344 lines
12 KiB
Python
344 lines
12 KiB
Python
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import warnings
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from pathlib import Path
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import matplotlib as mpl
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import matplotlib.patches as mpatches
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import matplotlib.pyplot as plt
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import numpy as np
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from mpl_toolkits.axes_grid1.axes_divider import make_axes_locatable
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from numpy.typing import NDArray
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from sklearn.decomposition import PCA
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def unique_targets(targets):
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"""Generate dictionary of integer indices and the corresponding targets."""
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return {target: i for i, target in enumerate(sorted(set(targets)))}
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def label2int(targets):
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"""Convert string and/or integer labels to integer labels (necessary for
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torch)."""
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_unique_targets = unique_targets(targets)
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targets = [_unique_targets[target] for target in targets]
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return targets
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def omega2lambda(omega: NDArray) -> NDArray:
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"""Normalize Ω (Omega) and return the CCM (Λ, Lambda)."""
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omega = omega / np.sqrt(np.trace(omega.T @ omega))
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lmbd = omega @ omega.T
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return lmbd
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def vis_ccm(
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ccm: NDArray,
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labels: NDArray | list[str | int] | bool = True,
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title="Classification correlation matrix",
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cmap: str = "bwr",
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important_labels: int | None = None,
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no_diagonal: bool = False,
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show_cip: bool = True,
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show_crp: bool = False,
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sort: bool = False,
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cutout: int | None = None,
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fontsize: float = 6,
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filename: str | Path | None = None,
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):
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"""Visualise the Classification Correlation Matrix (CCM), Classification
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Influence Profile (CIP) and Classification Relevance Profile (CRP).
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Parameters:
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-----------
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ccm : NDArray
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Classification Correlation Matrix (CCM) or Λ (Lambda) matrix.
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labels : NDArray or list of integers and/or strings or bool
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Supply a list of integers and/or strings. If `True`, generates an
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integer index. If `False`, doesn't show labels.
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title : str or None
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Title of the figure.
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cmap : str, default="bwr"
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For options of matplotlib colormaps, see:
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https://matplotlib.org/stable/tutorials/colors/colormaps.html
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important_labels : int, default=None
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Only show the `important_labels` most important labels.
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no_diagonal : bool, default=False
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Set the diagonal elements to zero.
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show_cip : bool, default=True
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Show the CIP.
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show_crp : bool, default=True
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Show the CRP.
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sort : bool, default=False
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Sort the features by their importance for classification (CIP).
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cutout : int or None, default=None
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If set, cuts out the `cutout` most important features and only shows
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those.
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fontsize : float, default=6
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Overall fontsize.
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filename : str or Path
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If a filename is given, the figure is saved to that path.
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"""
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font = {"fontsize": fontsize}
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# profiles
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cip = np.abs(ccm).sum(axis=0) / len(ccm)
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crp = np.diagonal(ccm)
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if labels is True:
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ax_labels = list(range(len(ccm)))
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else:
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ax_labels = labels
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if sort or cutout:
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if cutout is not None:
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greatest_importance = np.delete(np.argsort(cip)[::-1][:cutout], 2)
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else:
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greatest_importance = np.delete(np.argsort(cip)[::-1], 2)
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new_ccm = np.zeros((len(greatest_importance), len(greatest_importance)))
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for i, x in enumerate(greatest_importance):
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for j, y in enumerate(greatest_importance):
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new_ccm[i, j] = ccm[x, y]
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ccm = new_ccm
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ax_labels = [
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ax_labels[i].replace("m_", "").replace("p_", "")
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for i in greatest_importance.tolist()
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]
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# ax_labels = [ax_labels[i] for i in greatest_importance.tolist()]
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# profiles
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# cip = np.abs(ccm).sum(axis=0)
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# crp = np.diagonal(ccm)
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cip = cip[greatest_importance]
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crp = crp[greatest_importance]
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if no_diagonal:
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np.fill_diagonal(ccm, 0)
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if important_labels:
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greatest_importance = np.argsort(cip)[::-1][:important_labels]
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ax_labels = [
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l if i in greatest_importance else "" for i, l in enumerate(ax_labels)
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]
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if not labels:
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orig_labels = ax_labels
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ax_labels = [""] * len(ax_labels)
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fig, ax = plt.subplots()
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# matrix
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plt.title(title)
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maxi = max(-np.amin(ccm), np.amax(ccm)) * 1.1
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vmin = -maxi
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vmax = maxi
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cax = ax.imshow(ccm, interpolation="nearest", cmap=cmap, vmin=vmin, vmax=vmax)
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# plt.xticks(np.arange(0, len(ax_labels)))
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plt.yticks(np.arange(0, len(ax_labels)))
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# ax.set_xticklabels([""] * len(ax_labels))
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ax.set_yticklabels(ax_labels, fontdict=font)
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if show_cip or show_crp:
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plt.xticks([])
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else:
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plt.xticks(np.arange(0, len(ax_labels)))
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ax.set_xticklabels(ax_labels, fontdict=font)
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divider = make_axes_locatable(plt.gca())
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# colorbar
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ax_color = divider.append_axes("right", "5%", pad="10%")
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plt.colorbar(cax, cax=ax_color)
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if show_cip:
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ax_inf = divider.append_axes("bottom", "30%", pad="5%")
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ax_inf.plot(cip, marker=".", lw=0.6, ms=3, color="grey", label="CIP")
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if show_crp:
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ax_inf.plot(crp, marker=".", lw=0.6, ms=3, color="darkgrey", label="CRP")
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ax_inf.fill_between(range(len(ccm)), cip, crp, alpha=0.3, color="lightgrey")
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plt.legend(bbox_to_anchor=(1.43, 0.7), loc="center right")
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if show_cip or show_crp:
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ax_inf.set_xticks(np.arange(0, len(ax_labels)))
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ax_inf.set_xticklabels(ax_labels, fontdict=font)
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plt.xticks(rotation=45, ha="right")
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ax_inf.set_ylim(bottom=0)
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# plt.legend(bbox_to_anchor=(1.43, 0.7), loc="center right", fontsize=8)
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plt.tight_layout()
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if filename:
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plt.savefig(filename + ".png", dpi=600, bbox_inches="tight")
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plt.show()
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plt.close()
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def vis_data(
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data: NDArray,
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targets: NDArray | list[int | str] | None = None,
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prototypes: NDArray | None = None,
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prototype_labels: NDArray | list[int | str] | None = None,
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omega: NDArray | None = None,
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dimensions: int | None = None,
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title: str | None = None,
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size: float = 20,
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alpha: float = 0.5,
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cmap: str = "tab10",
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proto_marker: str = "o",
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proto_color: str = "r",
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filename: str | Path | None = None,
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):
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"""Visualise multidimensional data in one to three dimensions.
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Dimensionality reduction is achieved through either Principal Component
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Analysis (PCA) or, if the Ω (Omega) matrix is supplied, by projection into the
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latent space.
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Parameters
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----------
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data : NDArray
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Data array.
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targets : NDArray or list of integers and/or strings or None, default=None
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Supply a list of targets (class labels) as integers and/or strings. If
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`None`, it doesn't show labels.
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prototypes : NDArray or None, default=None
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If prototype array is supplied, they are displayed and highlighted (see
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`proto_marker` and `proto_color`).
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prototype_labels : NDArray or list of integers and/or strings or None,
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default=None
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Supply a list of targets (class labels) as integers and/or strings. If
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`None`, it doesn't show labels.
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omega : NDArray or None, default=None
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Ω (Omega) matrix for projection into latent space (see General Matrix
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Learning Vector Quantization (GMLVQ)). If not supplied, PCA is chosen
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for dimensionality reduction.
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dimensions : int or None, default=None
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Desired number of projection dimensions. If not supplied, chooses
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either according to shape of Ω (Omega) or `2` for PCA.
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title : str
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Title of the figure.
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size : float, default=20
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Size of the points.
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alpha : float, default=0.5
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Alpha transparency for data points (e.g. for better visibility of
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prototypes).
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cmap : str, default="tab10"
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Where to choose colours for classes from. For options of matplotlib
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colormaps, see:
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https://matplotlib.org/stable/tutorials/colors/colormaps.html
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proto_marker : str, default="o"
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For more options, see:
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https://matplotlib.org/stable/api/markers_api.html#module-matplotlib.markers
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proto_color : str, default="r"
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Highlighting color for prototypes. For more options, see:
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https://matplotlib.org/stable/gallery/color/named_colors.html#base-colors
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filename : str or Path
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If a filename is given, the figure is saved to that path.
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"""
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fig = plt.figure(1, figsize=(8, 6))
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n_data, n_dimensions = data.shape
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target_reverse = {i: target for i, target in enumerate(sorted(set(targets)))}
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method = ""
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if omega is not None:
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assert 1 <= omega.shape[1] <= 3, (
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"Omega needs to be within the 3 dimensions "
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"that humans are accustomed to."
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)
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if dimensions is None:
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dimensions = omega.shape[1]
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data = data @ omega
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prototypes = prototypes @ omega
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method = "omega"
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if omega.shape[1] == 1:
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data = np.concatenate((data, np.zeros((data.shape[0], 1))), axis=1)
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prototypes = np.concatenate(
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(prototypes, np.zeros((prototypes.shape[0], 1))), axis=1
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)
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if data.shape[1] >= 3:
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if dimensions is None:
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dimensions = 2
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pca = PCA(n_components=dimensions)
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data = pca.fit_transform(data)
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prototypes = pca.transform(prototypes)
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method = "PCA"
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# display data
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if data.shape[1] <= 2:
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ax = fig.add_subplot(111)
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scatter = ax.scatter(
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*data.T,
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c=label2int(targets),
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marker="o",
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s=size,
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edgecolors="none",
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cmap=cmap,
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alpha=alpha,
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)
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elif data.shape[1] == 3:
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ax = fig.add_subplot(111, projection="3d", elev=-150, azim=110)
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scatter = ax.scatter(
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*data.T,
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c=label2int(targets),
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marker="o",
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s=size,
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edgecolors="none",
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cmap=cmap,
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alpha=alpha,
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)
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# display prototypes(?)
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if prototypes is not None and prototype_labels is None:
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warnings.warn(
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"You forgot to supply labels to the prototypes to " "color them correctly."
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)
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if prototypes is not None and prototype_labels is not None:
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ax.scatter(
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*prototypes.T,
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c=label2int(prototype_labels),
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cmap=cmap,
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marker=proto_marker,
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s=size * 2,
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edgecolors=proto_color,
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linewidths=4,
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)
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# axis labels
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if method == "PCA":
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if pca.n_components >= 1:
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ax.set_xlabel(
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"1st eigenvector " f"({pca.explained_variance_ratio_[0]:.2%})"
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)
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if pca.n_components >= 2:
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ax.set_ylabel(
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"2nd eigenvector " f"({pca.explained_variance_ratio_[1]:.2%})"
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)
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if pca.n_components == 3:
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ax.set_zlabel(
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f"3rd eigenvector " f"({pca.explained_variance_ratio_[2]:.2%})"
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)
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ax.set_title("PCA directions")
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elif method == "omega":
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if data.shape[1] >= 1:
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ax.set_xlabel("projection dimension 1")
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if data.shape[1] >= 2:
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ax.set_ylabel("projection dimension 2")
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if data.shape[1] == 3:
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ax.set_zlabel("projection dimension 3")
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ax.set_title("Omega transform")
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cmap = mpl.colormaps[cmap].resampled(len(set(targets)))
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ax.legend(
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handles=[
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mpatches.Patch(color=cmap(t, alpha=alpha), label=target_reverse[t])
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for t in target_reverse
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]
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)
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if filename:
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plt.savefig(filename + ".png", dpi=600, bbox_inches="tight")
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plt.show()
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