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Orthogonal Matching Pursuit in Scikit-learn

Using orthogonal matching pursuit for recovering a sparse signal from a noisy measurement encoded with a dictionary.

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Version

In [1]:
import sklearn
sklearn.__version__
Out[1]:
'0.18.1'

Imports

In [2]:
import plotly.plotly as py
import plotly.graph_objs as go
import numpy as np
from sklearn.linear_model import OrthogonalMatchingPursuit
from sklearn.linear_model import OrthogonalMatchingPursuitCV
from sklearn.datasets import make_sparse_coded_signal

Calculations

In [3]:
n_components, n_features = 512, 100
n_nonzero_coefs = 17

# generate the data
###################
# y = Xw
# |x|_0 = n_nonzero_coefs
y, X, w = make_sparse_coded_signal(n_samples=1,
                                   n_components=n_components,
                                   n_features=n_features,
                                   n_nonzero_coefs=n_nonzero_coefs,
                                   random_state=0)

idx, = w.nonzero()

Distort the clean signal

In [4]:
y_noisy = y + 0.05 * np.random.randn(len(y))

Plot The Sparse Signal

In [5]:
data=[]

trace1 = go.Scatter(x=idx, y=w[idx], mode='markers',
                    marker=dict(color='blue'),
                    showlegend=False)
data.append(trace1)

for i in range(0, len(idx)):
    trace = go.Scatter(x= [idx[i], idx[i]], y=[0, w[idx][i]],
                       mode='lines',
                       line=dict(color='blue', width=1),
                       showlegend=False
                      )
    data.append(trace)
    
layout = go.Layout(title='The Sparse Signal', hovermode='closest')
fig = go.Figure(data=data, layout=layout)
In [6]:
py.iplot(fig)
Out[6]:

Plot The Noise-Free Reconstruction

In [7]:
omp = OrthogonalMatchingPursuit(n_nonzero_coefs=n_nonzero_coefs)
omp.fit(X, y)
coef = omp.coef_
idx_r, = coef.nonzero()
In [8]:
data=[]

trace1 = go.Scatter(x=idx_r, y=coef[idx_r], mode='markers',
                    marker=dict(color='blue'),
                    showlegend=False)
data.append(trace1)

for i in range(0, len(idx)):
    trace = go.Scatter(x= [idx_r[i], idx_r[i]], y=[0, coef[idx_r][i]],
                       mode='lines',
                       line=dict(color='blue', width=1), showlegend=False
                      )
    data.append(trace)
    
layout = go.Layout(title='Recovered Signal From Noise-Free Measurements',
                   hovermode='closest')
fig = go.Figure(data=data, layout=layout)
In [9]:
py.iplot(fig)
Out[9]:

Plot the Noisy Reconstruction With Number of Non-Zeros Set by CV

In [10]:
omp.fit(X, y_noisy)
coef = omp.coef_
idx_r, = coef.nonzero()
In [11]:
data=[]

trace1 = go.Scatter(x=idx_r, y=coef[idx_r], mode='markers',
                    marker=dict(color='blue'),
                    showlegend=False)
data.append(trace1)

for i in range(0, len(idx)):
    trace = go.Scatter(x= [idx_r[i], idx_r[i]], y=[0, coef[idx_r][i]],
                       mode='lines',
                       line=dict(color='blue', width=1),
                       showlegend=False
                      )
    data.append(trace)
    
layout = go.Layout(title='Recovered signal from noisy measurements with CV',
                   hovermode='closest')
fig = go.Figure(data=data, layout=layout)
In [12]:
py.iplot(fig)
Out[12]:
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