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A Little Book of Python for Multivariate Analysis

This booklet tells you how to use the Python ecosystem to carry out some simple multivariate analyses, with a focus on principal components analysis (PCA) and linear discriminant analysis (LDA).

This booklet assumes that the reader has some basic knowledge of multivariate analyses, and the principal focus of the booklet is not to explain multivariate analyses, but rather to explain how to carry out these analyses using Python.

If you are new to multivariate analysis, and want to learn more about any of the concepts presented here, there are a number of good resources, such as for example Multivariate Data Analysis by Hair et. al. or Applied Multivariate Data Analysis by Everitt and Dunn.

In the examples in this booklet, I will be using data sets from the UCI Machine Learning Repository [http://archive.ics.uci.edu/ml] .

Setting up the python environment
Install Python

Although there are a number of ways of getting Python to your system, for a hassle free install and quick start using, I highly recommend downloading and installing Anaconda [https://www.continuum.io/downloads] by Continuum [https://www.continuum.io] , which is a Python distribution that contains the core packages plus a large number of packages for scientific computing and tools to easily update them, install new ones, create virtual environments, and provide IDEs such as this one, the Jupyter notebook [https://jupyter.org] (formerly known as ipython notebook).

This notebook was created with python 2.7 version. For exact details, including versions of the other libraries, see the %watermark directive below.

Libraries

Python [https://en.wikipedia.org/wiki/Python_%28programming_language%29] can typically do less out of the box than other languages, and this is due to being a genaral programming language taking a more modular approach, relying on other packages for specialized tasks.

The following libraries are used here:

  • pandas [http://pandas.pydata.org] : The Python Data Analysis Library is used for storing the data in dataframes and manipulation.
  • numpy [http://www.numpy.org] : Python scientific computing library.
  • matplotlib [http://matplotlib.org] : Python plotting library.
  • seaborn [http://stanford.edu/~mwaskom/software/seaborn/] : Statistical data visualization based on matplotlib.
  • scikit-learn [http://scikit-learn.org/stable/] : Sklearn is a machine learning library for Python.
  • scipy.stats [http://docs.scipy.org/doc/scipy/reference/stats.html] : Provides a number of probability distributions and statistical functions.

These should have been installed for you if you have installed the Anaconda Python distribution.

The libraries versions are:

from __future__ import print_function, division # for compatibility with python 3.ximport warningswarnings.filterwarnings('ignore') # don't print out warnings%install_ext https://raw.githubusercontent.com/rasbt/watermark/master/watermark.py%load_ext watermark%watermark -v -m -p python,pandas,numpy,matplotlib,seaborn,scikit-learn,scipy -g
Installed watermark.py. To use it, type: %load_ext watermarkCPython 2.7.11IPython 4.0.3python 2.7.11pandas 0.17.1numpy 1.10.4matplotlib 1.5.1seaborn 0.7.0scikit-learn 0.17scipy 0.17.0compiler : GCC 4.2.1 (Apple Inc. build 5577)system : Darwinrelease : 13.4.0machine : x86_64processor : i386CPU cores : 4interpreter: 64bitGit hash : b584574b9a5080bac2e592d4432f9c17c1845c18
Importing the libraries
from pydoc import help # can type in the python console `help(name of function)` to get the documentationimport pandas as pdimport numpy as npimport matplotlib.pyplot as pltimport seaborn as snsfrom sklearn.preprocessing import scalefrom sklearn.decomposition import PCAfrom sklearn.discriminant_analysis import LinearDiscriminantAnalysisfrom scipy import statsfrom IPython.display import display, HTML# figures inline in notebook%matplotlib inlinenp.set_printoptions(suppress=True)DISPLAY_MAX_ROWS = 20 # number of max rows to print for a DataFramepd.set_option('display.max_rows', DISPLAY_MAX_ROWS)
Python console

A useful tool to have aside a notebook for quick experimentation and data visualization is a python console attached. Uncomment the following line if you wish to have one.

# %qtconsole
Reading Multivariate Analysis Data into Python

The first thing that you will want to do to analyse your multivariate data will be to read it into Python, and to plot the data. For data analysis an I will be using the Python Data Analysis Library [http://pandas.pydata.org] (pandas, imported as pd ), which provides a number of useful functions for reading and analyzing the data, as well as a DataFrame storage structure, similar to that found in other popular data analytics languages, such as R.

For example, the file http://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data contains data on concentrations of 13 different chemicals in wines grown in the same region in Italy that are derived from three different cultivars. The data set looks like this:

, 14.23 , 1.71 , 2.43 , 15.6 , , 2.8 , 3.06 , . , 2.29 , 5.64 , 1.04 , 3.92 , 1065 , 13.2 , 1.78 , 2.14 , 11.2 , , 2.65 , 2.76 , . , 1.28 , 4.38 , 1.05 , 3.4 , 1050 , 13.16 , 2.36 , 2.67 , 18.6 , , 2.8 , 3.24 , . , 2.81 , 5.68 , 1.03 , 3.17 , 1185 , 14.37 , 1.95 , 2.5 , 16.8 , , 3.85 , 3.49 , . , 2.18 , 7.8 , . , 3.45 , 1480 , 13.24 , 2.59 , 2.87 , , , 2.8 , 2.69 , . , 1.82 , 4.32 , 1.04 , 2.93 , ...

There is one row per wine sample. The first column contains the cultivar of a wine sample (labelled 1, 2 or 3), and the following thirteen columns contain the concentrations of the 13 different chemicals in that sample. The columns are separated by commas, i.e. it is a comma-separated (csv) file without a header row.

The data can be read in a pandas dataframe using the read_csv() function. The argument header=None tells the function that there is no header in the beginning of the file.

data = pd . read_csv ( "http://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data" , header = None ) data . columns = [ "V" + str ( i ) for i in range ( , len ( data . columns ) + )] # rename column names to be similar to R naming convention data . V1 = data . V1 . astype ( str ) X = data . loc [:, "V2" :] # independent variables data y = data . V1 # dependednt variable data data
V1V2V3V4V5V6V7V8V9V10V11V12V13V14
0114.231.712.4315.61272.803.060.282.295.6400001.043.921065
1113.201.782.1411.21002.652.760.261.284.3800001.053.401050
2113.162.36
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