except the contribution is always equal between the two sets and can't be controlled by the user).

You can repeat the same metric multiple times. For example, to treat the petal and sepal data separately in the iris dataset, but to use Euclidean distances for both, use:

metric = list("euclidean" = c("Petal.Width", "Petal.Length"),
              "euclidean" = c("Sepal.Width", "Sepal.Length"))

Indexing

As the iris example shows, using column names can be very verbose. Integer indexing is supported, so the equivalent of the above using integer indexing into the columns of iris is:

metric = list("euclidean" = 3:4, "euclidean" = 1:2)

but internally, uwot strips out the non-numeric columns from the data, and if you use Z-scaling (i.e. specify scale = "Z"), zero variance columns will also be removed. This is very likely to change the index of the columns. If you really want to use numeric column indexes, I strongly advise not using the scale argument and re-arranging your data frame if necessary so that all non-numeric columns come after the numeric columns.

Categorical columns

supervised UMAP allows for a factor column to be used. You may now also specify factor columns in the X data. Use the special metric name "categorical". For example, to use the Species factor in standard UMAP for iris along with the usual four numeric columns, use:

metric = list("euclidean" = 1:4, "categorical" = "Species")

Factor columns are treated differently from numeric columns:

• They are always treated separately, one column at a time. If you have two factor columns, cat1, and cat2, and you would like them included in UMAP, you should write:

metric = list("categorical" = "cat1", "categorical" = "cat2", ...)

As a convenience, you can also write:

metric = list("categorical" = c("cat1", "cat2"), ...)

but that doesn't combine cat1 and cat2 into one block, just saves some typing.

• Because of the way categorical data is intersected into a simplicial set, you cannot have an X metric that specifies only categorical entries. You must specify at least one of the standard Annoy metrics for numeric data. For iris, the following is an error:

# wrong and bad
metric = list("categorical" = "Species")

Specifying some numeric columns is required:

# OK
metric = list("categorical" = "Species", "euclidean" = 1:4)

• Factor columns not explicitly included in the metric are still removed as usual.
• Categorical data does not appear in the model returned when ret_model = TRUE and so does not affect the project of data used in umap_transform. You can still use the UMAP model to project new data, but factor columns in the new data are ignored (effectively working like supervised UMAP).

Overriding global options

Some global parameters can be overridden for a specific data block by providing a list as the value for the metric, containing the vector of columns as the only unnamed element, and then the over-riding keyword arguments. An example:

  umap(
    X,
    pca = 40,
    pca_center = TRUE,
    metric = list(
      euclidean = 1:200,
      euclidean = list(201:300, pca = NULL),
      manhattan = list(300:500, pca_center = FALSE)
    )
  )

In this case, the first euclidean block with be reduced to 40 dimensions by PCA with centering applied. The second euclidean block will not have PCA applied to it. The manhattan block will have PCA applied to it, but no centering is carried out.

Currently, only pca and pca_center are supported for overriding by this method, because this feature exists only to allow for the case where you have mixed real-valued and binary data, and you want to carry out PCA on both. It's typical to carry out centering on real-value data before PCA, but not to do so with binary data.

y data

The handling of y data has been extended to allow for data frames, and target_metric works like metric: multiple numeric blocks with different metrics can be specified, and categorical data can be specified with categorical. However, unlike X, the default behavior for y is to include all factor columns. Any numeric data found will be treated as one block, so if you have multiple numeric columns that you want treated separately, you should specify each column separately:

target_metric = list("euclidean" = 1, "euclidean" = 2, ...)

I suspect that the vast majority of y data is one column, so the default behavior will be fine most of the time.

jlmelville/uwot documentation built on April 25, 2024, 5:20 a.m.