multi_modal_figures

multi_modal_figures

Plotly figure builders for the multi-modal evaluation report.

Functions:

Name	Description
degree_to_radian	Convert degrees to radians.
gauge_chart	Render a semicircular gauge chart for a single evaluation score.
pie	Create a pie chart with privacy-grade color mapping.
scatter	Create a scatter trace for overlay plots.
histogram	Create a histogram trace for distribution plots.
get_auto_bins	Get common bin edges for the training and synthetic principal components.
generate_mia_figure	Generate a pie chart summarizing membership inference attack results.
generate_aia_figure	Generate a horizontal bar chart of per-column attribute inference risk.
correlation_heatmap	Generate a heatmap figure for a correlation matrix.
generate_combined_correlation_figure	Combine reference, output, and difference correlation heatmaps into one row.
scatter_plot	Create a scatter plot, capping the number of points to avoid browser crashes.
structure_stability_figure	Generate side-by-side PCA scatter plots for reference and output data.
combine_subplots	Combine multiple Plotly figures into a single-row subplot figure.
bar_chart	Generate a grouped bar chart comparing two categorical distributions.
histogram_figure	Generate overlaid histograms for a numeric distribution.
generate_text_structure_similarity_figures	Generate overlaid histograms of sentence/word/character distributions.
generate_text_semantic_similarity_figures	Generate a PCA scatter matrix for text embedding similarity.

degree_to_radian(degrees)

Convert degrees to radians.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def degree_to_radian(degrees):
    """Convert degrees to radians."""
    return degrees * pi / 180

gauge_chart(evaluation_score, degree_start=210, degree_end=-30, min=False, dps=False)

Render a semicircular gauge chart for a single evaluation score.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def gauge_chart(evaluation_score: EvaluationScore, degree_start=210, degree_end=-30, min=False, dps=False) -> go.Figure:
    """Render a semicircular gauge chart for a single evaluation score."""
    if isinstance(evaluation_score.grade, PrivacyGrade):
        dps = True

    radian_start = degree_to_radian(degree_start)
    radian_end = degree_to_radian(degree_end)

    fig = go.Figure()

    color = GRAPH_BACKGROUND_COLOR
    value = radian_start
    text = "--"

    if evaluation_score.score is not None:
        if dps:
            color = _REPORT_PALETTE[1]
        else:
            color = _REPORT_PALETTE[0]
        value = degree_to_radian(evaluation_score.score * (degree_end - degree_start) / 10 + degree_start)
        text = evaluation_score.score

    non_filled = np.linspace(value, radian_end, 200)

    # Draw non-filled part
    fig.add_trace(
        go.Scatter(
            x=cos(non_filled),
            y=sin(non_filled),
            mode="markers",
            marker_symbol="circle",
            marker_size=25 if not min else 10,
            marker=dict(color=GRAPH_BACKGROUND_COLOR),
            showlegend=False,
        )
    )
    if evaluation_score.score is not None:
        filled = np.linspace(radian_start, value, 200)

        # Draw filled part
        fig.add_trace(
            go.Scatter(
                x=cos(filled),
                y=sin(filled),
                mode="markers",
                marker_symbol="circle",
                marker_size=25 if not min else 10,
                marker=dict(
                    line=dict(color=color, width=1),
                    color=color,
                ),
                showlegend=False,
            )
        )

    fig.add_trace(
        go.Scatter(
            x=[0],
            y=[-0.05],
            mode="text",
            text=text,
            textfont=dict(color=color, size=55 if not min else 20),
            textposition="middle center",
            showlegend=False,
        )
    )

    fig.update_layout(
        margin=dict(l=0, r=0, t=0, b=0),
        xaxis_range=[-1.3, 1.3],
        yaxis_range=[-1, 1.3],
        xaxis_visible=False,
        xaxis_showticklabels=False,
        yaxis_visible=False,
        yaxis_showticklabels=False,
        template="plotly_white",
        width=215 if not min else 90,
        height=180 if not min else 75,
        xaxis_fixedrange=True,
        yaxis_fixedrange=True,
        hovermode=False,
    )

    return fig

pie(labels, values, textinfo='label+percent', sort=True)

Create a pie chart with privacy-grade color mapping.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def pie(
    labels: list[str],
    values: pd.Series,
    textinfo: str = "label+percent",
    sort: bool = True,
) -> go.Figure:
    """Create a pie chart with privacy-grade color mapping."""
    return go.Figure(
        data=[
            go.Pie(
                labels=labels,
                values=values,
                textinfo=textinfo,
                insidetextorientation="radial",
                marker=dict(
                    colors=[
                        INFERENCE_ATTACK_VALUES_FOR_GRAPHS[label] for label in labels if label not in [None, np.nan]
                    ]
                ),
                sort=sort,
                hovertemplate="%{label}<br>%{percent}<extra></extra>",
            )
        ]
    )

scatter(x, y, mode='markers', color=_REPORT_PALETTE[0], name='Reference')

Create a scatter trace for overlay plots.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def scatter(
    x: pd.Series,
    y: pd.Series,
    mode: str = "markers",
    color: str = _REPORT_PALETTE[0],
    name: str = "Reference",
) -> go.Scatter:
    """Create a scatter trace for overlay plots."""
    return go.Scatter(
        x=x,
        y=y,
        mode=mode,
        marker=dict(
            showscale=False,
            line=dict(width=0.5, color=color),
            color=color,
        ),
        opacity=0.7,
        name=name,
    )

histogram(x, color=_REPORT_PALETTE[0], name='Reference', **kwargs)

Create a histogram trace for distribution plots.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def histogram(
    x: pd.Series,
    color: str = _REPORT_PALETTE[0],
    name: str = "Reference",
    **kwargs,
) -> go.Histogram:
    """Create a histogram trace for distribution plots."""
    return go.Histogram(
        x=x,
        marker=dict(
            showscale=False,
            line=dict(width=0.5, color=color),
            color=color,
        ),
        name=name,
        opacity=0.7,
        showlegend=False,
        **kwargs,
    )

get_auto_bins(x1, x2)

Get common bin edges for the training and synthetic principal components.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def get_auto_bins(x1: pd.Series, x2: pd.Series) -> dict:
    """Get common bin edges for the training and synthetic principal components."""
    data = pd.concat([x1, x2]).to_numpy()
    edges = np.histogram_bin_edges(data, bins="auto")

    # Bin start, end, and size
    start = edges[0]
    end = edges[-1]
    bin_size = edges[1] - edges[0]

    return dict(start=start, end=end, size=bin_size)

generate_mia_figure(df)

Generate a pie chart summarizing membership inference attack results.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def generate_mia_figure(df: pd.DataFrame) -> go.Figure:
    """Generate a pie chart summarizing membership inference attack results."""
    # Done for legend ordering
    PROTECTION_COLUMN = "Protection"
    df[PROTECTION_COLUMN] = df[PROTECTION_COLUMN].astype("category")
    df[PROTECTION_COLUMN] = df[PROTECTION_COLUMN].cat.set_categories(
        [grade.value for grade in PrivacyGrade if grade.value != "Unavailable"], ordered=True
    )
    df.sort_values(by=PROTECTION_COLUMN, inplace=True, ascending=False)

    fig = pie(
        labels=cast(list[str], df[PROTECTION_COLUMN].dropna().astype(str).tolist()),
        values=df["Attack Percentage"].replace({0: np.nan}),
        sort=False,
    )
    fig.update_layout(
        margin=dict(l=0, r=0, t=24, b=0),
    )

    return fig

generate_aia_figure(df)

Generate a horizontal bar chart of per-column attribute inference risk.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def generate_aia_figure(df: pd.DataFrame) -> go.Figure:
    """Generate a horizontal bar chart of per-column attribute inference risk."""
    fig = go.Figure()
    df.sort_values(by="Risk", inplace=True, ascending=True)
    for grade in PrivacyGrade:
        if grade.value == "Unavailable":
            continue
        filtered_df = df.query(f"Protection == '{grade.value}'")
        bar = go.Bar(
            x=filtered_df["Risk"],
            y=filtered_df["Column"],
            orientation="h",
            marker=dict(color=[INFERENCE_ATTACK_VALUES_FOR_GRAPHS[grade.value]] * filtered_df.shape[0]),
            width=0.3,
            showlegend=True,
            name=grade.value,
        )

        scatter = go.Scatter(
            x=df["Risk"],
            y=df["Column"],
            mode="markers",
            marker=dict(
                color="rgb(124, 135, 233)",
                size=10,
                line=dict(width=2, color=INFERENCE_ATTACK_VALUES_FOR_GRAPHS[grade.value]),
            ),
            showlegend=False,
            hoverinfo="none",
        )
        fig.add_trace(bar)
        fig.add_trace(scatter)

    fig.update_xaxes(title_text="Protection", range=[0, 11])
    fig.update_yaxes(title_text="Column", range=[-1, df.shape[0]])
    fig.update_layout(
        legend_traceorder="reversed",
        height=35 * df.shape[0] + 200,
        width=900,
        margin=dict(l=0, r=0, t=24, b=0),
    )

    return fig

correlation_heatmap(matrix, name='Correlation')

Generate a heatmap figure for a correlation matrix.

Parameters:

Name	Type	Description	Default
matrix	DataFrame	Correlation matrix (columns are truncated to 15 chars for display).	required
name	str	Trace name used in the legend.	'Correlation'

Returns:

Type	Description
Figure	A Plotly Figure containing a single heatmap trace.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def correlation_heatmap(matrix: pd.DataFrame, name: str = "Correlation") -> go.Figure:
    """Generate a heatmap figure for a correlation matrix.

    Args:
        matrix: Correlation matrix (columns are truncated to 15 chars for display).
        name: Trace name used in the legend.

    Returns:
        A Plotly ``Figure`` containing a single heatmap trace.
    """
    fig = go.Figure()
    fields = [x if len(x) <= 15 else x[0:14] + "..." for x in matrix.columns]
    fig.add_trace(
        go.Heatmap(
            z=matrix,
            y=fields,
            x=fields,
            xgap=1,
            ygap=1,
            coloraxis="coloraxis",
            name=name,
        )
    )
    fig.update_layout(
        coloraxis=dict(
            colorscale=[
                [0.0, "#E8F3C6"],
                [0.25, "#94E2BA"],
                [0.5, "#31B8C0"],
                [0.75, "#4F78B3"],
                [1.0, "#76137F"],
            ],
            cmax=1.0,
            cmin=0,
        ),
        showlegend=False,
        xaxis=dict(visible=False),
        yaxis=dict(visible=False),
        margin=dict(l=6, r=6, t=24, b=12),
    )
    fig.update_yaxes(dtick=1)
    return fig

generate_combined_correlation_figure(reference_correlation, output_correlation, correlation_difference)

Combine reference, output, and difference correlation heatmaps into one row.

Parameters:

Name	Type	Description	Default
reference_correlation	DataFrame	Correlation matrix of the reference data.	required
output_correlation	DataFrame	Correlation matrix of the output data.	required
correlation_difference	DataFrame	Element-wise absolute difference matrix.	required

Returns:

Type	Description
Figure	A Plotly Figure with three side-by-side heatmap subplots.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def generate_combined_correlation_figure(
    reference_correlation: pd.DataFrame,
    output_correlation: pd.DataFrame,
    correlation_difference: pd.DataFrame,
) -> go.Figure:
    """Combine reference, output, and difference correlation heatmaps into one row.

    Args:
        reference_correlation: Correlation matrix of the reference data.
        output_correlation: Correlation matrix of the output data.
        correlation_difference: Element-wise absolute difference matrix.

    Returns:
        A Plotly ``Figure`` with three side-by-side heatmap subplots.
    """
    hovertext = _generate_correlation_hovertext(reference_correlation, output_correlation, correlation_difference)

    reference_correlation_figure = correlation_heatmap(reference_correlation, "Reference Correlations")
    output_correlation_figure = correlation_heatmap(output_correlation, "Output Correlations")
    correlation_difference_figure = correlation_heatmap(correlation_difference, "Difference of Correlations")

    fig = combine_subplots(
        figures=[
            reference_correlation_figure,
            output_correlation_figure,
            correlation_difference_figure,
        ],
        titles=[
            "Reference Correlations",
            "Output Correlations",
            "Correlation Difference",
        ],
    )

    fig.update_traces(hoverinfo="text", text=hovertext)

    fig.update_traces(yaxis="y1")

    fig.update_xaxes(visible=False, showticklabels=False, row=1, col=1)
    fig.update_xaxes(visible=False, showticklabels=False, row=1, col=2)
    fig.update_xaxes(visible=False, showticklabels=False, row=1, col=3)
    fig.update_yaxes(visible=False, showticklabels=False, row=1, col=1)

    fig.update_layout(height=400, width=900)

    return fig

scatter_plot(x, y, color=_REPORT_PALETTE[0], maximum_points=5000)

Create a scatter plot, capping the number of points to avoid browser crashes.

Parameters:

Name	Type	Description	Default
x	Series	Series of x-axis values.	required
y	Series	Series of y-axis values.	required
color		Marker color (defaults to the first palette color).	_REPORT_PALETTE[0]
maximum_points		Maximum number of points to render. 0 disables the cap (use with caution -- may crash the browser).	5000

Returns:

Type	Description
Figure	A Plotly Figure with a single scatter trace.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def scatter_plot(x: pd.Series, y: pd.Series, color=_REPORT_PALETTE[0], maximum_points=5000) -> go.Figure:
    """Create a scatter plot, capping the number of points to avoid browser crashes.

    Args:
        x: Series of x-axis values.
        y: Series of y-axis values.
        color: Marker color (defaults to the first palette color).
        maximum_points: Maximum number of points to render. ``0`` disables
            the cap (use with caution -- may crash the browser).

    Returns:
        A Plotly ``Figure`` with a single scatter trace.
    """
    # Sample training set to equal synthetic set or vice versa
    if maximum_points == 0:
        sample_size = min(len(x), len(y))
    else:
        sample_size = min(len(x), len(y), maximum_points)
    if len(x) > sample_size:
        x = x.sample(n=sample_size, random_state=777)
    if len(y) > sample_size:
        y = y.sample(n=sample_size, random_state=777)

    fig = go.Figure()
    fig.add_trace(
        go.Scatter(x=x, y=y, mode="markers", marker=dict(size=2, color=color), showlegend=False),
    )

    fig.update_xaxes(matches="x")
    fig.update_yaxes(matches="y")
    fig.update_layout(hovermode=False)

    return fig

structure_stability_figure(reference, output)

Generate side-by-side PCA scatter plots for reference and output data.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def structure_stability_figure(reference: pd.DataFrame, output: pd.DataFrame) -> go.Figure:
    """Generate side-by-side PCA scatter plots for reference and output data."""
    reference_scatter = scatter_plot(x=reference["pc1"], y=reference["pc2"])
    output_scatter = scatter_plot(x=output["pc1"], y=output["pc2"], color=_REPORT_PALETTE[1])
    fig = combine_subplots(
        figures=[reference_scatter, output_scatter],
        titles=["Reference Data", "Output Data"],
    )

    fig.update_layout(
        height=420,
        width=900,
        margin=dict(l=6, r=6, t=24, b=12),
    )
    fig.update_xaxes(title_text="pc1", row=1, col=1)
    fig.update_xaxes(title_text="pc1", row=1, col=2)
    fig.update_yaxes(title_text="pc2", row=1, col=1)
    fig.update_xaxes(matches="x")
    fig.update_yaxes(matches="y")

    return fig

combine_subplots(figures, titles=None, general_title=None, subplot_type='xy', shared_xaxes=True, shared_yaxes=True, height=None, margin=None)

Combine multiple Plotly figures into a single-row subplot figure.

Parameters:

Name	Type	Description	Default
figures	list[Figure]	Figures to combine (one subplot column each).	required
titles	list[str] | None	Per-subplot titles (same length as figures).	None
general_title	str | None	Overall figure title.	None
subplot_type	str	Plotly subplot type (e.g. "xy", "domain").	'xy'
shared_xaxes		Share x-axes across subplots.	True
shared_yaxes		Share y-axes across subplots.	True
height		Optional explicit figure height in pixels.	None
margin		Optional margin dict passed to update_layout.	None

Returns:

Type	Description
Figure	A single Plotly Figure containing all traces in one row.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def combine_subplots(
    figures: list[go.Figure],
    titles: list[str] | None = None,
    general_title: str | None = None,
    subplot_type: str = "xy",
    shared_xaxes=True,
    shared_yaxes=True,
    height=None,
    margin=None,
) -> go.Figure:
    """Combine multiple Plotly figures into a single-row subplot figure.

    Args:
        figures: Figures to combine (one subplot column each).
        titles: Per-subplot titles (same length as ``figures``).
        general_title: Overall figure title.
        subplot_type: Plotly subplot type (e.g. ``"xy"``, ``"domain"``).
        shared_xaxes: Share x-axes across subplots.
        shared_yaxes: Share y-axes across subplots.
        height: Optional explicit figure height in pixels.
        margin: Optional margin dict passed to ``update_layout``.

    Returns:
        A single Plotly ``Figure`` containing all traces in one row.
    """
    specs = [[{"type": subplot_type}] * len(figures)]

    fig = make_subplots(
        rows=1,
        cols=len(figures),
        specs=specs,
        shared_xaxes=shared_xaxes,
        shared_yaxes=shared_yaxes,
        subplot_titles=titles,
    )
    for i, f in enumerate(figures):
        for t in f.select_traces():
            fig.add_trace(trace=t, row=1, col=i + 1)
    # This is surprisingly expensive. We only need the last layout, though,
    # as long as all the subplots are of the same "type"
    # (used to update with every subfig layout).
    fig.layout.update(figures[-1].layout)
    if general_title:
        fig.update_layout(title_text="<b>" + general_title + "</b>")
    if height:
        fig.update_layout(height=height)
    if margin:
        fig.update_layout(margin=margin)

    return fig

bar_chart(reference_distribution, output_distribution)

Generate a grouped bar chart comparing two categorical distributions.

Parameters:

Name	Type	Description	Default
reference_distribution	dict	Mapping of {category: percentage} from the reference data.	required
output_distribution	dict	Mapping of {category: percentage} from the output data.	required

Returns:

Type	Description
Figure	A Plotly Figure with grouped bars for reference and output.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def bar_chart(reference_distribution: dict, output_distribution: dict) -> go.Figure:
    """Generate a grouped bar chart comparing two categorical distributions.

    Args:
        reference_distribution: Mapping of ``{category: percentage}`` from the reference data.
        output_distribution: Mapping of ``{category: percentage}`` from the output data.

    Returns:
        A Plotly ``Figure`` with grouped bars for reference and output.
    """
    columns = sorted(set(reference_distribution.keys()).union(output_distribution.keys()))
    reference_values = []
    output_values = []

    for column in columns:
        reference_values.append(reference_distribution.get(column, 0.0))
        output_values.append(output_distribution.get(column, 0.0))

    fig = go.Figure()
    fig.add_trace(
        go.Bar(
            x=columns,
            y=reference_values,
            name="Reference",
            marker=dict(color=_REPORT_PALETTE[0]),
            opacity=0.7,
            width=[] if len(columns) < 60 else [len(columns) / 150] * len(columns),
            hovertemplate="(%{x}, %{y:.2f})",
        )
    )
    fig.add_trace(
        go.Bar(
            x=columns,
            y=output_values,
            name="Output",
            marker=dict(color=_REPORT_PALETTE[1]),
            opacity=0.7,
            width=[] if len(columns) < 60 else [len(columns) / 150] * len(columns),
            hovertemplate="(%{x}, %{y:.2f})",
        )
    )
    fig.update_layout(
        yaxis_title_text="Percentage",
        bargap=_GRAPH_BARGAP,
        bargroupgap=_GRAPH_BARGROUPGAP,
        barmode="group",
        showlegend=False,
    )

    return fig

histogram_figure(reference, output)

Generate overlaid histograms for a numeric distribution.

Parameters:

Name	Type	Description	Default
reference	Series	Numeric reference series.	required
output	Series	Numeric output series.	required

Returns:

Type	Description
Figure | None	A Plotly Figure with overlaid reference/output histograms.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def histogram_figure(reference: pd.Series, output: pd.Series) -> go.Figure | None:
    """Generate overlaid histograms for a numeric distribution.

    Args:
        reference: Numeric reference series.
        output: Numeric output series.

    Returns:
        A Plotly ``Figure`` with overlaid reference/output histograms.
    """
    fig = go.Figure()
    fig.update_layout(
        yaxis_title_text="Percentage",
        bargap=_GRAPH_BARGAP,
        bargroupgap=_GRAPH_BARGROUPGAP,
        showlegend=False,
    )

    reference_copy = pd.Series(reference)
    reference_copy.dropna(inplace=True)
    output_copy = pd.Series(output)
    output_copy.dropna(inplace=True)

    # Quantile, min and max will fail on empty Series. Fail fast and return empty fig.
    if len(reference_copy) == 0 or len(output_copy) == 0:
        return fig

    max_range = max(max(reference_copy), max(output_copy)) + 1
    min_range = min(min(reference_copy), min(output_copy))

    # Calculate bin size for the plot, handling edge case of no variance as needed.
    binsize = 1
    if min_range == max_range:
        max_range = min_range + binsize
    else:
        # number of bins/bin size match the ones in JS divenrgence calculation.
        bins = get_numeric_distribution_bins(reference, output)
        binsize = bins[1] - bins[0]

    xbins = dict(start=min_range, end=max_range, size=binsize)
    fig.add_trace(
        histogram(
            x=reference_copy,
            histnorm="percent",
            xbins=xbins,
            hovertemplate="(%{x}, %{y:.2f})",
        )
    ).add_trace(
        histogram(
            x=output_copy,
            color=_REPORT_PALETTE[1],
            name="Output",
            histnorm="percent",
            xbins=xbins,
            hovertemplate="(%{x}, %{y:.2f})",
        )
    )
    return fig

generate_text_structure_similarity_figures(training_statistics, synthetic_statistics, title)

Generate overlaid histograms of sentence/word/character distributions.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def generate_text_structure_similarity_figures(
    training_statistics: pd.DataFrame, synthetic_statistics: pd.DataFrame, title: str
) -> go.Figure | None:
    """Generate overlaid histograms of sentence/word/character distributions."""
    statistics_keys = [
        "sentence_count",
        "average_words_per_sentence",
        "average_characters_per_word",
    ]
    figures = []
    for key in statistics_keys:
        if training_statistics.per_record_statistics.empty or synthetic_statistics.per_record_statistics.empty:
            break
        figure = histogram_figure(
            training_statistics.per_record_statistics[key],
            synthetic_statistics.per_record_statistics[key],
        )
        figures.append(figure)
    if not figures:
        return None

    result = combine_subplots(
        figures,
        titles=[
            "Sentence Count",
            "Words Per Sentence",
            "Characters Per Word",
        ],
        height=400,
        general_title=title,
        shared_xaxes=False,
        shared_yaxes=False,
        margin=dict(l=0, r=0, t=64, b=0),
    )
    result.update_layout(
        legend=dict(orientation="h", yanchor="bottom", y=1.02, xanchor="right", x=1),
    )
    return result

generate_text_semantic_similarity_figures(training_pca, synthetic_pca, title)

Generate a PCA scatter matrix for text embedding similarity.

Source code in src/nemo_safe_synthesizer/evaluation/components/multi_modal_figures.py

def generate_text_semantic_similarity_figures(
    training_pca: pd.DataFrame, synthetic_pca: pd.DataFrame, title: str
) -> go.Figure | None:
    """Generate a PCA scatter matrix for text embedding similarity."""
    figures = []
    for key in training_pca.columns:
        for subkey in synthetic_pca.columns:
            if key != subkey and key == training_pca.columns[-1]:
                continue
            fig = go.Figure()

            if key != subkey:
                fig.add_trace(
                    scatter(
                        x=training_pca[key],
                        y=training_pca[subkey],
                    )
                ).add_trace(
                    scatter(
                        x=synthetic_pca[key],
                        y=synthetic_pca[subkey],
                        color=_REPORT_PALETTE[1],
                        name="Output",
                    )
                )
            else:
                common_bins = get_auto_bins(
                    x1=training_pca[key],
                    x2=synthetic_pca[subkey],
                )
                fig.add_trace(
                    histogram(
                        x=training_pca[key],
                        histnorm="probability density",
                        xbins=common_bins,
                    )
                ).add_trace(
                    histogram(
                        x=synthetic_pca[subkey],
                        color=_REPORT_PALETTE[1],
                        name="Output",
                        histnorm="probability density",
                        xbins=common_bins,
                    )
                )

                fig.update_layout(
                    bargap=0,
                    barmode="overlay",
                )
            figures.append(fig)
    if not figures:
        return None
    result = combine_subplots(
        figures,
        height=400,
        general_title=title,
        shared_xaxes=False,
        shared_yaxes=False,
        margin=dict(l=0, r=0, t=64, b=0),
    )
    for key in training_pca.columns:
        for subkey in synthetic_pca.columns:
            if key != subkey and key == synthetic_pca.columns[-1]:
                continue
            col = synthetic_pca.columns.get_loc(key) + synthetic_pca.columns.get_loc(subkey) + 1  # ty: ignore[unsupported-operator]
            result.update_xaxes(
                title_text=key,
                row=1,
                col=col,
            ).update_yaxes(
                title_text=subkey,
                row=1,
                col=col,
            )

    result.update_layout(
        legend=dict(orientation="h", yanchor="bottom", y=1.02, xanchor="right", x=1),
    )
    return result