Заметка 3. Классификация на примере распознавания рукописных цифр. курса Введение в машинное обучение. Шокуров Антон В. shokurov.anton.v@yandex.ru http://машинноезрение.рф Версия 0.11

Анотация

Вводятся понятие классификации на базе библиотек scikit-learn. Рассмотрены как минимум следующие классификаторы: svm (Support Vector Machine, метод опорных векторов) включая ядровый трюк, MLP (Multi-layer Perceptron, Многослойный перцептрон, нейронные сети), SGD (Stochastic Gradient Descent, Стохастический градиентный спуск) и RidgeClassifier (ridge classification, гребневый классификатор). В процессе изложения показано насколько важную роль играют параметры того или иного метода.

Это предварительная версия! Любые замечания приветсвуются.

import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
%matplotlib inline

from sklearn import svm, metrics, linear_model, neural_network
from sklearn.datasets import load_digits

X = [[0, 0], [1, 1]]
y = [0, 1]

clf = svm.SVC( kernel = 'poly' ) #LinearSVC() #SVC()

clf.fit(X, y)

SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
  decision_function_shape='ovr', degree=3, gamma='auto', kernel='poly',
  max_iter=-1, probability=False, random_state=None, shrinking=True,
  tol=0.001, verbose=False)

x = np.linspace(-1, 2, 50)
y = np.linspace(-1, 2, 50)

Xx, Xy = np.meshgrid(x, y)
#Xy.shape, Xx[0].shape

#XX = []
Z = np.zeros( (x.shape[0], y.shape[0]) )
for i in range( x.shape[0] ):
    for j in range( y.shape[0] ):
        #print( [Xx[j][i], Xy[j][i]] )
        Z[i,j] = clf.decision_function( [[Xx[j][i], Xy[j][i]]] )
        #XX.append(  )
#Z.shap
Z

array([[-1.5       , -1.41094591, -1.32734235, ..., -0.41552521,
        -0.39658221, -0.375     ],
       [-1.41094591, -1.32734235, -1.2490172 , ..., -0.39658221,
        -0.375     , -0.35060646],
       [-1.32734235, -1.2490172 , -1.17579835, ..., -0.375     ,
        -0.35060646, -0.32322948],
       ...,
       [-0.41552521, -0.39658221, -0.375     , ...,  6.11873879,
         6.44778855,  6.78756726],
       [-0.39658221, -0.375     , -0.35060646, ...,  6.44778855,
         6.78756726,  7.13824703],
       [-0.375     , -0.35060646, -0.32322948, ...,  6.78756726,
         7.13824703,  7.5       ]])

np.c_[Xx.ravel(), Xy.ravel()]

array([[-1.        , -1.        ],
       [-0.93877551, -1.        ],
       [-0.87755102, -1.        ],
       ...,
       [ 1.87755102,  2.        ],
       [ 1.93877551,  2.        ],
       [ 2.        ,  2.        ]])

Xx.ravel()

array([-1.        , -0.93877551, -0.87755102, ...,  1.87755102,
        1.93877551,  2.        ])

np.c_[[1,2],[-2,-4]]

array([[ 1, -2],
       [ 2, -4]])

Z = clf.predict( np.c_[Xx.ravel(), Xy.ravel()] )
# Put the result into a color plot
Z = Z.reshape( Xx.shape )

#plt.plot( Z, c='r')
plt.contour(x, y, Z)

<matplotlib.contour.QuadContourSet at 0x7f4fde45f940>

digits = load_digits()

digits.keys()

dict_keys(['data', 'target', 'target_names', 'images', 'DESCR'])

digits['target'].shape

(1797,)

digits['images'][74]

array([[ 0.,  0., 13., 13.,  8.,  2.,  0.,  0.],
       [ 0.,  5., 16., 16., 16., 12.,  0.,  0.],
       [ 0.,  1., 15., 12.,  0.,  0.,  0.,  0.],
       [ 0.,  0., 12., 13.,  7.,  1.,  0.,  0.],
       [ 0.,  0.,  8., 16., 16., 12.,  0.,  0.],
       [ 0.,  0.,  0.,  4.,  9., 16.,  3.,  0.],
       [ 0.,  0.,  1.,  5., 14., 15.,  1.,  0.],
       [ 0.,  0., 10., 16., 16.,  6.,  0.,  0.]])

dig = digits['images'][74] #74
plt.imshow( dig )

<matplotlib.image.AxesImage at 0x7f4fde2865f8>

img = np.zeros((dig.shape[0], dig.shape[1], 3))
img[:,:,0] = dig
img[:,:,1] = dig
img[:,:,2] = dig
np.max(img), img.shape

(16.0, (8, 8, 3))

plt.imshow( img )

Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).

<matplotlib.image.AxesImage at 0x7f4fde1a7f98>

digits['target_names']

array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

clf.fit( digits['data'][:1400], digits['target'][:1400] )

SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
  decision_function_shape='ovr', degree=3, gamma='auto', kernel='poly',
  max_iter=-1, probability=False, random_state=None, shrinking=True,
  tol=0.001, verbose=False)

pred = clf.predict( digits['data'][1400:] )

pred[232], digits['target'][1400:][232]

(3, 3)

sum( digits['target'][1400:] == pred )

378

pred.shape

(397,)

378/397

0.9521410579345088

def train( clf, data, labels ):
    n = data.shape[0]
    perm = np.random.permutation( n )
    tr_n = int(0.85 * n)
    train = perm[ :tr_n ]
    valid = perm[ tr_n: ]

    train_dig = data[ train ]
    train_lab = labels[ train ]

    valid_dig = data[ valid ]
    valid_lab = labels[ valid ]

    clf.fit( train_dig, train_lab )

    val_cnt = sum( clf.predict( valid_dig ) == valid_lab ) 
    return clf.predict( valid_dig ), valid_lab #val_cnt / valid_lab.shape[0]

ll = []
for k in range( 2000 ):
    clf = svm.SVC( kernel = 'poly' )
    tr, vl = train( clf, digits['data'], digits['target'] )
    eq = tr == vl
    ll.append( np.sum(eq)/eq.shape[0] )

ll

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np.mean(ll), np.std(ll)

(0.9881685185185185, 0.0060978191586077545)

params = sp.stats.t.fit( ll )
params

(87.43591832853579, 0.9881944573672035, 0.00602764768205021)

dat=sp.stats.norm.pdf( np.arange(0.965, 1, 0.001 ), loc = params[1], scale = params[2] )

np.arange(0.965, 1, 0.01)

array([0.965, 0.975, 0.985, 0.995])

plt.hist( ll, 30 )
plt.plot( np.arange(0.965, 1, 0.001), dat*8 )

[<matplotlib.lines.Line2D at 0x7f4fde11b390>]

clf = svm.SVC( kernel = 'poly' )
pred, valid = train( clf, digits['data'], digits['target'] )

?metrics.classification_report

print( metrics.classification_report( [1,1,1,1,2,1], [1,2,1,1,2,2] ) )

             precision    recall  f1-score   support

          1       1.00      0.60      0.75         5
          2       0.33      1.00      0.50         1

avg / total       0.89      0.67      0.71         6

print( metrics.classification_report( [0,2,2], [1,2,1] ) )

             precision    recall  f1-score   support

          0       0.00      0.00      0.00         1
          1       0.00      0.00      0.00         0
          2       1.00      0.50      0.67         2

avg / total       0.67      0.33      0.44         3

/data/conda/anaconda3/envs/data_analysis/lib/python3.6/site-packages/sklearn/metrics/classification.py:1135: UndefinedMetricWarning: Precision and F-score are ill-defined and being set to 0.0 in labels with no predicted samples.
  'precision', 'predicted', average, warn_for)
/data/conda/anaconda3/envs/data_analysis/lib/python3.6/site-packages/sklearn/metrics/classification.py:1137: UndefinedMetricWarning: Recall and F-score are ill-defined and being set to 0.0 in labels with no true samples.
  'recall', 'true', average, warn_for)

print( metrics.classification_report( pred, valid ) )

             precision    recall  f1-score   support

          0       1.00      1.00      1.00        28
          1       1.00      0.96      0.98        25
          2       1.00      1.00      1.00        31
          3       1.00      0.97      0.98        33
          4       1.00      1.00      1.00        31
          5       1.00      0.96      0.98        23
          6       1.00      1.00      1.00        24
          7       1.00      1.00      1.00        29
          8       0.95      1.00      0.98        20
          9       0.93      1.00      0.96        26

avg / total       0.99      0.99      0.99       270

clf = linear_model.RidgeClassifier()
pred, valid = train( clf, digits['data'], digits['target'] )

qq = pred == valid
#q3q

sum(qq)/qq.shape[0]

0.9296296296296296

clf = svm.LinearSVC()
pred, valid = train( clf, digits['data'], digits['target'] )
qq = pred == valid
sum(qq)/qq.shape[0]

0.9407407407407408

clf.support_vectors_.shape

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-43-204150e58c58> in <module>
----> 1 clf.support_vectors_.shape

AttributeError: 'LinearSVC' object has no attribute 'support_vectors_'

clf = svm.SVC()
pred, valid = train( clf, digits['data'], digits['target'] )
qq = pred == valid
sum(qq)/qq.shape[0]

0.5481481481481482

clf = svm.SVC( gamma = 0.001 )
pred, valid = train( clf, digits['data'], digits['target'] )
qq = pred == valid
sum(qq)/qq.shape[0]

0.9740740740740741

clf = neural_network.MLPClassifier( )
pred, valid = train( clf, digits['data'], digits['target'] )
qq = pred == valid
sum(qq)/qq.shape[0]

0.9814814814814815

clf = linear_model.SGDClassifier()
pred, valid = train( clf, digits['data'], digits['target'] )
qq = pred == valid
sum(qq)/qq.shape[0]

/data/conda/anaconda3/envs/data_analysis/lib/python3.6/site-packages/sklearn/linear_model/stochastic_gradient.py:128: FutureWarning: max_iter and tol parameters have been added in <class 'sklearn.linear_model.stochastic_gradient.SGDClassifier'> in 0.19. If both are left unset, they default to max_iter=5 and tol=None. If tol is not None, max_iter defaults to max_iter=1000. From 0.21, default max_iter will be 1000, and default tol will be 1e-3.
  "and default tol will be 1e-3." % type(self), FutureWarning)

0.9296296296296296