Why can't LinearSVC do this simple classification?

I'm trying to do the following simple classification using the LinearSVC object in scikit-learn. I've tried using both version 0.10 and 0.14. Using the code:

from sklearn.svm import LinearSVC, SVC
from numpy import *

data = array([[ 1007.,  1076.],
              [ 1017.,  1009.],
              [ 2021.,  2029.],
              [ 2060.,  2085.]])
groups = array([1, 1, 2, 2])

svc = LinearSVC()
svc.fit(data, groups)
svc.predict(data)

I get the output:

array([2, 2, 2, 2])

However, if I replace the classifier with

svc = SVC(kernel='linear')

then I get the result

array([ 1.,  1.,  2.,  2.])

which is correct. Does anyone know why using LinearSVC would botch this simple problem?

Solution

The algorithm underlying LinearSVC is very sensitive to extreme values in its input:

>>> svc = LinearSVC(verbose=1)
>>> svc.fit(data, groups)
[LibLinear]....................................................................................................
optimization finished, #iter = 1000

WARNING: reaching max number of iterations
Using -s 2 may be faster (also see FAQ)

Objective value = -0.001256
nSV = 4
LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,
     intercept_scaling=1, loss='l2', multi_class='ovr', penalty='l2',
     random_state=None, tol=0.0001, verbose=1)

(The warning refers to the LibLinear FAQ, since scikit-learn's LinearSVC is based on that library.)

You should normalize before fitting:

>>> from sklearn.preprocessing import scale
>>> data = scale(data)
>>> svc.fit(data, groups)
[LibLinear]...
optimization finished, #iter = 39
Objective value = -0.240988
nSV = 4
LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,
     intercept_scaling=1, loss='l2', multi_class='ovr', penalty='l2',
     random_state=None, tol=0.0001, verbose=1)
>>> svc.predict(data)
array([1, 1, 2, 2])