In [2]:
# Visualize cosine similarity from 0 to 359
def compute_cosine_similarity(x: np.ndarray, y: np.ndarray) -> float:
# Adjacency / Hypotenuse
return np.dot(x, y) / (np.linalg.norm(x) * np.linalg.norm(y))
x = np.array([1, 0])
theta_list = []
cosine_similarity_list = []
y_list = []
for degree in range(0, 360):
theta = np.radians(degree)
y = np.array([np.cos(theta), np.sin(theta)])
cosine_similarity = compute_cosine_similarity(x, y)
theta_list.append(degree)
cosine_similarity_list.append(cosine_similarity)
y_list.append(y)
fig, ax = plt.subplots()
def animate(frame):
y = y_list[frame]
ax.clear()
ax.set_xlim(-2, 2)
ax.set_ylim(-2, 2)
ax.set_xticks([-2, -1, 0, 1, 2])
ax.set_yticks([-2, -1, 0, 1, 2])
ax.set_aspect("equal")
ax.grid(True, alpha=0.3)
ax.arrow(0, 0, x[0], x[1], head_width=0.05, color="blue")
ax.arrow(0, 0, y[0], y[1], head_width=0.05, color="green")
ax.add_patch(Arc((0, 0), 2.0, 2.0, angle=0, theta1=0, theta2=360, color="gray", linestyle="--", linewidth=0.3))
ax.add_patch(Arc((0, 0), 0.4, 0.4, angle=0, theta1=0, theta2=frame, color="red", linestyle="dotted"))
ax.text(
x[0] + 0.1,
x[1] + 0.1,
s=f"({x[0]:.2f}, {x[1]:.2f})",
horizontalalignment="left",
verticalalignment="top",
color="blue"
)
ax.text(
y[0] + 0.1,
y[1] + 0.1,
s=f"({y[0]:.2f}, {y[1]:.2f})",
horizontalalignment="left",
verticalalignment="top",
color="green"
)
ax.text(0, -1.3, s=r"$\theta$" + f"={frame}°", fontsize=10, horizontalalignment="center", color="red")
ax.text(0, -1.5, s=f"similarity={cosine_similarity_list[frame]:.5f}", fontsize=10, horizontalalignment="center")
return ()
anim = animation.FuncAnimation(fig, animate, frames=len(y_list), interval=50, blit=True, repeat=False)
plt.close(fig)
HTML(anim.to_jshtml())
Out[2]: