def _fit(self, X, skip_num_points=0):
        """Fit the model using X as training data.

        Note that sparse arrays can only be handled by method='exact'.
        It is recommended that you convert your sparse array to dense
        (e.g. `X.toarray()`) if it fits in memory, or otherwise using a
        dimensionality reduction technique (e.g. TruncatedSVD).

        Parameters
        ----------
        X : array, shape (n_samples, n_features) or (n_samples, n_samples)
            If the metric is 'precomputed' X must be a square distance
            matrix. Otherwise it contains a sample per row. Note that this
            when method='barnes_hut', X cannot be a sparse array and if need be
            will be converted to a 32 bit float array. Method='exact' allows
            sparse arrays and 64bit floating point inputs.

        skip_num_points : int (optional, default:0)
            This does not compute the gradient for points with indices below
            `skip_num_points`. This is useful when computing transforms of new
            data where you'd like to keep the old data fixed.
        """
        if self.method not in ['barnes_hut', 'exact']:
            raise ValueError("'method' must be 'barnes_hut' or 'exact'")
        if self.angle < 0.0 or self.angle > 1.0:
            raise ValueError("'angle' must be between 0.0 - 1.0")
        if self.metric == "precomputed":
            if isinstance(self.init, string_types) and self.init == 'pca':
                raise ValueError("The parameter init=\"pca\" cannot be "
                                 "used with metric=\"precomputed\".")
            if X.shape[0] != X.shape[1]:
                raise ValueError("X should be a square distance matrix")
            if np.any(X < 0):
                raise ValueError("All distances should be positive, the "
                                 "precomputed distances given as X is not "
                                 "correct")
        if self.method == 'barnes_hut' and sp.issparse(X):
            raise TypeError('A sparse matrix was passed, but dense '
                            'data is required for method="barnes_hut". Use '
                            'X.toarray() to convert to a dense numpy array if '
                            'the array is small enough for it to fit in '
                            'memory. Otherwise consider dimensionality '
                            'reduction techniques (e.g. TruncatedSVD)')
        else:
            X = check_array(X, accept_sparse=['csr', 'csc', 'coo'],
                            dtype=[np.float32, np.float64])
        if self.method == 'barnes_hut' and self.n_components > 3:
            raise ValueError("'n_components' should be inferior to 4 for the "
                             "barnes_hut algorithm as it relies on "
                             "quad-tree or oct-tree.")
        random_state = check_random_state(self.random_state)

        if self.early_exaggeration < 1.0:
            raise ValueError("early_exaggeration must be at least 1, but is {}"
                             .format(self.early_exaggeration))

        if self.n_iter < 250:
            raise ValueError("n_iter should be at least 250")

        n_samples = X.shape[0]

        neighbors_nn = None
        if self.method == "exact":
            # Retrieve the distance matrix, either using the precomputed one or
            # computing it.
            if self.metric == "precomputed":
                distances = X
            else:
                if self.verbose:
                    print("[t-SNE] Computing pairwise distances...")

                if self.metric == "euclidean":
                    distances = pairwise_distances(X, metric=self.metric,
                                                   squared=True)
                else:
                    distances = pairwise_distances(X, metric=self.metric)

                if np.any(distances < 0):
                    raise ValueError("All distances should be positive, the "
                                     "metric given is not correct")

            # compute the joint probability distribution for the input space
            P = _joint_probabilities(distances, self.perplexity, self.verbose)
            assert np.all(np.isfinite(P)), "All probabilities should be finite"
            assert np.all(P >= 0), "All probabilities should be non-negative"
            assert np.all(P <= 1), ("All probabilities should be less "
                                    "or then equal to one")

        else:
            # Cpmpute the number of nearest neighbors to find.
            # LvdM uses 3 * perplexity as the number of neighbors.
            # In the event that we have very small # of points
            # set the neighbors to n - 1.
            k = min(n_samples - 1, int(3. * self.perplexity + 1))

            if self.verbose:
                print("[t-SNE] Computing {} nearest neighbors...".format(k))

            # Find the nearest neighbors for every point
            neighbors_method = 'ball_tree'
            if (self.metric == 'precomputed'):
                neighbors_method = 'brute'
            knn = AnnoyIndex(X.shape[1], metric='euclidean')
            t0 = time()
            for i in range(n_samples):
                knn.add_item(i, X[i, :])
            knn.build(50)
            duration = time() - t0
            if self.verbose:
                print("[t-SNE] Indexed {} samples in {:.3f}s...".format(
                    n_samples, duration))

            t0 = time()
            neighbors_nn = np.zeros((n_samples, k), dtype=int)
            distances_nn = np.zeros((n_samples, k))
            for i in range(n_samples):
                (neighbors_nn[i, :], distances_nn[i, :]) = knn.get_nns_by_vector(
                    X[i, :], k, include_distances=True
                )
            duration = time() - t0
            if self.verbose:
                print("[t-SNE] Computed neighbors for {} samples in {:.3f}s..."
                      .format(n_samples, duration))

            # Free the memory used by the ball_tree
            del knn

            if self.metric == "euclidean":
                # knn return the euclidean distance but we need it squared
                # to be consistent with the 'exact' method. Note that the
                # the method was derived using the euclidean method as in the
                # input space. Not sure of the implication of using a different
                # metric.
                distances_nn **= 2

            # compute the joint probability distribution for the input space
            P = _joint_probabilities_nn(distances_nn, neighbors_nn,
                                        self.perplexity, self.verbose)

        if isinstance(self.init, np.ndarray):
            X_embedded = self.init
        elif self.init == 'pca':
            pca = PCA(n_components=self.n_components, svd_solver='randomized',
                      random_state=random_state)
            X_embedded = pca.fit_transform(X).astype(np.float32, copy=False)
        elif self.init == 'random':
            # The embedding is initialized with iid samples from Gaussians with
            # standard deviation 1e-4.
            X_embedded = 1e-4 * random_state.randn(
                n_samples, self.n_components).astype(np.float32)
        else:
            raise ValueError("'init' must be 'pca', 'random', or "
                             "a numpy array")

        # Degrees of freedom of the Student's t-distribution. The suggestion
        # degrees_of_freedom = n_components - 1 comes from
        # "Learning a Parametric Embedding by Preserving Local Structure"
        # Laurens van der Maaten, 2009.
        degrees_of_freedom = max(self.n_components - 1.0, 1)

        return self._tsne(P, degrees_of_freedom, n_samples, random_state,
                          X_embedded=X_embedded,
                          neighbors=neighbors_nn,
                          skip_num_points=skip_num_points)
Fit the model using X as training data.

        Note that sparse arrays can only be handled by method='exact'.
        It is recommended that you convert your sparse array to dense
        (e.g. `X.toarray()`) if it fits in memory, or otherwise using a
        dimensionality reduction technique (e.g. TruncatedSVD).

        Parameters
        ----------
        X : array, shape (n_samples, n_features) or (n_samples, n_samples)
            If the metric is 'precomputed' X must be a square distance
            matrix. Otherwise it contains a sample per row. Note that this
            when method='barnes_hut', X cannot be a sparse array and if need be
            will be converted to a 32 bit float array. Method='exact' allows
            sparse arrays and 64bit floating point inputs.

        skip_num_points : int (optional, default:0)
            This does not compute the gradient for points with indices below
            `skip_num_points`. This is useful when computing transforms of new
            data where you'd like to keep the old data fixed.