add esig opt dependency and cdf plotting

pyproject.toml

@@ -38,6 +38,9 @@ dependencies = [
 ]
 
 [project.optional-dependencies]
+signatures = [
+  'esig; python_version < "3.10"',
+]
 test = [
   "pytest >=6",
   "pytest-cov >=3",

src/signature_mahalanobis_knn/utils.py

@@ -40,9 +40,9 @@ def plot_roc_curve(
         roc_auc = roc_auc_score(y_true, y_score)
 
     plt.title(f"Receiver Operating Characteristic {title}")
-    plt.plot(fp_rate, tp_rate, "b", label=f"AUC = {round(roc_auc, 2)}")
+    plt.plot(fp_rate, tp_rate, "b", label=f"AUC = {round(roc_auc, 2)}", linewidth=2)
     plt.legend(loc="lower right")
-    plt.plot([0, 1], [0, 1], "r--")
+    plt.plot([0, 1], [0, 1], "r--", linewidth=2)
     plt.xlim([0, 1])
     plt.ylim([0, 1])
     plt.ylabel("True Positive Rate")
@@ -162,3 +162,87 @@ def compute_auc(
         plot=plot,
         title=title,
     )
+
+
+def plot_cdf_given_dists(
+    distances_in: np.ndarray,
+    distances_out: np.ndarray,
+    bins: int | np.array = 50,
+    xrange: tuple[float, float] | None = None,
+    xticks: list[float] | None = None,
+    xlog: bool = False,
+    xlog_base: int = 10,
+    title: str = "",
+):
+    """
+    Plot an empirical cumulative distributions of the
+    distances of inliers and outliers.
+
+    Parameters
+    ----------
+    distances_in : np.ndarray
+        KNN distances for the inlier data points.
+    distances_out : np.ndarray
+        KNN distances for the outlier data points.
+    bins : int | np.array, optional
+        Number of bins or the bins, by default 10.
+        If int, then the bins will be equally spaced.
+        If array, then the sequence defines the bin edges.
+    xrange : tuple[float, float] | None, optional
+        Range of the x-axis, by default None.
+        If None, then the range will be the minimum and maximum
+        of the distances.
+    xticks : list[float] | None, optional
+        Tick values of the x-axis, by default None.
+        If None, then the ticks will be automatically generated.
+    xlog : bool, optional
+        Whether to use log scale for the x-axis, by default False.
+    xlog_base : int, optional
+        Base of the log scale, by default 10.
+        Only used when xlog is True.
+    title : str, optional
+        Title for the ROC curve plot, by default "".
+        Only used when plot is True.
+    """
+    # obtain the empirical cumulative distribution functions
+    sorted_inlier = np.sort(distances_in)
+    cumulative_inliers = np.arange(1, len(sorted_inlier) + 1) / len(sorted_inlier)
+    sorted_outlier = np.sort(distances_out)
+    cumulative_outliers = np.arange(1, len(sorted_outlier) + 1) / len(sorted_outlier)
+
+    # define the empirical cumulative distribution functions
+    def empirical_cdf_inliers(x):
+        return np.interp(x, sorted_inlier, cumulative_inliers, left=0.0, right=1.0)
+
+    def empirical_cdf_outliers(x):
+        return np.interp(x, sorted_outlier, cumulative_outliers, left=0.0, right=1.0)
+
+    # obtain the range of x to evaluate the ECDFs
+    xmin = min(np.min(distances_in), np.min(distances_out))
+    xmax = max(np.max(distances_in), np.max(distances_out))
+    x = np.linspace(xmin, xmax, bins)
+
+    # plot the cumulative functions
+    plt.plot(
+        x,
+        empirical_cdf_inliers(x),
+        c="blue",
+        label="inliers",
+        linestyle="--",
+        linewidth=2,
+    )
+    plt.plot(x, empirical_cdf_outliers(x), c="orange", label="anomalies", linewidth=2)
+    plt.grid()
+    if title != "":
+        plt.title(title)
+    plt.legend(loc="lower right")
+    if xrange is not None:
+        plt.xlim(xrange)
+    if xticks is not None:
+        plt.xticks(xticks)
+    if xlog:
+        plt.xscale("log", base=xlog_base)
+    plt.ylim([0, 1])
+    plt.ylabel("Cumulative probability")
+    plt.xlabel("Conformance")
+    plt.show()