# fuzzy_simplicial_set

### cuml.manifold.umap.fuzzy_simplicial_set(X, n_neighbors, random_state=None, metric='euclidean', metric_kwds=None, knn_indices=None, knn_dists=None, set_op_mix_ratio=1.0, local_connectivity=1.0, verbose=False)[[source]](https://github.com/NVIDIA/cuml/blob/93418baf5/python/cuml/cuml/manifold/umap/umap.pyx#L1693)

Given a set of data X, a neighborhood size, and a measure of distance
compute the fuzzy simplicial set (here represented as a fuzzy graph in
the form of a sparse matrix) associated to the data. This is done by
locally approximating geodesic distance at each point, creating a fuzzy
simplicial set for each such point, and then combining all the local
fuzzy simplicial sets into a global one via a fuzzy union.

* **Parameters:**
  **X: array of shape (n_samples, n_features)**
  : The data to be modelled as a fuzzy simplicial set.

  **n_neighbors: int**
  : The number of neighbors to use to approximate geodesic distance.
    Larger numbers induce more global estimates of the manifold that can
    miss finer detail, while smaller values will focus on fine manifold
    structure to the detriment of the larger picture.

  **random_state: numpy RandomState or equivalent**
  : A state capable being used as a numpy random state.

  **metric: string (default=’euclidean’).**
  : Distance metric to use. Supported distances are [‘l1, ‘cityblock’,
    ‘taxicab’, ‘manhattan’, ‘euclidean’, ‘l2’, ‘sqeuclidean’, ‘canberra’,
    ‘minkowski’, ‘chebyshev’, ‘linf’, ‘cosine’, ‘correlation’, ‘hellinger’,
    ‘hamming’, ‘jaccard’]
    Metrics that take arguments (such as minkowski) can have arguments
    passed via the metric_kwds dictionary.
    Note: The ‘jaccard’ distance metric is only supported for sparse
    inputs.

  **metric_kwds: dict (optional, default=None)**
  : Metric argument

  **knn_indices: array of shape (n_samples, n_neighbors) (optional)**
  : If the k-nearest neighbors of each point has already been calculated
    you can pass them in here to save computation time. This should be
    an array with the indices of the k-nearest neighbors as a row for
    each data point.

  **knn_dists: array of shape (n_samples, n_neighbors) (optional)**
  : If the k-nearest neighbors of each point has already been calculated
    you can pass them in here to save computation time. This should be
    an array with the distances of the k-nearest neighbors as a row for
    each data point.

  **set_op_mix_ratio: float (optional, default 1.0)**
  : Interpolate between (fuzzy) union and intersection as the set operation
    used to combine local fuzzy simplicial sets to obtain a global fuzzy
    simplicial sets. Both fuzzy set operations use the product t-norm.
    The value of this parameter should be between 0.0 and 1.0; a value of
    1.0 will use a pure fuzzy union, while 0.0 will use a pure fuzzy
    intersection.

  **local_connectivity: int (optional, default 1)**
  : The local connectivity required – i.e. the number of nearest
    neighbors that should be assumed to be connected at a local level.
    The higher this value the more connected the manifold becomes
    locally. In practice this should be not more than the local intrinsic
    dimension of the manifold.

  **verbose: bool (optional, default False)**
  : Whether to report information on the current progress of the algorithm.
* **Returns:**
  fuzzy_simplicial_set: coo_matrix
  : A fuzzy simplicial set represented as a sparse matrix. The (i, j) entry
    of the matrix represents the membership strength of the 1-simplex
    between the ith and jth sample points.

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