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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def simplicial_set_embedding( data, graph, n_components, initial_alpha, a, b, gamma, negative_sample_rate, n_epochs, init, random_state, metric, metric_kwds, verbose, ):
 """Perform a fuzzy simplicial set embedding, using a specified initialisation method and then minimizing the fuzzy set cross entropy between the 1-skeletons of the high and low dimensional fuzzy simplicial sets. Parameters data: array of shape (n_samples, n_features) The source data to be embedded by UMAP. graph: sparse matrix The 1-skeleton of the high dimensional fuzzy simplicial set as represented by a graph for which we require a sparse matrix for the (weighted) adjacency matrix. n_components: int The dimensionality of the euclidean space into which to embed the data. initial_alpha: float Initial learning rate for the SGD. a: float Parameter of differentiable approximation of right adjoint functor b: float Parameter of differentiable approximation of right adjoint functor gamma: float Weight to apply to negative samples. negative_sample_rate: int (optional, default 5) The number of negative samples to select per positive sample in the optimization process. Increasing this value will result in greater repulsive force being applied, greater optimization cost, but slightly more accuracy. n_epochs: int (optional, default 0) The number of training epochs to be used in optimizing the low dimensional embedding. Larger values result in more accurate embeddings. If 0 is specified a value will be selected based on the size of the input dataset (200 for large datasets, 500 for small). init: string How to initialize the low dimensional embedding. Options are: * 'spectral': use a spectral embedding of the fuzzy 1-skeleton * 'random': assign initial embedding positions at random. * A numpy array of initial embedding positions. random_state: numpy RandomState or equivalent A state capable being used as a numpy random state. metric: string The metric used to measure distance in high dimensional space; used if multiple connected components need to be layed out. metric_kwds: dict Key word arguments to be passed to the metric function; used if multiple connected components need to be layed out. verbose: bool (optional, default False) Whether to report information on the current progress of the algorithm. Returns ------- embedding: array of shape (n_samples, n_components) The optimized of ``graph`` into an ``n_components`` dimensional euclidean space. """

    graph = graph.tocoo()
    graph.sum_duplicates()
    n_vertices = graph.shape[1]

    if n_epochs <= 0:
        # For smaller datasets we can use more epochs
        if graph.shape[0] <= 10000:
            n_epochs = 500
        else:
            n_epochs = 200

    graph.data[graph.data < (graph.data.max() / float(n_epochs))] = 0.0
    graph.eliminate_zeros()

    if isinstance(init, str) and init == "random":
        embedding = random_state.uniform(
            low=-10.0, high=10.0, size=(graph.shape[0], n_components)
        ).astype(np.float32)
    elif isinstance(init, str) and init == "spectral":
        # We add a little noise to avoid local minima for optimization to come
        initialisation = spectral_layout(
            data,
            graph,
            n_components,
            random_state,
            metric=metric,
            metric_kwds=metric_kwds,
        )
        expansion = 10.0 / np.abs(initialisation).max()
        embedding = (initialisation * expansion).astype(
            np.float32
        ) + random_state.normal(
            scale=0.0001, size=[graph.shape[0], n_components]
        ).astype(
            np.float32
        )
    else:
        init_data = np.array(init)
        if len(init_data.shape) == 2:
            if np.unique(init_data, axis=0).shape[0] < init_data.shape[0]:
                tree = KDTree(init_data)
                dist, ind = tree.query(init_data, k=2)
                nndist = np.mean(dist[:, 1])
                embedding = init_data + np.random.normal(
                    scale=0.001 * nndist, size=init_data.shape
                ).astype(np.float32)
            else:
                embedding = init_data

    epochs_per_sample = make_epochs_per_sample(graph.data, n_epochs)

    head = graph.row
    tail = graph.col

    rng_state = random_state.randint(INT32_MIN, INT32_MAX, 3).astype(np.int64)
    embedding = optimize_layout(
        embedding,
        embedding,
        head,
        tail,
        n_epochs,
        n_vertices,
        epochs_per_sample,
        a,
        b,
        rng_state,
        gamma,
        initial_alpha,
        negative_sample_rate,
        verbose=verbose,
    )

    return embedding