# Pre-processing for UMAP and t-SNE

        sc.settings.set_figure_params(dpi=200, facecolor="white")
        # Normalizing to median total counts
        sc.pp.normalize_total(adata)
        # Logarithmize the data
        sc.pp.log1p(adata)

        # feature selection
        n_valid = adata.X.shape[1]
        sc.pp.highly_variable_genes(adata, n_top_genes=min(2000, n_valid))
        # dimensionality Reduction
        sc.tl.pca(adata)
        # nearest neighbor graph constuction and visualization
        sc.pp.neighbors(adata)
        # UMAP
        sc.tl.umap(adata)

        # clustering
        # Using the igraph implementation and a fixed number of iterations can be significantly faster, especially for larger datasets
        sc.tl.leiden(adata, flavor="igraph", n_iterations=2)

        n_cells = adata.n_obs
        perplexity = min(30, max(2, (n_cells - 1) // 3))

        # t-SNE
        sc.tl.tsne(adata, perplexity=perplexity)

        # Create a Plotly-based UMAP scatter plot with Leiden clusters
        umap_df = pd.DataFrame(adata.obsm["X_umap"], columns=["UMAP1", "UMAP2"])
        umap_df["leiden"] = adata.obs["leiden"].values

        # UMAP in plotly
        opacity = 0.7
        # modify dot size
        dot_size = 3
        fig_umap = px.scatter(
            umap_df,
            x="UMAP1",
            y="UMAP2",
            color="leiden",
            title="UMAP with Leiden Clusters (Retained Cells Only)",
            width=width,
            height=height,
            opacity=opacity,
        ).update_traces(marker={"size": dot_size})  # Set the dot size

        # Center title and reduce margin
        fig_umap.update_layout(title_x=0.5, margin={"t": 30, "l": 10, "r": 10, "b": 20})

        # t-SNE plot in plotly
        tsne_df = pd.DataFrame(adata.obsm["X_tsne"], columns=["TSNE1", "TSNE2"])
        tsne_df["leiden"] = adata.obs["leiden"].values

        fig_tsne = px.scatter(
            tsne_df,
            x="TSNE1",
            y="TSNE2",
            color="leiden",
            title="t-SNE with Leiden Clusters (Retained Cells Only)",
            width=480,
            height=360,
            opacity=0.7,
        ).update_traces(marker={"size": 3})