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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 <small><i>This notebook was put together by Jake Vanderplas. Source and license info is on GitHub.</i></small>
Introduction to Scikit-Learn
Step1:  This may seem like a trivial task, but it is a simple version of a very important concept.
By drawing this separating line, we have learned a model which can generalize to new
data
Step2:  Again, this is an example of fitting a model to data, such that the model can make
generalizations about new data.  The model has been learned from the training
data, and can be used to predict the result of test data
Step3:  Quick Question
Step4:  This data is four dimensional, but we can visualize two of the dimensions
at a time using a simple scatter-plot
Step5:  Quick Exercise
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Python Code:
%matplotlib inline
import matplotlib.pyplot as plt
plt.style.use('seaborn')
# Import the example plot from the figures directory
from fig_code import plot_sgd_separator
plot_sgd_separator()
Explanation: <small><i>This notebook was put together by Jake Vanderplas. Source and license info is on GitHub.</i></small>
Introduction to Scikit-Learn: Machine Learning with Python
This session will cover the basics of Scikit-Learn, a popular package containing a collection of tools for machine learning written in Python. See more at http://scikit-learn.org.
Outline
Main Goal: To introduce the central concepts of machine learning, and how they can be applied in Python using the Scikit-learn Package.
Definition of machine learning
Data representation in scikit-learn
Introduction to the Scikit-learn API
About Scikit-Learn
Scikit-Learn is a Python package designed to give access to well-known machine learning algorithms within Python code, through a clean, well-thought-out API. It has been built by hundreds of contributors from around the world, and is used across industry and academia.
Scikit-Learn is built upon Python's NumPy (Numerical Python) and SciPy (Scientific Python) libraries, which enable efficient in-core numerical and scientific computation within Python. As such, scikit-learn is not specifically designed for extremely large datasets, though there is some work in this area.
For this short introduction, I'm going to stick to questions of in-core processing of small to medium datasets with Scikit-learn.
What is Machine Learning?
In this section we will begin to explore the basic principles of machine learning.
Machine Learning is about building programs with tunable parameters (typically an
array of floating point values) that are adjusted automatically so as to improve
their behavior by adapting to previously seen data.
Machine Learning can be considered a subfield of Artificial Intelligence since those
algorithms can be seen as building blocks to make computers learn to behave more
intelligently by somehow generalizing rather that just storing and retrieving data items
like a database system would do.
We'll take a look at two very simple machine learning tasks here.
The first is a classification task: the figure shows a
collection of two-dimensional data, colored according to two different class
labels. A classification algorithm may be used to draw a dividing boundary
between the two clusters of points:
End of explanation
from fig_code import plot_linear_regression
plot_linear_regression()
Explanation: This may seem like a trivial task, but it is a simple version of a very important concept.
By drawing this separating line, we have learned a model which can generalize to new
data: if you were to drop another point onto the plane which is unlabeled, this algorithm
could now predict whether it's a blue or a red point.
If you'd like to see the source code used to generate this, you can either open the
code in the figures directory, or you can load the code using the %load magic command:
The next simple task we'll look at is a regression task: a simple best-fit line
to a set of data:
End of explanation
from IPython.core.display import Image, display
display(Image(filename='images/iris_setosa.jpg'))
print("Iris Setosa\n")
display(Image(filename='images/iris_versicolor.jpg'))
print("Iris Versicolor\n")
display(Image(filename='images/iris_virginica.jpg'))
print("Iris Virginica")
Explanation: Again, this is an example of fitting a model to data, such that the model can make
generalizations about new data.  The model has been learned from the training
data, and can be used to predict the result of test data:
here, we might be given an x-value, and the model would
allow us to predict the y value.  Again, this might seem like a trivial problem,
but it is a basic example of a type of operation that is fundamental to
machine learning tasks.
Representation of Data in Scikit-learn
Machine learning is about creating models from data: for that reason, we'll start by
discussing how data can be represented in order to be understood by the computer.  Along
with this, we'll build on our matplotlib examples from the previous section and show some
examples of how to visualize data.
Most machine learning algorithms implemented in scikit-learn expect data to be stored in a
two-dimensional array or matrix.  The arrays can be
either numpy arrays, or in some cases scipy.sparse matrices.
The size of the array is expected to be [n_samples, n_features]
n_samples:   The number of samples: each sample is an item to process (e.g. classify).
  A sample can be a document, a picture, a sound, a video, an astronomical object,
  a row in database or CSV file,
  or whatever you can describe with a fixed set of quantitative traits.
n_features:  The number of features or distinct traits that can be used to describe each
  item in a quantitative manner.  Features are generally real-valued, but may be boolean or
  discrete-valued in some cases.
The number of features must be fixed in advance. However it can be very high dimensional
(e.g. millions of features) with most of them being zeros for a given sample. This is a case
where scipy.sparse matrices can be useful, in that they are
much more memory-efficient than numpy arrays.
(Figure from the Python Data Science Handbook)
A Simple Example: the Iris Dataset
As an example of a simple dataset, we're going to take a look at the
iris data stored by scikit-learn.
The data consists of measurements of three different species of irises.
There are three species of iris in the dataset, which we can picture here:
End of explanation
from sklearn.datasets import load_iris
iris = load_iris()
iris.keys()
n_samples, n_features = iris.data.shape
print((n_samples, n_features))
print(iris.data[10])
print(iris.data.shape)
print(iris.target.shape)
print(iris.target)
print(iris.target_names)
Explanation: Quick Question:
If we want to design an algorithm to recognize iris species, what might the data be?
Remember: we need a 2D array of size [n_samples x n_features].
What would the n_samples refer to?
What might the n_features refer to?
Remember that there must be a fixed number of features for each sample, and feature
number i must be a similar kind of quantity for each sample.
Loading the Iris Data with Scikit-Learn
Scikit-learn has a very straightforward set of data on these iris species.  The data consist of
the following:
Features in the Iris dataset:
sepal length in cm
sepal width in cm
petal length in cm
petal width in cm
Target classes to predict:
Iris Setosa
Iris Versicolour
Iris Virginica
scikit-learn embeds a copy of the iris CSV file along with a helper function to load it into numpy arrays:
End of explanation
import numpy as np
import matplotlib.pyplot as plt
x_index = 2
y_index = 1
# this formatter will label the colorbar with the correct target names
formatter = plt.FuncFormatter(lambda i, *args: iris.target_names[int(i)])
plt.scatter(iris.data[:, x_index], iris.data[:, y_index],
            c=iris.target, cmap=plt.cm.get_cmap('RdYlBu', 3))
plt.colorbar(ticks=[0, 1, 2], format=formatter)
plt.clim(-0.5, 2.5)
plt.xlabel(iris.feature_names[x_index])
plt.ylabel(iris.feature_names[y_index]);
Explanation: This data is four dimensional, but we can visualize two of the dimensions
at a time using a simple scatter-plot:
End of explanation
from sklearn import datasets
# Type datasets.fetch_<TAB> or datasets.load_<TAB> in IPython to see all possibilities
# datasets.fetch_
# datasets.load_
Explanation: Quick Exercise:
Change x_index and y_index in the above script
and find a combination of two parameters
which maximally separate the three classes.
This exercise is a preview of dimensionality reduction, which we'll see later.
Other Available Data
They come in three flavors:
Packaged Data: these small datasets are packaged with the scikit-learn installation,
  and can be downloaded using the tools in sklearn.datasets.load_*
Downloadable Data: these larger datasets are available for download, and scikit-learn
  includes tools which streamline this process.  These tools can be found in
  sklearn.datasets.fetch_*
Generated Data: there are several datasets which are generated from models based on a
  random seed.  These are available in the sklearn.datasets.make_*
You can explore the available dataset loaders, fetchers, and generators using IPython's
tab-completion functionality.  After importing the datasets submodule from sklearn,
type
datasets.load_ + TAB
or
datasets.fetch_ + TAB
or
datasets.make_ + TAB
to see a list of available functions.
End of explanation
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