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scikit-learn Tutorials（4）

2016-02-22 22:45 274 查看

Unsupervised learning: seeking representations of the data 无监督学习：寻找数据表示

Clustering: grouping observations together 簇

The problem solved in clustering
Given the iris dataset, if we knew that there were 3 types of iris, but did not have access to a taxonomist to label them: we could try a clustering task: split the observations
into well-separated group called clusters.

K-means clustering

Note that there exist a lot of different clustering criteria and associated algorithms. The simplest clustering algorithm is K-means.

>>>

>>> from sklearn import cluster, datasets
>>> iris = datasets.load_iris()
>>> X_iris = iris.data
>>> y_iris = iris.target

>>> k_means = cluster.KMeans(n_clusters=3)
>>> k_means.fit(X_iris)
KMeans(copy_x=True, init='k-means++', ...
>>> print(k_means.labels_[::10])
[1 1 1 1 1 0 0 0 0 0 2 2 2 2 2]
>>> print(y_iris[::10])
[0 0 0 0 0 1 1 1 1 1 2 2 2 2 2]

Warning

There is absolutely no guarantee of recovering a ground truth. First, choosing the right number of clusters is hard. Second, the algorithm is sensitive to initialization, and can fall into local minima, although scikit-learn employs several tricks to mitigate
this issue.


Bad initialization	8 clusters	Ground truth

Don’t over-interpret clustering results

Application example: vector quantization

Clustering in general and KMeans, in particular, can be seen as a way of choosing a small number of exemplars to compress the information. The problem is sometimes known as vector
quantization. For instance, this can be used to posterize an image:

>>>

>>> import scipy as sp
>>> try:
...    face = sp.face(gray=True)
... except AttributeError:
...    from scipy import misc
...    face = misc.face(gray=True)     #face.shape=(768,1024)
>>> X = face.reshape((-1, 1)) # We need an (n_sample, n_feature) array  X.shape=(786432, 1)
>>> k_means = cluster.KMeans(n_clusters=5, n_init=1) #n_init查看api还是不太明白是啥意思

>>> k_means.fit(X)
KMeans(copy_x=True, init='k-means++', ...
>>> values = k_means.cluster_centers_.squeeze()

#k_means.cluster_centers_.shaoe=(5,1)    values.shape(1,5)  中心点坐标值

>>> labels = k_means.labels_>>> face_compressed = np.choose(labels, values) #按照每个像素点标签的值，把族的中心点值赋上去>>> face_compressed.shape = face.shape #reshape


Raw image	K-means quantization	Equal bins	Image histogram

Hierarchical agglomerative clustering: Ward #这个没看

A Hierarchical clustering method
is a type of cluster analysis that aims to build a hierarchy of clusters. In general, the various approaches of this technique are either:

Agglomerative - bottom-up approaches: each observation starts in its own cluster, and clusters are iterativelly merged in such a way to minimize a linkage criterion. This approach is particularly interesting
when the clusters of interest are made of only a few observations. When the number of clusters is large, it is much more computationally efficient than k-means.
Divisive - top-down approaches: all observations start in one cluster, which is iteratively split as one moves down the hierarchy. For estimating large numbers of clusters, this approach is both slow (due to all
observations starting as one cluster, which it splits recursively) and statistically ill-posed.

Connectivity-constrained clustering

With agglomerative clustering, it is possible to specify which samples can be clustered together by giving a connectivity graph. Graphs in the scikit are represented by their adjacency matrix.
Often, a sparse matrix is used. This can be useful, for instance, to retrieve connected regions (sometimes also referred to as connected components) when clustering an image:

import matplotlib.pyplot as plt

from sklearn.feature_extraction.image import grid_to_graph
from sklearn.cluster import AgglomerativeClustering
from sklearn.utils.testing import SkipTest
from sklearn.utils.fixes import sp_version

if sp_version < (0, 12):
raise SkipTest("Skipping because SciPy version earlier than 0.12.0 and "
"thus does not include the scipy.misc.face() image.")

###############################################################################
# Generate data
try:
face = sp.face(gray=True)
except AttributeError:
# Newer versions of scipy have face in misc
from scipy import misc
face = misc.face(gray=True)

# Resize it to 10% of the original size to speed up the processing
face = sp.misc.imresize(face, 0.10) / 255.

Feature agglomeration
特征聚类目的和PCA一样，减少特征

We have seen that sparsity could be used to mitigate the curse of dimensionality, i.e an insufficient amount of observations compared to the number of features. Another approach is to merge together similar features: feature agglomeration.
This approach can be implemented by clustering in the feature direction, in other words clustering the transposed data.

>>>

>>> digits = datasets.load_digits()
>>> images = digits.images
>>> X = np.reshape(images, (len(images), -1))  #images.shape=(1797, 8, 8)

#  len(images)=1797     X.shape=(1797, 64)
>>> connectivity = grid_to_graph(*images[0].shape)   #连通性？？？

>>> agglo = cluster.FeatureAgglomeration(connectivity=connectivity,n_clusters=32)
>>> agglo.fit(X)
FeatureAgglomeration(affinity='euclidean', compute_full_tree='auto',...
>>> X_reduced = agglo.transform(X)     #Z=X*Ureduce

>>> X_approx = agglo.inverse_transform(X_reduced)    #X=Z*Ureduce.T
>>> images_approx = np.reshape(X_approx, images.shape)

transform
and
inverse_transform
methods
类似PCA中Z与X的转化

Some estimators expose a

transform

method, for instance to reduce
the dimensionality of the dataset.

Decompositions: from a signal to components and loadings

Components and loadings
If X is our multivariate data, then the problem that we are trying to solve is to rewrite it on a different observational basis: we want to learn loadings L and a set of components C such that X
= L C. Different criteria exist to choose the components

Principal component analysis: PCA

Principal component analysis (PCA) selects the successive
components that explain the maximum variance in the signal.

The point cloud spanned by the observations above is very flat in one direction: one of the three univariate features can almost be exactly computed using the other two. PCA finds the directions in which the data is not flat

When used to transform data, PCA can reduce the dimensionality of the data by projecting on a principal subspace.

>>>

>>> # Create a signal with only 2 useful dimensions
>>> x1 = np.random.normal(size=100)
>>> x2 = np.random.normal(size=100)
>>> x3 = x1 + x2
>>> X = np.c_[x1, x2, x3]

>>> from sklearn import decomposition    #PCA的包
>>> pca = decomposition.PCA()
>>> pca.fit(X)
PCA(copy=True, n_components=None, whiten=False)
>>> print(pca.explained_variance_)
[  2.18565811e+00   1.19346747e+00   8.43026679e-32]    #解释方差要大于0.99

>>> # As we can see, only the 2 first components are useful
>>> pca.n_components = 2                #成分数
>>> X_reduced = pca.fit_transform(X)
>>> X_reduced.shape
(100, 2)

Independent Component Analysis: ICA 独立成分分析

Independent
component analysis (ICA) selects components so that the distribution of their loadings carries a maximum amount of independent information. It is able to recover non-Gaussian independent signals:

>>>

>>> # Generate sample data
>>> time = np.linspace(0, 10, 2000)
>>> s1 = np.sin(2 * time)  # Signal 1 : sinusoidal signal
>>> s2 = np.sign(np.sin(3 * time))  # Signal 2 : square signal
>>> S = np.c_[s1, s2]
>>> S += 0.2 * np.random.normal(size=S.shape)  # Add noise
>>> S /= S.std(axis=0)  # Standardize data
>>> # Mix data
>>> A = np.array([[1, 1], [0.5, 2]])  # Mixing matrix
>>> X = np.dot(S, A.T)  # Generate observations       #np.dot 矩阵相乘

>>> # Compute ICA
>>> ica = decomposition.FastICA()
>>> S_ = ica.fit_transform(X)  # Get the estimated sources
>>> A_ = ica.mixing_.T
>>> np.allclose(X,  np.dot(S_, A_) + ica.mean_)
True

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标签： 机器学习 scikit-learn

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