Link similar columns¶

network • correlation

Calculates all pair-wise column dependencies (by default mutual information).

Create a new network dataset where nodes (rows) represent the original dataset's variables (its columns), and links represent dependencies between variables (i.e. associations/correlations). By default the step measures "mutual information" between variables.

In effect, all pair-wise "correlations" between the original dataset's columns are calculated. A threshold is then applied to extract only the largest (most interesting) "correlations". These are then translated into network links between nodes representing the original variables. Each node/row in the new dataset will also contain information about its correlation with all other nodes (variables).

Note: in this first version, only quantitative and categorical variables will be analyzed (but not tags, lists, embeddings etc.). You can pass a dataset with arbitrary column types, but those not supported by the selected correlation method will be ignored in the result.

Usage¶

The following are the step's expected inputs and outputs and their specific types.

Step signature

link_similar_columns(ds_in: dataset, {
    "param": value
}) -> (ds_out: dataset)

where the object {"param": value} is optional in most cases and if present may contain any of the parameters described in the corresponding section below.

Example¶

The following example calculates all correlations without filtering, leading to a fully connected correlation network unless some correlations are exactly 0.

Example call (in recipe editor)

links_similar_columns(ds) -> (corrs)

More examples

The following example removes correlations below the 75^th percentile, creating a network only connecting the most correlated variables.

Example call (in recipe editor)

links_similar_columns(ds, {
  "min_similarity_quantile": 0.75,
}) -> (corrs)

Inputs¶

ds_in: dataset

Input dataset containing arbitrary columns to calculate "correlations" for.

Outputs¶

ds_out: dataset

A dataset containing M rows and M+2 columns (where M is the number of columns in the input dataset). Each row represents a variable in the original dataset, and the columns contain the "correlations" with the remaining variables. An additional 2 columns ("targets" and "weights") contain links connecting original variables to other variables they're correlated with.

Parameters¶

method: string = "mutual_information"

Correlation method/statistic. Which statistic to use to measure variable association/correlation.

The default is "mutual_information", which applies scikit-learn`s k-nearest neighbors implementations (see here and here). It supports both categorical and quantitative variables, is relatively fast, but doesn't have a natural upper bound (i.e. values are not in the range [0, 1]).

The "distance_correlation" method also supports both categorical and quantitative variables, and has a natural upper bound of 1. It's relatively slow though, so make sure to select a reasonable value for n_samples.

"distance_correlation_fast" uses an optimized implementation of distance correlation, but only supports quantitative variables.

"pearson" is the standard Pearson correlation coefficient, which also only supports quantitative variables.

Lastly, "predictive_power" calculates a version of the predictive power score (PPS). This essentially fits a decision tree to predict variable y using only variable x as a predictor, and measures it performance relative to a dummy/baseline prediction. It supports both categorical and quantitative variables.

Must be one of: "mutual_information", "distance_correlation", "distance_correlation_fast", "pearson", "predictive_power"

min_similarity: number = 0.0

Absolute similarity threshold. The minimum "correlation" for the creation of a link between two variables.

min_similarity_quantile: number = 0.5

Similarity threshold expressed as a quantile. E.g. a value of 0.6 means the bottom 60% of "correlations" will be discarded. Both minima (absolute and quantile) must be exceeded for a link to be created.

Range: 0.0 ≤ min_similarity_quantile ≤ 1

missing_weight: number | null

Replacement for discarded correlations. The weight of links whose correlations don't pass the minimum threshold. Links with weights of null will be discarded (the default behavior). Can be set e.g. to 0, to generate all possible links.

n_samples: integer = 2000

Number of Samples. It represents the maximum number of samples to use when measuring "correlations".

top_n_links: integer | null

Maximum number of links per node. Ranks the links by weight and keeps only the most similar targets.

random_seed: integer = 0

The random seed used if applicable for selected method