118 lines
3.1 KiB
Python
118 lines
3.1 KiB
Python
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import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib.transforms as trans
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import io
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def line(ax, x, y, **args):
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'''line between two points x,y'''
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ax.plot([x[0], y[0]], [x[1], y[1]], **args)
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def angle(v):
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'''angle of a vector wrt x axis'''
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return np.arctan2(v[1], v[0])
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def proj_hist(a, b, w):
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'''returns a file-like object of the w-projection histogram'''
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fig = plt.figure(figsize=(3, 3))
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ax = fig.add_subplot(111)
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ax.set_aspect(0.04)
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ax.axis('off')
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plt.hist(a @ w, color='xkcd:dark yellow', zorder=2)
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plt.hist(b @ w, color='xkcd:pale purple', zorder=1)
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buf = io.BytesIO()
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fig.savefig(buf, transparent=True)
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plt.close(fig)
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buf.seek(0)
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return plt.imread(buf)
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def place_im(ax, im, transform):
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'''place an image into an Axes by applying a transformation'''
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im = ax.imshow(im, interpolation='none',
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extent=[-2, 4, -3, 2],
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zorder=2)
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trans_data = transform + ax.transData
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im.set_transform(trans_data)
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def main():
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# rotation by π/2 matrix
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rot = np.array([[0, -1], [1, 0]])
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# covariance
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cov = np.array([[0.33, 0.15], [0.15, 0.12]])
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# means
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m1 = np.array([-1.2, 0.5])
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m2 = np.array([0.6, 0])
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np.random.seed(3)
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a = np.random.multivariate_normal(m1, cov, 100)
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b = np.random.multivariate_normal(m2, cov, 100)
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# w₁: naive projection onto m1-m2 plane
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w1 = (m1 - m2) / np.linalg.norm(m1 - m2)
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# w₂: Fisher projection
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w2 = np.linalg.inv(cov) @ (m1 - m2)
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w2 /= np.linalg.norm(w2)
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#plt.rcParams['font.size'] = 8
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fig, axes = plt.subplots(
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1, 2, figsize=(6, 9),
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subplot_kw=dict(aspect='equal'))
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# naive projection
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ax = axes[0]
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ax.set_title('naïve projection', loc='right')
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ax.set_xlim(-5.0, 3.5)
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ax.set_ylim(-3.5, 2.0)
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ax.scatter(*a.T, edgecolor='xkcd:slate grey', c='xkcd:dark yellow')
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ax.scatter(*b.T, edgecolor='xkcd:slate grey', c='xkcd:pale purple')
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dir = rot @ w1
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line(ax, m1, m2, c='xkcd:charcoal')
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line(ax, (m1 + m2)/2, (m1 + m2)/2 + 2.2*dir, c='xkcd:charcoal')
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line(ax, dir*2.1 - 2.0*w1, dir*2.1 + 2.6*w1, c='xkcd:charcoal')
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place_im(
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ax,
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proj_hist(a, b, w1),
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trans.Affine2D()
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.rotate(angle(w1))
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.translate(*dir*3.113)
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.translate(*w1*(-0.7)))
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# fisher projection
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ax = axes[1]
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ax.set_title('Fisher projection', loc='right')
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ax.set_xlim(-5.0, 3.5)
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ax.set_ylim(-3.5, 2.0)
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ax.scatter(*a.T, edgecolor='xkcd:slate grey', c='xkcd:dark yellow')
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ax.scatter(*b.T, edgecolor='xkcd:slate grey', c='xkcd:pale purple')
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dir = rot @ w2
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line(ax, m1, m2, c='xkcd:charcoal')
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line(ax, (m1 + m2)/2, (m1 + m2)/2 + 2.75*dir, c='xkcd:charcoal')
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line(ax, dir*2.9 - 1.2*w2, dir*2.9 + 2.3*w2, c='xkcd:charcoal')
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place_im(
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ax,
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proj_hist(a, b, w2),
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trans.Affine2D()
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.rotate(angle(w2))
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.scale(0.75)
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.translate(*dir*3.90)
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.translate(*w2*(-0.3)))
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plt.tight_layout()
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#plt.savefig('notes/images/7-fisher.pdf', bbox_inches='tight')
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plt.show()
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if __name__ == '__main__':
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main()
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