def visualize_hierarchy(
    topic_model,
    orientation: str = "left",
    topics: List[int] = None,
    top_n_topics: int = None,
    use_ctfidf: bool = True,
    custom_labels: Union[bool, str] = False,
    title: str = "<b>Hierarchical Clustering</b>",
    width: int = 1000,
    height: int = 600,
    hierarchical_topics: pd.DataFrame = None,
    linkage_function: Callable[[csr_matrix], np.ndarray] = None,
    distance_function: Callable[[csr_matrix], csr_matrix] = None,
    color_threshold: int = 1,
) -> go.Figure:
    """Visualize a hierarchical structure of the topics.

    A ward linkage function is used to perform the
    hierarchical clustering based on the cosine distance
    matrix between topic embeddings (either c-TF-IDF or the embeddings from the embedding model).

    Arguments:
        topic_model: A fitted BERTopic instance.
        orientation: The orientation of the figure.
                     Either 'left' or 'bottom'
        topics: A selection of topics to visualize
        top_n_topics: Only select the top n most frequent topics
        use_ctfidf: Whether to calculate distances between topics based on c-TF-IDF embeddings. If False, the embeddings
                    from the embedding model are used.
        custom_labels: If bool, whether to use custom topic labels that were defined using
                       `topic_model.set_topic_labels`.
                       If `str`, it uses labels from other aspects, e.g., "Aspect1".
                       NOTE: Custom labels are only generated for the original
                       un-merged topics.
        title: Title of the plot.
        width: The width of the figure. Only works if orientation is set to 'left'
        height: The height of the figure. Only works if orientation is set to 'bottom'
        hierarchical_topics: A dataframe that contains a hierarchy of topics
                             represented by their parents and their children.
                             NOTE: The hierarchical topic names are only visualized
                             if both `topics` and `top_n_topics` are not set.
        linkage_function: The linkage function to use. Default is:
                          `lambda x: sch.linkage(x, 'ward', optimal_ordering=True)`
                          NOTE: Make sure to use the same `linkage_function` as used
                          in `topic_model.hierarchical_topics`.
        distance_function: The distance function to use on the c-TF-IDF matrix. Default is:
                           `lambda x: 1 - cosine_similarity(x)`.
                            You can pass any function that returns either a square matrix of
                            shape (n_samples, n_samples) with zeros on the diagonal and
                            non-negative values or condensed distance matrix of shape
                            (n_samples * (n_samples - 1) / 2,) containing the upper
                            triangular of the distance matrix.
                           NOTE: Make sure to use the same `distance_function` as used
                           in `topic_model.hierarchical_topics`.
        color_threshold: Value at which the separation of clusters will be made which
                         will result in different colors for different clusters.
                         A higher value will typically lead in less colored clusters.

    Returns:
        fig: A plotly figure

    Examples:
    To visualize the hierarchical structure of
    topics simply run:

    ```python
    topic_model.visualize_hierarchy()
    ```

    If you also want the labels visualized of hierarchical topics,
    run the following:

    ```python
    # Extract hierarchical topics and their representations
    hierarchical_topics = topic_model.hierarchical_topics(docs)

    # Visualize these representations
    topic_model.visualize_hierarchy(hierarchical_topics=hierarchical_topics)
    ```

    If you want to save the resulting figure:

    ```python
    fig = topic_model.visualize_hierarchy()
    fig.write_html("path/to/file.html")
    ```
    <iframe src="../../getting_started/visualization/hierarchy.html"
    style="width:1000px; height: 680px; border: 0px;""></iframe>
    """
    if distance_function is None:
        distance_function = lambda x: 1 - cosine_similarity(x)

    if linkage_function is None:
        linkage_function = lambda x: sch.linkage(x, "ward", optimal_ordering=True)

    # Select topics based on top_n and topics args
    freq_df = topic_model.get_topic_freq()
    freq_df = freq_df.loc[freq_df.Topic != -1, :]
    if topics is not None:
        topics = list(topics)
    elif top_n_topics is not None:
        topics = sorted(freq_df.Topic.to_list()[:top_n_topics])
    else:
        topics = sorted(freq_df.Topic.to_list())

    # Select embeddings
    all_topics = sorted(list(topic_model.get_topics().keys()))
    indices = np.array([all_topics.index(topic) for topic in topics])

    # Select topic embeddings
    embeddings = select_topic_representation(topic_model.c_tf_idf_, topic_model.topic_embeddings_, use_ctfidf)[0][
        indices
    ]

    # Annotations
    if hierarchical_topics is not None and len(topics) == len(freq_df.Topic.to_list()):
        annotations = _get_annotations(
            topic_model=topic_model,
            hierarchical_topics=hierarchical_topics,
            embeddings=embeddings,
            distance_function=distance_function,
            linkage_function=linkage_function,
            orientation=orientation,
            custom_labels=custom_labels,
        )
    else:
        annotations = None

    # wrap distance function to validate input and return a condensed distance matrix
    distance_function_viz = lambda x: validate_distance_matrix(distance_function(x), embeddings.shape[0])
    # Create dendogram
    fig = ff.create_dendrogram(
        embeddings,
        orientation=orientation,
        distfun=distance_function_viz,
        linkagefun=linkage_function,
        hovertext=annotations,
        color_threshold=color_threshold,
    )

    # Create nicer labels
    axis = "yaxis" if orientation == "left" else "xaxis"
    if isinstance(custom_labels, str):
        new_labels = [
            [[str(x), None]] + topic_model.topic_aspects_[custom_labels][x] for x in fig.layout[axis]["ticktext"]
        ]
        new_labels = ["_".join([label[0] for label in labels[:4]]) for labels in new_labels]
        new_labels = [label if len(label) < 30 else label[:27] + "..." for label in new_labels]
    elif topic_model.custom_labels_ is not None and custom_labels:
        new_labels = [
            topic_model.custom_labels_[topics[int(x)] + topic_model._outliers] for x in fig.layout[axis]["ticktext"]
        ]
    else:
        new_labels = [
            [[str(topics[int(x)]), None]] + topic_model.get_topic(topics[int(x)]) for x in fig.layout[axis]["ticktext"]
        ]
        new_labels = ["_".join([label[0] for label in labels[:4]]) for labels in new_labels]
        new_labels = [label if len(label) < 30 else label[:27] + "..." for label in new_labels]

    # Stylize layout
    fig.update_layout(
        plot_bgcolor="#ECEFF1",
        template="plotly_white",
        title={
            "text": f"{title}",
            "x": 0.5,
            "xanchor": "center",
            "yanchor": "top",
            "font": dict(size=22, color="Black"),
        },
        hoverlabel=dict(bgcolor="white", font_size=16, font_family="Rockwell"),
    )

    # Stylize orientation
    if orientation == "left":
        fig.update_layout(
            height=200 + (15 * len(topics)),
            width=width,
            yaxis=dict(tickmode="array", ticktext=new_labels),
        )

        # Fix empty space on the bottom of the graph
        y_max = max([trace["y"].max() + 5 for trace in fig["data"]])
        y_min = min([trace["y"].min() - 5 for trace in fig["data"]])
        fig.update_layout(yaxis=dict(range=[y_min, y_max]))

    else:
        fig.update_layout(
            width=200 + (15 * len(topics)),
            height=height,
            xaxis=dict(tickmode="array", ticktext=new_labels),
        )

    if hierarchical_topics is not None:
        for index in [0, 3]:
            axis = "x" if orientation == "left" else "y"
            xs = [data["x"][index] for data in fig.data if (data["text"] and data[axis][index] > 0)]
            ys = [data["y"][index] for data in fig.data if (data["text"] and data[axis][index] > 0)]
            hovertext = [data["text"][index] for data in fig.data if (data["text"] and data[axis][index] > 0)]

            fig.add_trace(
                go.Scatter(
                    x=xs,
                    y=ys,
                    marker_color="black",
                    hovertext=hovertext,
                    hoverinfo="text",
                    mode="markers",
                    showlegend=False,
                )
            )
    return fig
Visualize a hierarchical structure of the topics.

    A ward linkage function is used to perform the
    hierarchical clustering based on the cosine distance
    matrix between topic embeddings (either c-TF-IDF or the embeddings from the embedding model).

    Arguments:
        topic_model: A fitted BERTopic instance.
        orientation: The orientation of the figure.
                     Either 'left' or 'bottom'
        topics: A selection of topics to visualize
        top_n_topics: Only select the top n most frequent topics
        use_ctfidf: Whether to calculate distances between topics based on c-TF-IDF embeddings. If False, the embeddings
                    from the embedding model are used.
        custom_labels: If bool, whether to use custom topic labels that were defined using
                       `topic_model.set_topic_labels`.
                       If `str`, it uses labels from other aspects, e.g., "Aspect1".
                       NOTE: Custom labels are only generated for the original
                       un-merged topics.
        title: Title of the plot.
        width: The width of the figure. Only works if orientation is set to 'left'
        height: The height of the figure. Only works if orientation is set to 'bottom'
        hierarchical_topics: A dataframe that contains a hierarchy of topics
                             represented by their parents and their children.
                             NOTE: The hierarchical topic names are only visualized
                             if both `topics` and `top_n_topics` are not set.
        linkage_function: The linkage function to use. Default is:
                          `lambda x: sch.linkage(x, 'ward', optimal_ordering=True)`
                          NOTE: Make sure to use the same `linkage_function` as used
                          in `topic_model.hierarchical_topics`.
        distance_function: The distance function to use on the c-TF-IDF matrix. Default is:
                           `lambda x: 1 - cosine_similarity(x)`.
                            You can pass any function that returns either a square matrix of
                            shape (n_samples, n_samples) with zeros on the diagonal and
                            non-negative values or condensed distance matrix of shape
                            (n_samples * (n_samples - 1) / 2,) containing the upper
                            triangular of the distance matrix.
                           NOTE: Make sure to use the same `distance_function` as used
                           in `topic_model.hierarchical_topics`.
        color_threshold: Value at which the separation of clusters will be made which
                         will result in different colors for different clusters.
                         A higher value will typically lead in less colored clusters.

    Returns:
        fig: A plotly figure

    Examples:
    To visualize the hierarchical structure of
    topics simply run:

    ```python
    topic_model.visualize_hierarchy()
    ```

    If you also want the labels visualized of hierarchical topics,
    run the following:

    ```python
    # Extract hierarchical topics and their representations
    hierarchical_topics = topic_model.hierarchical_topics(docs)

    # Visualize these representations
    topic_model.visualize_hierarchy(hierarchical_topics=hierarchical_topics)
    ```

    If you want to save the resulting figure:

    ```python
    fig = topic_model.visualize_hierarchy()
    fig.write_html("path/to/file.html")
    ```
    <iframe src="../../getting_started/visualization/hierarchy.html"
    style="width:1000px; height: 680px; border: 0px;""></iframe>
    
bertopic/plotting/_hierarchy.py