Ex 3: The iris 鳶尾花資料集

機器學習資料集/ 範例三: The iris dataset

http://scikit-learn.org/stable/auto_examples/datasets/plot_iris_dataset.html

這個範例目的是介紹機器學習範例資料集中的iris 鳶尾花資料集

(一)引入函式庫及內建手寫數字資料庫

#這行是在ipython notebook的介面裏專用，如果在其他介面則可以拿掉
%matplotlib inline

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from sklearn import datasets
from sklearn.decomposition import PCA

# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2]  # we only take the first two features.
Y = iris.target

x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5

plt.figure(2, figsize=(8, 6))
plt.clf()
# Plot the training points
plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.Paired)
plt.xlabel('Sepal length')
plt.ylabel('Sepal width')

plt.xlim(x_min, x_max)
plt.ylim(y_min, y_max)
plt.xticks(())
plt.yticks(())

png

(二)資料集介紹

iris = datasets.load_iris() 將一個dict型別資料存入iris，我們可以用下面程式碼來觀察裏面資料

for key,value in iris.items() :
    try:
        print (key,value.shape)
    except:
        print (key)
print(iris['feature_names'])

顯示	說明
('target_names', (3L,))	共有三種鳶尾花 setosa, versicolor, virginica
('data', (150L, 4L))	有150筆資料，共四種特徵
('target', (150L,))	這150筆資料各是那一種鳶尾花
DESCR	資料之描述
feature_names	四個特徵代表的意義，分別為 萼片(sepal)之長與寬以及花瓣(petal)之長與寬

為了用視覺化方式呈現這個資料集，下面程式碼首先使用PCA演算法將資料維度降低至3

X_reduced = PCA(n_components=3).fit_transform(iris.data)

接下來將三個維度的資料立用mpl_toolkits.mplot3d.Axes3D 建立三維繪圖空間，並利用 scatter以三個特徵資料數值當成座標繪入空間，並以三種iris之數值 Y，來指定資料點的顏色。我們可以看出三種iris中，有一種明顯的可以與其他兩種區別，而另外兩種則無法明顯區別。

# To getter a better understanding of interaction of the dimensions
# plot the first three PCA dimensions
fig = plt.figure(1, figsize=(8, 6))
ax = Axes3D(fig, elev=-150, azim=110)
ax.scatter(X_reduced[:, 0], X_reduced[:, 1], X_reduced[:, 2], c=Y,
           cmap=plt.cm.Paired)
ax.set_title("First three PCA directions")
ax.set_xlabel("1st eigenvector")
ax.w_xaxis.set_ticklabels([])
ax.set_ylabel("2nd eigenvector")
ax.w_yaxis.set_ticklabels([])
ax.set_zlabel("3rd eigenvector")
ax.w_zaxis.set_ticklabels([])

plt.show()

png

#接著我們嘗試將這個機器學習資料之描述檔顯示出來
print(iris['DESCR'])

Iris Plants Database

Notes
-----
Data Set Characteristics:
    :Number of Instances: 150 (50 in each of three classes)
    :Number of Attributes: 4 numeric, predictive attributes and the class
    :Attribute Information:
        - sepal length in cm
        - sepal width in cm
        - petal length in cm
        - petal width in cm
        - class:
                - Iris-Setosa
                - Iris-Versicolour
                - Iris-Virginica
    :Summary Statistics:

    ============== ==== ==== ======= ===== ====================
                    Min  Max   Mean    SD   Class Correlation
    ============== ==== ==== ======= ===== ====================
    sepal length:   4.3  7.9   5.84   0.83    0.7826
    sepal width:    2.0  4.4   3.05   0.43   -0.4194
    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)
    petal width:    0.1  2.5   1.20  0.76     0.9565  (high!)
    ============== ==== ==== ======= ===== ====================

    :Missing Attribute Values: None
    :Class Distribution: 33.3% for each of 3 classes.
    :Creator: R.A. Fisher
    :Donor: Michael Marshall ([e-mail])
    :Date: July, 1988

This is a copy of UCI ML iris datasets.
http://archive.ics.uci.edu/ml/datasets/Iris

The famous Iris database, first used by Sir R.A Fisher

This is perhaps the best known database to be found in the
pattern recognition literature.  Fisher's paper is a classic in the field and
is referenced frequently to this day.  (See Duda & Hart, for example.)  The
data set contains 3 classes of 50 instances each, where each class refers to a
type of iris plant.  One class is linearly separable from the other 2; the
latter are NOT linearly separable from each other.

References
----------
   - Fisher,R.A. "The use of multiple measurements in taxonomic problems"
     Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions to
     Mathematical Statistics" (John Wiley, NY, 1950).
   - Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis.
     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.
   - Dasarathy, B.V. (1980) "Nosing Around the Neighborhood: A New System
     Structure and Classification Rule for Recognition in Partially Exposed
     Environments".  IEEE Transactions on Pattern Analysis and Machine
     Intelligence, Vol. PAMI-2, No. 1, 67-71.
   - Gates, G.W. (1972) "The Reduced Nearest Neighbor Rule".  IEEE Transactions
     on Information Theory, May 1972, 431-433.
   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al"s AUTOCLASS II
     conceptual clustering system finds 3 classes in the data.
   - Many, many more ...

這個描述檔說明了這個資料集是在 1936年時由Fisher建立，為圖形識別領域之重要經典範例。共例用四種特徵來分類三種鳶尾花

(三)應用範例介紹

在整個scikit-learn應用範例中，有以下幾個範例是利用了這組iris資料集。

• 分類法 Classification

  • EX 3: Plot classification probability

• 特徵選擇 Feature Selection

  • Ex 5: Test with permutations the significance of a classification score

  • Ex 6: Univariate Feature Selection

• 通用範例 General Examples

  • Ex 2: Concatenating multiple feature extraction methods