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# `sklearn.metrics.pairwise`.pairwise_kernels

sklearn.metrics.pairwise.pairwise_kernels(X, Y=None, metric='linear', *, filter_params=False, n_jobs=None, **kwds)

  Compute the kernel between arrays X and optional array Y.

  This method takes either a vector array or a kernel matrix, and returns a kernel matrix. If the input is a vector array, the kernels are computed. If the input is a kernel matrix, it is returned instead.

  This method provides a safe way to take a kernel matrix as input, while preserving compatibility with many other algorithms that take a vector array.

  If Y is given (default is None), then the returned matrix is the pairwise kernel between the arrays from both X and Y.

  Valid values for metric are:

    [‘additive_chi2’, ‘chi2’, ‘linear’, ‘poly’, ‘polynomial’, ‘rbf’, ‘laplacian’, ‘sigmoid’, ‘cosine’]

  Read more in the User Guide.

  Parameters:
    X ndarray of shape (n_samples_X, n_samples_X) or (n_samples_X, n_features)

      Array of pairwise kernels between samples, or a feature array. The shape of the array should be (n_samples_X, n_samples_X) if metric == “precomputed” and (n_samples_X, n_features) otherwise.

    Y ndarray of shape (n_samples_Y, n_features), default=None

      A second feature array only if X has shape (n_samples_X, n_features).

    metric str or callable, default=”linear”

      The metric to use when calculating kernel between instances in a feature array. If metric is a string, it must be one of the metrics in pairwise.PAIRWISE_KERNEL_FUNCTIONS. If metric is “precomputed”, X is assumed to be a kernel matrix. Alternatively, if metric is a callable function, it is called on each pair of instances (rows) and the resulting value recorded. The callable should take two rows from X as input and return the corresponding kernel value as a single number. This means that callables from `sklearn.metrics.pairwise` are not allowed, as they operate on matrices, not single samples. Use the string identifying the kernel instead.

    filter_params bool, default=False

      Whether to filter invalid parameters or not.

    n_jobs int, default=None

      The number of jobs to use for the computation. This works by breaking down the pairwise matrix into n_jobs even slices and computing them in parallel.

      `None` means 1 unless in a `joblib.parallel_backend` context. `-1` means using all processors. See Glossary for more details.

    **kwds optional keyword parameters

      Any further parameters are passed directly to the kernel function.

  Returns:
    K ndarray of shape (n_samples_X, n_samples_X) or (n_samples_X, n_samples_Y)

      A kernel matrix K such that K_{i, j} is the kernel between the ith and jth vectors of the given matrix X, if Y is None. If Y is not None, then K_{i, j} is the kernel between the ith array from X and the jth array from Y.

  Notes

  If metric is ‘precomputed’, Y is ignored and X is returned.