Fit the Radius nearest neighbors classifier from the training data set.

For classification, provided labels need to be consecutive non-negative integers. If your labels does not meet this condition please use Scholar.Preprocessing.ordinal_encode

Currently 2D labels are only supported for regression tasks.

Options

• :radius - Radius of neighborhood The default value is 1.0.

• :num_classes (pos_integer/0) - Number of classes in provided labels

• :weights - Weight function used in prediction. Possible values:

  • :uniform - uniform weights. All points in each neighborhood are weighted equally.

  • :distance - weight points by the inverse of their distance. in this case, closer neighbors of a query point will have a greater influence than neighbors which are further away.

  The default value is :uniform.

• :metric - The function that measures the pairwise distance between two points. Possible values:

  • {:minkowski, p} - Minkowski metric. By changing value of p parameter (a positive number or :infinity) we can set Manhattan (1), Euclidean (2), Chebyshev (:infinity), or any arbitrary $L_p$ metric.

  • :cosine - Cosine metric.

  • Anonymous function of arity 2 that takes two rank-2 tensors.

  The default value is &Scholar.Metrics.Distance.pairwise_minkowski/2.

• :task - Task that will be performed using Radius Nearest Neighbors. Possible values:

  • :classification - Classifier implementing the Radius Nearest Neighbors vote.

  • :regression - Regression based on Radius Nearest Neighbors. The target is predicted by local interpolation of the targets associated of the nearest neighbors in the training set.

  The default value is :classification.

Return Values

The function returns a struct with the following parameters:

• :data - Training data.

• :labels - Labels of each point.

• :weights - Weight function used in prediction.

• :num_classes - Number of classes in provided labels.

• :task - Task that will be performed using Radius Nearest Neighbors. For :classification task, model will be a classifier implementing the Radius Nearest Neighbors vote. For :regression task, model is a regressor based on Radius Nearest Neighbors.

• :metric - The metric function used.

• :radius - Radius of neighborhood.

Examples

iex> x = Nx.tensor([[1, 2], [2, 4], [1, 3], [2, 5]])
iex> y = Nx.tensor([1, 0, 1, 1])
iex> Scholar.Neighbors.RadiusNearestNeighbors.fit(x, y, num_classes: 2)
%Scholar.Neighbors.RadiusNearestNeighbors{
  data: Nx.tensor(
    [
      [1, 2],
      [2, 4],
      [1, 3],
      [2, 5]
    ]
  ),
  labels: Nx.tensor(
    [1, 0, 1, 1]
  ),
  weights: :uniform,
  num_classes: 2,
  task: :classification,
  metric: &Scholar.Metrics.Distance.pairwise_minkowski/2,
  radius: 1.0
}

Makes predictions with the given model on inputs x.

Return Values

It returns a tensor with predicted class labels.

Examples

iex> x = Nx.tensor([[1, 2], [2, 4], [1, 3], [2, 5]])
iex> y = Nx.tensor([1, 0, 1, 1])
iex> model = Scholar.Neighbors.RadiusNearestNeighbors.fit(x, y, num_classes: 2)
iex> Scholar.Neighbors.RadiusNearestNeighbors.predict(model, Nx.tensor([[1.9, 4.3], [1.1, 2.0]]))
Nx.tensor(
  [0, 1]
)

Return probability estimates for the test data x.

Return Values

It returns a typle with tensor with probabilities of classes and mask of outliers. They are arranged in lexicographic order.

Examples

iex> x = Nx.tensor([[1, 2], [2, 4], [1, 3], [2, 5]])
iex> y = Nx.tensor([1, 0, 1, 1])
iex> model = Scholar.Neighbors.RadiusNearestNeighbors.fit(x, y, num_classes: 2)
iex> Scholar.Neighbors.RadiusNearestNeighbors.predict_probability(model, Nx.tensor([[1.9, 4.3], [1.1, 2.0]]))
{Nx.tensor(
  [
    [0.5, 0.5],
    [0.0, 1.0]
  ]
),
Nx.tensor(
  [0, 0], type: :u8
)}

Find the Radius neighbors of a point.

Return Values

Returns indices of the selected neighbor points as a mask (1 if a point is a neighbor, 0 otherwise) and their respective distances.

Examples

iex> x = Nx.tensor([[1, 2], [2, 4], [1, 3], [2, 5]])
iex> y = Nx.tensor([1, 0, 1, 1])
iex> model = Scholar.Neighbors.RadiusNearestNeighbors.fit(x, y, num_classes: 2)
iex> Scholar.Neighbors.RadiusNearestNeighbors.radius_neighbors(model, Nx.tensor([[1.9, 4.3], [1.1, 2.0]]))
{Nx.tensor(
  [
    [2.469818353652954, 0.3162313997745514, 1.5811394453048706, 0.7071067690849304],
    [0.10000114142894745, 2.1931710243225098, 1.0049877166748047, 3.132091760635376]
  ]
),
Nx.tensor(
  [
    [0, 1, 0, 1],
    [1, 0, 0, 0]
  ], type: :u8
)}