import numpy as np import numba from warnings import warn try: import pandas as pd import datashader as ds import datashader.transfer_functions as tf import datashader.bundling as bd import matplotlib.pyplot as plt import colorcet import matplotlib.colors import matplotlib.cm import bokeh.plotting as bpl import bokeh.transform as btr import holoviews as hv import holoviews.operation.datashader as hd except ImportError: warn( """The umap.plot package requires extra plotting libraries to be installed. You can install these via pip using pip install umap-learn[plot] or via conda using conda install pandas matplotlib datashader bokeh holoviews colorcet scikit-image """ ) raise ImportError( "umap.plot requires pandas matplotlib datashader bokeh holoviews scikit-image and colorcet to be " "installed" ) from None import sklearn.decomposition import sklearn.cluster import sklearn.neighbors from matplotlib.patches import Patch from umap.utils import submatrix, average_nn_distance from bokeh.plotting import show as show_interactive from bokeh.plotting import output_file, output_notebook from bokeh.layouts import column from bokeh.models import CustomJS, TextInput from matplotlib.pyplot import show as show_static from warnings import warn fire_cmap = matplotlib.colors.LinearSegmentedColormap.from_list("fire", colorcet.fire) darkblue_cmap = matplotlib.colors.LinearSegmentedColormap.from_list( "darkblue", colorcet.kbc ) darkgreen_cmap = matplotlib.colors.LinearSegmentedColormap.from_list( "darkgreen", colorcet.kgy ) darkred_cmap = matplotlib.colors.LinearSegmentedColormap.from_list( "darkred", colors=colorcet.linear_kry_5_95_c72[:192], N=256 ) darkpurple_cmap = matplotlib.colors.LinearSegmentedColormap.from_list( "darkpurple", colorcet.linear_bmw_5_95_c89 ) plt.register_cmap("fire", fire_cmap) plt.register_cmap("darkblue", darkblue_cmap) plt.register_cmap("darkgreen", darkgreen_cmap) plt.register_cmap("darkred", darkred_cmap) plt.register_cmap("darkpurple", darkpurple_cmap) def _to_hex(arr): return [matplotlib.colors.to_hex(c) for c in arr] @numba.vectorize(["uint8(uint32)", "uint8(uint32)"]) def _red(x): return (x & 0xFF0000) >> 16 @numba.vectorize(["uint8(uint32)", "uint8(uint32)"]) def _green(x): return (x & 0x00FF00) >> 8 @numba.vectorize(["uint8(uint32)", "uint8(uint32)"]) def _blue(x): return x & 0x0000FF _themes = { "fire": { "cmap": "fire", "color_key_cmap": "rainbow", "background": "black", "edge_cmap": "fire", }, "viridis": { "cmap": "viridis", "color_key_cmap": "Spectral", "background": "black", "edge_cmap": "gray", }, "inferno": { "cmap": "inferno", "color_key_cmap": "Spectral", "background": "black", "edge_cmap": "gray", }, "blue": { "cmap": "Blues", "color_key_cmap": "tab20", "background": "white", "edge_cmap": "gray_r", }, "red": { "cmap": "Reds", "color_key_cmap": "tab20b", "background": "white", "edge_cmap": "gray_r", }, "green": { "cmap": "Greens", "color_key_cmap": "tab20c", "background": "white", "edge_cmap": "gray_r", }, "darkblue": { "cmap": "darkblue", "color_key_cmap": "rainbow", "background": "black", "edge_cmap": "darkred", }, "darkred": { "cmap": "darkred", "color_key_cmap": "rainbow", "background": "black", "edge_cmap": "darkblue", }, "darkgreen": { "cmap": "darkgreen", "color_key_cmap": "rainbow", "background": "black", "edge_cmap": "darkpurple", }, } _diagnostic_types = np.array(["pca", "ica", "vq", "local_dim", "neighborhood"]) def _get_embedding(umap_object): if hasattr(umap_object, "embedding_"): return umap_object.embedding_ elif hasattr(umap_object, "embedding"): return umap_object.embedding else: raise ValueError("Could not find embedding attribute of umap_object") def _get_metric(umap_object): if hasattr(umap_object, "metric"): return umap_object.metric else: # Assume euclidean if no attribute per cuML.UMAP return "euclidean" def _get_metric_kwds(umap_object): if hasattr(umap_object, "_metric_kwds"): return umap_object._metric_kwds else: # Assume no keywords exist return {} def _embed_datashader_in_an_axis(datashader_image, ax): img_rev = datashader_image.data[::-1] mpl_img = np.dstack([_blue(img_rev), _green(img_rev), _red(img_rev)]) ax.imshow(mpl_img) return ax def _nhood_search(umap_object, nhood_size): if hasattr(umap_object, "_small_data") and umap_object._small_data: dmat = sklearn.metrics.pairwise_distances(umap_object._raw_data) indices = np.argpartition(dmat, nhood_size)[:, :nhood_size] dmat_shortened = submatrix(dmat, indices, nhood_size) indices_sorted = np.argsort(dmat_shortened) indices = submatrix(indices, indices_sorted, nhood_size) dists = submatrix(dmat_shortened, indices_sorted, nhood_size) else: rng_state = np.empty(3, dtype=np.int64) indices, dists = umap_object._knn_search_index.query( umap_object._raw_data, k=nhood_size, ) return indices, dists @numba.jit() def _nhood_compare(indices_left, indices_right): """Compute Jaccard index of two neighborhoods""" result = np.empty(indices_left.shape[0]) for i in range(indices_left.shape[0]): intersection_size = np.intersect1d(indices_left[i], indices_right[i]).shape[0] union_size = np.unique(np.hstack([indices_left[i], indices_right[i]])).shape[0] result[i] = float(intersection_size) / float(union_size) return result def _get_extent(points): """Compute bounds on a space with appropriate padding""" min_x = np.nanmin(points[:, 0]) max_x = np.nanmax(points[:, 0]) min_y = np.nanmin(points[:, 1]) max_y = np.nanmax(points[:, 1]) extent = ( np.round(min_x - 0.05 * (max_x - min_x)), np.round(max_x + 0.05 * (max_x - min_x)), np.round(min_y - 0.05 * (max_y - min_y)), np.round(max_y + 0.05 * (max_y - min_y)), ) return extent def _select_font_color(background): if background == "black": font_color = "white" elif background.startswith("#"): mean_val = np.mean( [int("0x" + c) for c in (background[1:3], background[3:5], background[5:7])] ) if mean_val > 126: font_color = "black" else: font_color = "white" else: font_color = "black" return font_color def _datashade_points( points, ax=None, labels=None, values=None, cmap="Blues", color_key=None, color_key_cmap="Spectral", background="white", width=800, height=800, show_legend=True, alpha=255, ): """Use datashader to plot points""" extent = _get_extent(points) canvas = ds.Canvas( plot_width=width, plot_height=height, x_range=(extent[0], extent[1]), y_range=(extent[2], extent[3]), ) data = pd.DataFrame(points, columns=("x", "y")) legend_elements = None # Color by labels if labels is not None: if labels.shape[0] != points.shape[0]: raise ValueError( "Labels must have a label for " "each sample (size mismatch: {} {})".format( labels.shape[0], points.shape[0] ) ) data["label"] = pd.Categorical(labels) aggregation = canvas.points(data, "x", "y", agg=ds.count_cat("label")) if color_key is None and color_key_cmap is None: result = tf.shade(aggregation, how="eq_hist", alpha=alpha) elif color_key is None: unique_labels = np.unique(labels) num_labels = unique_labels.shape[0] color_key = _to_hex( plt.get_cmap(color_key_cmap)(np.linspace(0, 1, num_labels)) ) legend_elements = [ Patch(facecolor=color_key[i], label=k) for i, k in enumerate(unique_labels) ] result = tf.shade( aggregation, color_key=color_key, how="eq_hist", alpha=alpha ) else: legend_elements = [ Patch(facecolor=color_key[k], label=k) for k in color_key.keys() ] result = tf.shade( aggregation, color_key=color_key, how="eq_hist", alpha=alpha ) # Color by values elif values is not None: if values.shape[0] != points.shape[0]: raise ValueError( "Values must have a value for " "each sample (size mismatch: {} {})".format( values.shape[0], points.shape[0] ) ) unique_values = np.unique(values) if unique_values.shape[0] >= 256: min_val, max_val = np.min(values), np.max(values) bin_size = (max_val - min_val) / 255.0 data["val_cat"] = pd.Categorical( np.round((values - min_val) / bin_size).astype(np.int16) ) aggregation = canvas.points(data, "x", "y", agg=ds.count_cat("val_cat")) color_key = _to_hex(plt.get_cmap(cmap)(np.linspace(0, 1, 256))) result = tf.shade( aggregation, color_key=color_key, how="eq_hist", alpha=alpha ) else: data["val_cat"] = pd.Categorical(values) aggregation = canvas.points(data, "x", "y", agg=ds.count_cat("val_cat")) color_key_cols = _to_hex( plt.get_cmap(cmap)(np.linspace(0, 1, unique_values.shape[0])) ) color_key = dict(zip(unique_values, color_key_cols)) result = tf.shade( aggregation, color_key=color_key, how="eq_hist", alpha=alpha ) # Color by density (default datashader option) else: aggregation = canvas.points(data, "x", "y", agg=ds.count()) result = tf.shade(aggregation, cmap=plt.get_cmap(cmap), alpha=alpha) if background is not None: result = tf.set_background(result, background) if ax is not None: _embed_datashader_in_an_axis(result, ax) if show_legend and legend_elements is not None: ax.legend(handles=legend_elements) return ax else: return result def _matplotlib_points( points, ax=None, labels=None, values=None, cmap="Blues", color_key=None, color_key_cmap="Spectral", background="white", width=800, height=800, show_legend=True, alpha=None, ): """Use matplotlib to plot points""" point_size = 100.0 / np.sqrt(points.shape[0]) legend_elements = None if ax is None: dpi = plt.rcParams["figure.dpi"] fig = plt.figure(figsize=(width / dpi, height / dpi)) ax = fig.add_subplot(111) ax.set_facecolor(background) # Color by labels if labels is not None: if labels.shape[0] != points.shape[0]: raise ValueError( "Labels must have a label for " "each sample (size mismatch: {} {})".format( labels.shape[0], points.shape[0] ) ) if color_key is None: unique_labels = np.unique(labels) num_labels = unique_labels.shape[0] color_key = plt.get_cmap(color_key_cmap)(np.linspace(0, 1, num_labels)) legend_elements = [ Patch(facecolor=color_key[i], label=unique_labels[i]) for i, k in enumerate(unique_labels) ] if isinstance(color_key, dict): colors = pd.Series(labels).map(color_key) unique_labels = np.unique(labels) legend_elements = [ Patch(facecolor=color_key[k], label=k) for k in unique_labels ] else: unique_labels = np.unique(labels) if len(color_key) < unique_labels.shape[0]: raise ValueError( "Color key must have enough colors for the number of labels" ) new_color_key = { k: matplotlib.colors.to_hex(color_key[i]) for i, k in enumerate(unique_labels) } legend_elements = [ Patch(facecolor=color_key[i], label=k) for i, k in enumerate(unique_labels) ] colors = pd.Series(labels).map(new_color_key) ax.scatter(points[:, 0], points[:, 1], s=point_size, c=colors, alpha=alpha) # Color by values elif values is not None: if values.shape[0] != points.shape[0]: raise ValueError( "Values must have a value for " "each sample (size mismatch: {} {})".format( values.shape[0], points.shape[0] ) ) ax.scatter( points[:, 0], points[:, 1], s=point_size, c=values, cmap=cmap, alpha=alpha ) # No color (just pick the midpoint of the cmap) else: color = plt.get_cmap(cmap)(0.5) ax.scatter(points[:, 0], points[:, 1], s=point_size, c=color) if show_legend and legend_elements is not None: ax.legend(handles=legend_elements) return ax def show(plot_to_show): """Display a plot, either interactive or static. Parameters ---------- plot_to_show: Output of a plotting command (matplotlib axis or bokeh figure) The plot to show Returns ------- None """ if isinstance(plot_to_show, plt.Axes): show_static() elif isinstance(plot_to_show, bpl.Figure): show_interactive(plot_to_show) elif isinstance(plot_to_show, hv.core.spaces.DynamicMap): show_interactive(hv.render(plot_to_show), backend="bokeh") else: raise ValueError( "The type of ``plot_to_show`` was not valid, or not understood." ) def points( umap_object, labels=None, values=None, theme=None, cmap="Blues", color_key=None, color_key_cmap="Spectral", background="white", width=800, height=800, show_legend=True, subset_points=None, ax=None, alpha=None, ): """Plot an embedding as points. Currently this only works for 2D embeddings. While there are many optional parameters to further control and tailor the plotting, you need only pass in the trained/fit umap model to get results. This plot utility will attempt to do the hard work of avoiding overplotting issues, and make it easy to automatically colour points by a categorical labelling or numeric values. This method is intended to be used within a Jupyter notebook with ``%matplotlib inline``. Parameters ---------- umap_object: trained UMAP object A trained UMAP object that has a 2D embedding. labels: array, shape (n_samples,) (optional, default None) An array of labels (assumed integer or categorical), one for each data sample. This will be used for coloring the points in the plot according to their label. Note that this option is mutually exclusive to the ``values`` option. values: array, shape (n_samples,) (optional, default None) An array of values (assumed float or continuous), one for each sample. This will be used for coloring the points in the plot according to a colorscale associated to the total range of values. Note that this option is mutually exclusive to the ``labels`` option. theme: string (optional, default None) A color theme to use for plotting. A small set of predefined themes are provided which have relatively good aesthetics. Available themes are: * 'blue' * 'red' * 'green' * 'inferno' * 'fire' * 'viridis' * 'darkblue' * 'darkred' * 'darkgreen' cmap: string (optional, default 'Blues') The name of a matplotlib colormap to use for coloring or shading points. If no labels or values are passed this will be used for shading points according to density (largely only of relevance for very large datasets). If values are passed this will be used for shading according the value. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. color_key: dict or array, shape (n_categories) (optional, default None) A way to assign colors to categoricals. This can either be an explicit dict mapping labels to colors (as strings of form '#RRGGBB'), or an array like object providing one color for each distinct category being provided in ``labels``. Either way this mapping will be used to color points according to the label. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. color_key_cmap: string (optional, default 'Spectral') The name of a matplotlib colormap to use for categorical coloring. If an explicit ``color_key`` is not given a color mapping for categories can be generated from the label list and selecting a matching list of colors from the given colormap. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. background: string (optional, default 'white) The color of the background. Usually this will be either 'white' or 'black', but any color name will work. Ideally one wants to match this appropriately to the colors being used for points etc. This is one of the things that themes handle for you. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. width: int (optional, default 800) The desired width of the plot in pixels. height: int (optional, default 800) The desired height of the plot in pixels show_legend: bool (optional, default True) Whether to display a legend of the labels subset_points: array, shape (n_samples,) (optional, default None) A way to select a subset of points based on an array of boolean values. ax: matplotlib axis (optional, default None) The matplotlib axis to draw the plot to, or if None, which is the default, a new axis will be created and returned. alpha: float (optional, default: None) The alpha blending value, between 0 (transparent) and 1 (opaque). Returns ------- result: matplotlib axis The result is a matplotlib axis with the relevant plot displayed. If you are using a notebooks and have ``%matplotlib inline`` set then this will simply display inline. """ # if not hasattr(umap_object, "embedding_"): # raise ValueError( # "UMAP object must perform fit on data before it can be visualized" # ) if theme is not None: cmap = _themes[theme]["cmap"] color_key_cmap = _themes[theme]["color_key_cmap"] background = _themes[theme]["background"] if labels is not None and values is not None: raise ValueError( "Conflicting options; only one of labels or values should be set" ) if alpha is not None: if not 0.0 <= alpha <= 1.0: raise ValueError("Alpha must be between 0 and 1 inclusive") points = _get_embedding(umap_object) if subset_points is not None: if len(subset_points) != points.shape[0]: raise ValueError( "Size of subset points ({}) does not match number of input points ({})".format( len(subset_points), points.shape[0] ) ) points = points[subset_points] if labels is not None: labels = labels[subset_points] if values is not None: values = values[subset_points] if points.shape[1] != 2: raise ValueError("Plotting is currently only implemented for 2D embeddings") font_color = _select_font_color(background) if ax is None: dpi = plt.rcParams["figure.dpi"] fig = plt.figure(figsize=(width / dpi, height / dpi)) ax = fig.add_subplot(111) if points.shape[0] <= width * height // 10: ax = _matplotlib_points( points, ax, labels, values, cmap, color_key, color_key_cmap, background, width, height, show_legend, alpha, ) else: # Datashader uses 0-255 as the range for alpha, with 255 as the default if alpha is not None: alpha = alpha * 255 else: alpha = 255 ax = _datashade_points( points, ax, labels, values, cmap, color_key, color_key_cmap, background, width, height, show_legend, alpha, ) ax.set(xticks=[], yticks=[]) if _get_metric(umap_object) != "euclidean": ax.text( 0.99, 0.01, "UMAP: metric={}, n_neighbors={}, min_dist={}".format( _get_metric(umap_object), umap_object.n_neighbors, umap_object.min_dist ), transform=ax.transAxes, horizontalalignment="right", color=font_color, ) else: ax.text( 0.99, 0.01, "UMAP: n_neighbors={}, min_dist={}".format( umap_object.n_neighbors, umap_object.min_dist ), transform=ax.transAxes, horizontalalignment="right", color=font_color, ) return ax def connectivity( umap_object, edge_bundling=None, edge_cmap="gray_r", show_points=False, labels=None, values=None, theme=None, cmap="Blues", color_key=None, color_key_cmap="Spectral", background="white", width=800, height=800, ): """Plot connectivity relationships of the underlying UMAP simplicial set data structure. Internally UMAP will make use of what can be viewed as a weighted graph. This graph can be plotted using the layout provided by UMAP as a potential diagnostic view of the embedding. Currently this only works for 2D embeddings. While there are many optional parameters to further control and tailor the plotting, you need only pass in the trained/fit umap model to get results. This plot utility will attempt to do the hard work of avoiding overplotting issues and provide options for plotting the points as well as using edge bundling for graph visualization. Parameters ---------- umap_object: trained UMAP object A trained UMAP object that has a 2D embedding. edge_bundling: string or None (optional, default None) The edge bundling method to use. Currently supported are None or 'hammer'. See the datashader docs on graph visualization for more details. edge_cmap: string (default 'gray_r') The name of a matplotlib colormap to use for shading/ coloring the edges of the connectivity graph. Note that the ``theme``, if specified, will override this. show_points: bool (optional False) Whether to display the points over top of the edge connectivity. Further options allow for coloring/ shading the points accordingly. labels: array, shape (n_samples,) (optional, default None) An array of labels (assumed integer or categorical), one for each data sample. This will be used for coloring the points in the plot according to their label. Note that this option is mutually exclusive to the ``values`` option. values: array, shape (n_samples,) (optional, default None) An array of values (assumed float or continuous), one for each sample. This will be used for coloring the points in the plot according to a colorscale associated to the total range of values. Note that this option is mutually exclusive to the ``labels`` option. theme: string (optional, default None) A color theme to use for plotting. A small set of predefined themes are provided which have relatively good aesthetics. Available themes are: * 'blue' * 'red' * 'green' * 'inferno' * 'fire' * 'viridis' * 'darkblue' * 'darkred' * 'darkgreen' cmap: string (optional, default 'Blues') The name of a matplotlib colormap to use for coloring or shading points. If no labels or values are passed this will be used for shading points according to density (largely only of relevance for very large datasets). If values are passed this will be used for shading according the value. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. color_key: dict or array, shape (n_categories) (optional, default None) A way to assign colors to categoricals. This can either be an explicit dict mapping labels to colors (as strings of form '#RRGGBB'), or an array like object providing one color for each distinct category being provided in ``labels``. Either way this mapping will be used to color points according to the label. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. color_key_cmap: string (optional, default 'Spectral') The name of a matplotlib colormap to use for categorical coloring. If an explicit ``color_key`` is not given a color mapping for categories can be generated from the label list and selecting a matching list of colors from the given colormap. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. background: string (optional, default 'white) The color of the background. Usually this will be either 'white' or 'black', but any color name will work. Ideally one wants to match this appropriately to the colors being used for points etc. This is one of the things that themes handle for you. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. width: int (optional, default 800) The desired width of the plot in pixels. height: int (optional, default 800) The desired height of the plot in pixels Returns ------- result: matplotlib axis The result is a matplotlib axis with the relevant plot displayed. If you are using a notbooks and have ``%matplotlib inline`` set then this will simply display inline. """ if theme is not None: cmap = _themes[theme]["cmap"] color_key_cmap = _themes[theme]["color_key_cmap"] edge_cmap = _themes[theme]["edge_cmap"] background = _themes[theme]["background"] points = _get_embedding(umap_object) point_df = pd.DataFrame(points, columns=("x", "y")) point_size = 100.0 / np.sqrt(points.shape[0]) if point_size > 1: px_size = int(np.round(point_size)) else: px_size = 1 if show_points: edge_how = "log" else: edge_how = "eq_hist" coo_graph = umap_object.graph_.tocoo() edge_df = pd.DataFrame( np.vstack([coo_graph.row, coo_graph.col, coo_graph.data]).T, columns=("source", "target", "weight"), ) edge_df["source"] = edge_df.source.astype(np.int32) edge_df["target"] = edge_df.target.astype(np.int32) extent = _get_extent(points) canvas = ds.Canvas( plot_width=width, plot_height=height, x_range=(extent[0], extent[1]), y_range=(extent[2], extent[3]), ) if edge_bundling is None: edges = bd.directly_connect_edges(point_df, edge_df, weight="weight") elif edge_bundling == "hammer": warn( "Hammer edge bundling is expensive for large graphs!\n" "This may take a long time to compute!" ) edges = bd.hammer_bundle(point_df, edge_df, weight="weight") else: raise ValueError("{} is not a recognised bundling method".format(edge_bundling)) edge_img = tf.shade( canvas.line(edges, "x", "y", agg=ds.sum("weight")), cmap=plt.get_cmap(edge_cmap), how=edge_how, ) edge_img = tf.set_background(edge_img, background) if show_points: point_img = _datashade_points( points, None, labels, values, cmap, color_key, color_key_cmap, None, width, height, False, ) if px_size > 1: point_img = tf.dynspread(point_img, threshold=0.5, max_px=px_size) result = tf.stack(edge_img, point_img, how="over") else: result = edge_img font_color = _select_font_color(background) dpi = plt.rcParams["figure.dpi"] fig = plt.figure(figsize=(width / dpi, height / dpi)) ax = fig.add_subplot(111) _embed_datashader_in_an_axis(result, ax) ax.set(xticks=[], yticks=[]) ax.text( 0.99, 0.01, "UMAP: n_neighbors={}, min_dist={}".format( umap_object.n_neighbors, umap_object.min_dist ), transform=ax.transAxes, horizontalalignment="right", color=font_color, ) return ax def diagnostic( umap_object, diagnostic_type="pca", nhood_size=15, local_variance_threshold=0.8, ax=None, cmap="viridis", point_size=None, background="white", width=800, height=800, ): """Provide a diagnostic plot or plots for a UMAP embedding. There are a number of plots that can be helpful for diagnostic purposes in understanding your embedding. Currently these are restricted to methods of coloring a scatterplot of the embedding to show more about how the embedding is representing the data. The first class of such plots uses a linear method that preserves global structure well to embed the data into three dimensions, and then interprets such coordinates as a color space -- coloring the points by their location in the linear global structure preserving embedding. In such plots one should look for discontinuities of colour, and consider overall global gradients of color. The diagnostic types here are ``'pca'``, ``'ica'``, and ``'vq'`` (vector quantization). The second class consider the local neighbor structure. One can either look at how well the neighbor structure is preserved, or how the estimated local dimension of the data varies. Both of these are available, although the local dimension estimation is the preferred option. You can access these are diagnostic types ``'local_dim'`` and ``'neighborhood'``. Finally the diagnostic type ``'all'`` will provide a grid of diagnostic plots. Parameters ---------- umap_object: trained UMAP object A trained UMAP object that has a 2D embedding. diagnostic_type: str (optional, default 'pca') The type of diagnostic plot to show. The options are * 'pca' * 'ica' * 'vq' * 'local_dim' * 'neighborhood' * 'all' nhood_size: int (optional, default 15) The size of neighborhood to compare for local neighborhood preservation estimates. local_variance_threshold: float (optional, default 0.8) To estimate the local dimension we consider a PCA of the local neighborhood and estimate the dimension as that which provides ``local_variance_threshold`` or more of the ``variance_explained_ratio``. ax: matlotlib axis (optional, default None) A matplotlib axis to plot to, or, if None, a new axis will be created and returned. cmap: str (optional, default 'viridis') The name of a matplotlib colormap to use for coloring points if the ``'local_dim'`` or ``'neighborhood'`` option are selected. point_size: int (optional, None) If provided this will fix the point size for the plot(s). If None then a suitable point size will be estimated from the data. Returns ------- result: matplotlib axis The result is a matplotlib axis with the relevant plot displayed. If you are using a notbooks and have ``%matplotlib inline`` set then this will simply display inline. """ points = _get_embedding(umap_object) if points.shape[1] != 2: raise ValueError("Plotting is currently only implemented for 2D embeddings") if point_size is None: point_size = 100.0 / np.sqrt(points.shape[0]) if ax is None: dpi = plt.rcParams["figure.dpi"] if diagnostic_type in ("local_dim", "neighborhood"): width *= 1.1 font_color = _select_font_color(background) if ax is None and diagnostic_type != "all": fig = plt.figure() ax = fig.add_subplot(111) if diagnostic_type == "pca": color_proj = sklearn.decomposition.PCA(n_components=3).fit_transform( umap_object._raw_data ) color_proj -= np.min(color_proj) color_proj /= np.max(color_proj, axis=0) ax.scatter(points[:, 0], points[:, 1], s=point_size, c=color_proj, alpha=0.66) ax.set_title("Colored by RGB coords of PCA embedding") ax.text( 0.99, 0.01, "UMAP: n_neighbors={}, min_dist={}".format( umap_object.n_neighbors, umap_object.min_dist ), transform=ax.transAxes, horizontalalignment="right", color=font_color, ) ax.set(xticks=[], yticks=[]) elif diagnostic_type == "ica": color_proj = sklearn.decomposition.FastICA(n_components=3).fit_transform( umap_object._raw_data ) color_proj -= np.min(color_proj) color_proj /= np.max(color_proj, axis=0) ax.scatter(points[:, 0], points[:, 1], s=point_size, c=color_proj, alpha=0.66) ax.set_title("Colored by RGB coords of FastICA embedding") ax.text( 0.99, 0.01, "UMAP: n_neighbors={}, min_dist={}".format( umap_object.n_neighbors, umap_object.min_dist ), transform=ax.transAxes, horizontalalignment="right", color=font_color, ) ax.set(xticks=[], yticks=[]) elif diagnostic_type == "vq": color_projector = sklearn.cluster.KMeans(n_clusters=3).fit( umap_object._raw_data ) color_proj = sklearn.metrics.pairwise_distances( umap_object._raw_data, color_projector.cluster_centers_ ) color_proj -= np.min(color_proj) color_proj /= np.max(color_proj, axis=0) ax.scatter(points[:, 0], points[:, 1], s=point_size, c=color_proj, alpha=0.66) ax.set_title("Colored by RGB coords of Vector Quantization") ax.text( 0.99, 0.01, "UMAP: n_neighbors={}, min_dist={}".format( umap_object.n_neighbors, umap_object.min_dist ), transform=ax.transAxes, horizontalalignment="right", color=font_color, ) ax.set(xticks=[], yticks=[]) elif diagnostic_type == "neighborhood": highd_indices, highd_dists = _nhood_search(umap_object, nhood_size) tree = sklearn.neighbors.KDTree(points) lowd_dists, lowd_indices = tree.query(points, k=nhood_size) accuracy = _nhood_compare( highd_indices.astype(np.int32), lowd_indices.astype(np.int32) ) vmin = np.percentile(accuracy, 5) vmax = np.percentile(accuracy, 95) ax.scatter( points[:, 0], points[:, 1], s=point_size, c=accuracy, cmap=cmap, vmin=vmin, vmax=vmax, ) ax.set_title("Colored by neighborhood Jaccard index") ax.text( 0.99, 0.01, "UMAP: n_neighbors={}, min_dist={}".format( umap_object.n_neighbors, umap_object.min_dist ), transform=ax.transAxes, horizontalalignment="right", color=font_color, ) ax.set(xticks=[], yticks=[]) norm = matplotlib.colors.Normalize(vmin=vmin, vmax=vmax) mappable = matplotlib.cm.ScalarMappable(norm=norm, cmap=cmap) mappable.set_array(accuracy) plt.colorbar(mappable, ax=ax) elif diagnostic_type == "local_dim": highd_indices, highd_dists = _nhood_search(umap_object, umap_object.n_neighbors) data = umap_object._raw_data local_dim = np.empty(data.shape[0], dtype=np.int64) for i in range(data.shape[0]): pca = sklearn.decomposition.PCA().fit(data[highd_indices[i]]) local_dim[i] = np.where( np.cumsum(pca.explained_variance_ratio_) > local_variance_threshold )[0][0] vmin = np.percentile(local_dim, 5) vmax = np.percentile(local_dim, 95) ax.scatter( points[:, 0], points[:, 1], s=point_size, c=local_dim, cmap=cmap, vmin=vmin, vmax=vmax, ) ax.set_title("Colored by approx local dimension") ax.text( 0.99, 0.01, "UMAP: n_neighbors={}, min_dist={}".format( umap_object.n_neighbors, umap_object.min_dist ), transform=ax.transAxes, horizontalalignment="right", color=font_color, ) ax.set(xticks=[], yticks=[]) norm = matplotlib.colors.Normalize(vmin=vmin, vmax=vmax) mappable = matplotlib.cm.ScalarMappable(norm=norm, cmap=cmap) mappable.set_array(local_dim) plt.colorbar(mappable, ax=ax) elif diagnostic_type == "all": cols = int(len(_diagnostic_types) ** 0.5 // 1) rows = len(_diagnostic_types) // cols + 1 fig, axs = plt.subplots(rows, cols, figsize=(10, 10), constrained_layout=True) axs = axs.flat for ax in axs[len(_diagnostic_types) :]: ax.remove() for ax, plt_type in zip(axs, _diagnostic_types): diagnostic( umap_object, diagnostic_type=plt_type, ax=ax, point_size=point_size / 4.0, ) else: raise ValueError( "Unknown diagnostic; should be one of " + ", ".join(list(_diagnostic_types)) + ' or "all"' ) return ax def interactive( umap_object, labels=None, values=None, hover_data=None, theme=None, cmap="Blues", color_key=None, color_key_cmap="Spectral", background="white", width=800, height=800, point_size=None, subset_points=None, interactive_text_search=False, interactive_text_search_columns=None, interactive_text_search_alpha_contrast=0.95, alpha=None, ): """Create an interactive bokeh plot of a UMAP embedding. While static plots are useful, sometimes a plot that supports interactive zooming, and hover tooltips for individual points is much more desireable. This function provides a simple interface for creating such plots. The result is a bokeh plot that will be displayed in a notebook. Note that more complex tooltips etc. will require custom code -- this is merely meant to provide fast and easy access to interactive plotting. Parameters ---------- umap_object: trained UMAP object A trained UMAP object that has a 2D embedding. labels: array, shape (n_samples,) (optional, default None) An array of labels (assumed integer or categorical), one for each data sample. This will be used for coloring the points in the plot according to their label. Note that this option is mutually exclusive to the ``values`` option. values: array, shape (n_samples,) (optional, default None) An array of values (assumed float or continuous), one for each sample. This will be used for coloring the points in the plot according to a colorscale associated to the total range of values. Note that this option is mutually exclusive to the ``labels`` option. hover_data: DataFrame, shape (n_samples, n_tooltip_features) (optional, default None) A dataframe of tooltip data. Each column of the dataframe should be a Series of length ``n_samples`` providing a value for each data point. Column names will be used for identifying information within the tooltip. theme: string (optional, default None) A color theme to use for plotting. A small set of predefined themes are provided which have relatively good aesthetics. Available themes are: * 'blue' * 'red' * 'green' * 'inferno' * 'fire' * 'viridis' * 'darkblue' * 'darkred' * 'darkgreen' cmap: string (optional, default 'Blues') The name of a matplotlib colormap to use for coloring or shading points. If no labels or values are passed this will be used for shading points according to density (largely only of relevance for very large datasets). If values are passed this will be used for shading according the value. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. color_key: dict or array, shape (n_categories) (optional, default None) A way to assign colors to categoricals. This can either be an explicit dict mapping labels to colors (as strings of form '#RRGGBB'), or an array like object providing one color for each distinct category being provided in ``labels``. Either way this mapping will be used to color points according to the label. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. color_key_cmap: string (optional, default 'Spectral') The name of a matplotlib colormap to use for categorical coloring. If an explicit ``color_key`` is not given a color mapping for categories can be generated from the label list and selecting a matching list of colors from the given colormap. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. background: string (optional, default 'white') The color of the background. Usually this will be either 'white' or 'black', but any color name will work. Ideally one wants to match this appropriately to the colors being used for points etc. This is one of the things that themes handle for you. Note that if theme is passed then this value will be overridden by the corresponding option of the theme. width: int (optional, default 800) The desired width of the plot in pixels. height: int (optional, default 800) The desired height of the plot in pixels point_size: int (optional, default None) The size of each point marker subset_points: array, shape (n_samples,) (optional, default None) A way to select a subset of points based on an array of boolean values. interactive_text_search: bool (optional, default False) Whether to include a text search widget above the interactive plot interactive_text_search_columns: list (optional, default None) Columns of data source to search. Searches labels and hover_data by default. interactive_text_search_alpha_contrast: float (optional, default 0.95) Alpha value for points matching text search. Alpha value for points not matching text search will be 1 - interactive_text_search_alpha_contrast alpha: float (optional, default: None) The alpha blending value, between 0 (transparent) and 1 (opaque). Returns ------- """ if theme is not None: cmap = _themes[theme]["cmap"] color_key_cmap = _themes[theme]["color_key_cmap"] background = _themes[theme]["background"] if labels is not None and values is not None: raise ValueError( "Conflicting options; only one of labels or values should be set" ) if alpha is not None: if not 0.0 <= alpha <= 1.0: raise ValueError("Alpha must be between 0 and 1 inclusive") points = _get_embedding(umap_object) if subset_points is not None: if len(subset_points) != points.shape[0]: raise ValueError( "Size of subset points ({}) does not match number of input points ({})".format( len(subset_points), points.shape[0] ) ) points = points[subset_points] if points.shape[1] != 2: raise ValueError("Plotting is currently only implemented for 2D embeddings") if point_size is None: point_size = 100.0 / np.sqrt(points.shape[0]) data = pd.DataFrame(_get_embedding(umap_object), columns=("x", "y")) if labels is not None: data["label"] = labels if color_key is None: unique_labels = np.unique(labels) num_labels = unique_labels.shape[0] color_key = _to_hex( plt.get_cmap(color_key_cmap)(np.linspace(0, 1, num_labels)) ) if isinstance(color_key, dict): data["color"] = pd.Series(labels).map(color_key) else: unique_labels = np.unique(labels) if len(color_key) < unique_labels.shape[0]: raise ValueError( "Color key must have enough colors for the number of labels" ) new_color_key = {k: color_key[i] for i, k in enumerate(unique_labels)} data["color"] = pd.Series(labels).map(new_color_key) colors = "color" elif values is not None: data["value"] = values palette = _to_hex(plt.get_cmap(cmap)(np.linspace(0, 1, 256))) colors = btr.linear_cmap( "value", palette, low=np.min(values), high=np.max(values) ) else: colors = matplotlib.colors.rgb2hex(plt.get_cmap(cmap)(0.5)) if subset_points is not None: data = data[subset_points] if hover_data is not None: hover_data = hover_data[subset_points] if points.shape[0] <= width * height // 10: if hover_data is not None: tooltip_dict = {} for col_name in hover_data: data[col_name] = hover_data[col_name] tooltip_dict[col_name] = "@{" + col_name + "}" tooltips = list(tooltip_dict.items()) else: tooltips = None if alpha is not None: data["alpha"] = alpha else: data["alpha"] = 1 # bpl.output_notebook(hide_banner=True) # this doesn't work for non-notebook use data_source = bpl.ColumnDataSource(data) plot = bpl.figure( width=width, height=height, tooltips=tooltips, background_fill_color=background, ) plot.circle( x="x", y="y", source=data_source, color=colors, size=point_size, alpha="alpha", ) plot.grid.visible = False plot.axis.visible = False if interactive_text_search: text_input = TextInput(value="", title="Search:") if interactive_text_search_columns is None: interactive_text_search_columns = [] if hover_data is not None: interactive_text_search_columns.extend(hover_data.columns) if labels is not None: interactive_text_search_columns.append("label") if len(interactive_text_search_columns) == 0: warn( "interactive_text_search_columns set to True, but no hover_data or labels provided." "Please provide hover_data or labels to use interactive text search." ) else: callback = CustomJS( args=dict( source=data_source, matching_alpha=interactive_text_search_alpha_contrast, non_matching_alpha=1 - interactive_text_search_alpha_contrast, search_columns=interactive_text_search_columns, ), code=""" var data = source.data; var text_search = cb_obj.value; var search_columns_dict = {} for (var col in search_columns){ search_columns_dict[col] = search_columns[col] } // Loop over columns and values // If there is no match for any column for a given row, change the alpha value var string_match = false; for (var i = 0; i < data.x.length; i++) { string_match = false for (var j in search_columns_dict) { if (String(data[search_columns_dict[j]][i]).includes(text_search) ) { string_match = true } } if (string_match){ data['alpha'][i] = matching_alpha }else{ data['alpha'][i] = non_matching_alpha } } source.change.emit(); """, ) text_input.js_on_change("value", callback) plot = column(text_input, plot) # bpl.show(plot) else: if hover_data is not None: warn( "Too many points for hover data -- tooltips will not" "be displayed. Sorry; try subssampling your data." ) if interactive_text_search: warn( "Too many points for text search." "Sorry; try subssampling your data." ) if alpha is not None: warn("Alpha parameter will not be applied on holoviews plots") hv.extension("bokeh") hv.output(size=300) hv.opts.defaults(hv.opts.RGB(bgcolor=background, xaxis=None, yaxis=None)) if labels is not None: point_plot = hv.Points(data, kdims=["x", "y"]) plot = hd.datashade( point_plot, aggregator=ds.count_cat("color"), color_key=color_key, cmap=plt.get_cmap(cmap), width=width, height=height, ) elif values is not None: min_val = data.values.min() val_range = data.values.max() - min_val data["val_cat"] = pd.Categorical( (data.values - min_val) // (val_range // 256) ) point_plot = hv.Points(data, kdims=["x", "y"], vdims=["val_cat"]) plot = hd.datashade( point_plot, aggregator=ds.count_cat("val_cat"), cmap=plt.get_cmap(cmap), width=width, height=height, ) else: point_plot = hv.Points(data, kdims=["x", "y"]) plot = hd.datashade( point_plot, aggregator=ds.count(), cmap=plt.get_cmap(cmap), width=width, height=height, ) return plot def nearest_neighbour_distribution(umap_object, bins=25, ax=None): """Create a histogram of the average distance to each points nearest neighbors. Parameters ---------- umap_object: trained UMAP object A trained UMAP object that has an embedding. bins: int (optional, default 25) Number of bins to put the points into ax: matlotlib axis (optional, default None) A matplotlib axis to plot to, or, if None, a new axis will be created and returned. Returns ------- """ nn_distances = average_nn_distance(umap_object.graph_) if ax is None: fig = plt.figure() ax = fig.add_subplot(111) ax.set_xlabel(f"Average distance to nearest neighbors") ax.set_ylabel("Frequency") ax.hist(nn_distances, bins=bins) return ax