Visualize qn art

common/utils.py

@@ -37,6 +37,7 @@ def plot_gaussian_contours_fading(
     - color: A 4D numpy array including RGB and alpha channels to specify the color and initial opacity.
     - max_std: Max standard deviations to draw contours to. Default is 2.
     - sigma_steps: Step size in standard deviations for each contour. Default is 0.25.
+    - linewidth: width of boundary line
 
     """
     from matplotlib.patches import Ellipse
@@ -75,12 +76,13 @@ def plot_gaussian_contours_covariance(
 
 
     Parameters:
-        - ax: Matplotlib axis object. If None, creates a new figure and axis.
+    - ax: Matplotlib axis object. If None, creates a new figure and axis.
     - mean: A numpy array representing the mean (μ) of the distribution.
     - covariance: A 2x2 numpy array representing the covariance matrix of the distribution.
     - color: A 4D numpy array including RGB and alpha channels to specify the color and initial opacity.
     - max_std: Max standard deviations to draw contours to. Default is 2.
     - sigma_steps: Step size in standard deviations for each contour. Default is 0.25.
+    - linewidth: width of boundary line
 
     """
     from matplotlib.patches import Ellipse
@@ -109,3 +111,38 @@ def plot_gaussian_contours_covariance(
         ax.add_patch(ellipse)
 
 
+def plot_weight_matrix_as_ellipse(
+        ax: Axes,
+        s: float,
+        W: np.ndarray,
+        mean: np.ndarray,
+        color: np.ndarray,
+        linewidth: int = 1
+):
+    """
+    Plots the transformation of a unit circle by the weight matrix W as an ellipse.
+
+    Parameters:
+    - ax: Matplotlib axis object. If None, creates a new figure and axis.
+    - mean: The center point (x, y) of the ellipse.
+    - s: Scalar to scale the weight matrix W.
+    - W: 2x2 weight matrix.
+    - color: Color of the ellipse.
+    - linewidth: width of boundary line
+    """
+    # Compute the transformation matrix
+    transform_matrix = W[:2, :2]
+
+    # Generate points on a unit circle
+    theta = np.linspace(0, 2 * np.pi, 100)
+    circle = np.array([np.cos(theta), np.sin(theta)])  # Unit circle
+
+    # Apply the linear transformation to the circle to get an ellipse
+    ellipse = 0.25*s * s * (transform_matrix @ circle)
+
+    # Shift the ellipse to the specified mean
+    ellipse[0, :] += mean[0]
+    ellipse[1, :] += mean[1]
+
+    # Plotting
+    ax.plot(ellipse[0, :], ellipse[1, :], color=color, linewidth=linewidth)

elementary/QuadraticNeuronART.py

@@ -9,9 +9,10 @@
 """
 
 import numpy as np
-from typing import Optional
+from typing import Optional, Iterable
+from matplotlib.axes import Axes
 from common.BaseART import BaseART
-from common.utils import normalize, l2norm2
+from common.utils import normalize, l2norm2, plot_weight_matrix_as_ellipse
 
 def prepare_data(data: np.ndarray) -> np.ndarray:
     normalized = normalize(data)
@@ -78,3 +79,14 @@ def update(self, i: np.ndarray, w: np.ndarray, params, cache: Optional[dict] = N
     def new_weight(self, i: np.ndarray, params: dict) -> np.ndarray:
         w_new = np.identity(self.dim_)
         return np.concatenate([w_new.flatten(), i, [params["s_init"]]])
+
+    def plot_cluster_bounds(self, ax: Axes, colors: Iterable, linewidth: int = 1):
+        # kinda works
+        from matplotlib.patches import Rectangle
+        for w, col in zip(self.W, colors):
+            dim2 = self.dim_ * self.dim_
+            w_ = w[:dim2].reshape((self.dim_, self.dim_))
+            b = w[dim2:-1]
+            s = w[-1]
+            plot_weight_matrix_as_ellipse(ax, s, w_, b, col)
+

examples/test_quadratic_neuron_art.py

@@ -23,7 +23,7 @@ def cluster_blobs():
 
     params = {
         "rho": 0.9,
-        "s_init": 1.0,
+        "s_init": 0.9,
         "lr_b": 0.1,
         "lr_w": 0.1,
         "lr_s": 0.1