Learning Data Mining with Python - Second Edition

The Python programming language is a fantastic, versatile, and an easy to use language.

For this book, we will be using Python 3.5, which is available for your system from the Python Organization's website https://www.python.org/downloads/. However, I recommend that you use Anaconda to install Python, which you can download from the official website at https://www.continuum.io/downloads.

In this book, I assume that you have some knowledge of programming and Python itself. You do not need to be an expert with Python to complete this book, although a good level of knowledge will help. I will not be explaining general code structures and syntax in this book, except where it is different from what is considered normal python coding practice.

If you do not have any experience with programming, I recommend that you pick up the Learning Python book from Packt Publishing, or the book Dive Into Python, available online at www.diveintopython3.net

The Python organization also maintains a list of two online tutorials for those new to Python:

               https://wiki.python.org/moin/BeginnersGuide/NonProgrammers

                https://wiki.python.org/moin/BeginnersGuide/ProgrammersWindows users will need to set an environment variable to use Python from the command line, where other systems will usually be immediately executable. We set it in the following steps

Once you have Python running on your system, you should be able to open a command prompt and can run the following code to be sure it has installed correctly.

    $ python
    Python 3.5.1 (default, Apr 11 2014, 13:05:11)
    [GCC 4.8.2] on Linux
    Type "help", "copyright", "credits" or "license" for more 
      information.
    >>> print("Hello, world!")
Hello, world!
    >>> exit()

Note that we will be using the dollar sign ($) to denote that a command that you type into the terminal (also called a shell or cmd on Windows). You do not need to type this character (or retype anything that already appears on your screen). Just type in the rest of the line and press Enter.

After you have the above "Hello, world!" example running, exit the program and move on to installing a more advanced environment to run Python code, the Jupyter Notebook.

Jupyter is a platform for Python development that contains some tools and environments for running Python and has more features than the standard interpreter. It contains the powerful Jupyter Notebook, which allows you to write programs in a web browser. It also formats your code, shows output, and allows you to annotate your scripts. It is a great tool for exploring datasets and we will be using it as our main environment for the code in this book.

To install the Jupyter Notebook on your computer, you can type the following into a command line prompt (not into Python):

$ conda install jupyter notebook

You will not need administrator privileges to install this, as Anaconda keeps packages in the user's directory.

With the Jupyter Notebook installed, you can launch it with the following:

$ jupyter notebook

Running this command will do two things. First, it will create a Jupyter Notebook instance - the backend - that will run in the command prompt you just used. Second, it will launch your web browser and connect to this instance, allowing you to create a new notebook. It will look something like the following screenshot (where you need to replace /home/bob with your current working directory):

To stop the Jupyter Notebook from running, open the command prompt that has the instance running (the one you used earlier to run the jupyter notebook   command). Then, press Ctrl + C and you will be prompted Shutdown this notebook server (y/[n])?. Type y and press Enter and the Jupyter Notebook will shut down.

The scikit-learn package is a machine learning library, written in Python (but also containing code in other languages). It contains numerous algorithms, datasets, utilities, and frameworks for performing machine learning. Scikit-learnis built upon the scientific python stack, including libraries such as the NumPy and SciPy for speed. Scikit-learn is fast and scalable in many instances and useful for all skill ranges from beginners to advanced research users. We will cover more details of scikit-learn in Chapter 2, Classifying with scikit-learn Estimators.

To install scikit-learn, you can use the conda utility that comes with Python 3, which will also install the NumPy and SciPy libraries if you do not already have them. Open a terminal with administrator/root privileges and enter the following command:

$ conda install scikit-learn

Users of major Linux distributions such as Ubuntu or Red Hat may wish to install the official package from their package manager.

Those wishing to install the latest version by compiling the source, or view more detailed installation instructions, can go to http://scikit-learn.org/stable/install.html and refer the official documentation on installing scikit-learn.

Affinity analysis is a type of data mining that gives similarity between samples (objects). This could be the similarity between the following:

We can measure affinity in several ways. For instance, we can record how frequently two products are purchased together. We can also record the accuracy of the statement when a person buys object 1 and when they buy object 2. Other ways to measure affinity include computing the similarity between samples, which we will cover in later chapters.

The dataset can be downloaded from the code package supplied with the book, or from the official GitHub repository at:  https://github.com/dataPipelineAU/LearningDataMiningWithPython2 Download this file and save it on your computer, noting the path to the dataset. It is easiest to put it in the directory you'll run your code from, but we can load the dataset from anywhere on your computer.

For this example, I recommend that you create a new folder on your computer to store your dataset and code. From here, open your Jupyter Notebook, navigate to this folder, and create a new notebook.

The dataset we are going to use for this example is a NumPy two-dimensional array, which is a format that underlies most of the examples in the rest of the book. The array looks like a table, with rows representing different samples and columns representing different features.

The cells represent the value of a specific feature of a specific sample. To illustrate, we can load the dataset with the following code:

import numpy as np 
dataset_filename = "affinity_dataset.txt" 
X = np.loadtxt(dataset_filename)

Enter the previous code into the first cell of your (Jupyter) Notebook. You can then run the code by pressing Shift + Enter (which will also add a new cell for the next section of code). After the code is run, the square brackets to the left-hand side of the first cell will be assigned an incrementing number, letting you know that this cell has completed. The first cell should look like the following:

This dataset has 100 samples and five features, which we will need to know for the later code. Let's extract those values using the following code:

n_samples, n_features = X.shape

If you choose to store the dataset somewhere other than the directory your Jupyter Notebooks are in, you will need to change the dataset_filename value to the new location.

Next, we can show some of the rows of the dataset to get an understanding of the data. Enter the following line of code into the next cell and run it, to print the first five lines of the dataset:

print(X[:5])

The result will show you which items were bought in the first five transactions listed:

[[ 0.  1.  0.  0.  0.] 
 [ 1.  1.  0.  0.  0.] 
 [ 0.  0.  1.  0.  1.] 
 [ 1.  1.  0.  0.  0.] 
 [ 0.  0.  1.  1.  1.]]

features = ["bread", "milk", "cheese", "apples", "bananas"]

We wish to find rules of the type If a person buys product X, then they are likely to purchase product Y. We can quite easily create a list of all the rules in our dataset by simply finding all occasions when two products are purchased together. However, we then need a way to determine good rules from bad ones allowing us to choose specific products to recommend.

We can evaluate rules of this type in many ways, on which we will focus on two: support and confidence.

Support is the number of times that a rule occurs in a dataset, which is computed by simply counting the number of samples for which the rule is valid. It can sometimes be normalized by dividing by the total number of times the premise of the rule is valid, but we will simply count the total for this implementation.

While the support measures how often a rule exists, confidence measures how accurate they are when they can be used. You can compute this by determining the percentage of times the rule applies when the premise applies. We first count how many times a rule applies to our data and divide it by the number of samples where the premise (the if statement) occurs.

As an example, we will compute the support and confidence for the rule if a person buys apples, they also buy bananas.

As the following example shows, we can tell whether someone bought apples in a transaction, by checking the value of sample[3], where we assign a sample to a row of our matrix:

sample = X[2]

Similarly, we can check if bananas were bought in a transaction by seeing if the value of sample[4] is equal to 1 (and so on). We can now compute the number of times our rule exists in our dataset and, from that, the confidence and support.

Now we need to compute these statistics for all rules in our database. We will do this by creating a dictionary for both valid rules and invalid rules. The key to this dictionary will be a tuple (premise and conclusion). We will store the indices, rather than the actual feature names. Therefore, we would store (3 and 4) to signify the previous rule If a person buys apples, they will also buy bananas. If the premise and conclusion are given, the rule is considered valid. While if the premise is given but the conclusion is not, the rule is considered invalid for that sample.

The following steps will help us to compute the confidence and support for all possible rules:

from collections import defaultdict 
valid_rules = defaultdict(int) 
invalid_rules = defaultdict(int) 
num_occurences = defaultdict(int)

for sample in X:
    for premise in range(n_features):
    if sample[premise] == 0: continue
# Record that the premise was bought in another transaction
    num_occurences[premise] += 1
    for conclusion in range(n_features):
    if premise == conclusion: 
# It makes little sense to
    measure if X -> X.
    continue
    if sample[conclusion] == 1:
# This person also bought the conclusion item
    valid_rules[(premise, conclusion)] += 1

If the premise is valid for this sample (it has a value of 1), then we record this and check each conclusion of our rule. We skip over any conclusion that is the same as the premise-this would give us rules such as: if a person buys Apples, then they buy Apples, which obviously doesn't help us much.

We have now completed computing the necessary statistics and can now compute the support and confidence for each rule. As before, the support is simply our valid_rules value:

support = valid_rules

We can compute the confidence in the same way, but we must loop over each rule to compute this:

confidence = defaultdict(float)
for premise, conclusion in valid_rules.keys():
    rule = (premise, conclusion)
    confidence[rule] = valid_rules[rule] / num_occurences [premise]

We now have a dictionary with the support and confidence for each rule. We can create a function that will print out the rules in a readable format. The signature of the rule takes the premise and conclusion indices, the support and confidence dictionaries we just computed, and the features array that tells us what the features mean. Then we print out the Support and Confidence of this rule:

for premise, conclusion in confidence:
    premise_name = features[premise]
    conclusion_name = features[conclusion]
    print("Rule: If a person buys {0} they will also 
          buy{1}".format(premise_name, conclusion_name))
    print(" - Confidence: {0:.3f}".format
          (confidence[(premise,conclusion)]))
    print(" - Support: {0}".format(support
                                   [(premise, 
                                     conclusion)]))
    print("")

We can test the code by calling it in the following way-feel free to experiment with different premises and conclusions:

for premise, conclusion in confidence:
    premise_name = features[premise]
    conclusion_name = features[conclusion]
    print("Rule: If a person buys {0} they will also 
          buy{1}".format(premise_name, conclusion_name))
    print(" - Confidence: {0:.3f}".format
          (confidence[(premise,conclusion)]))
    print(" - Support: {0}".format(support
                                   [(premise, 
                                     conclusion)]))
    print("")

Now that we can compute the support and confidence of all rules, we want to be able to find the best rules. To do this, we perform a ranking and print the ones with the highest values. We can do this for both the support and confidence values.

To find the rules with the highest support, we first sort the support dictionary. Dictionaries do not support ordering by default; the items() function gives us a list containing the data in the dictionary. We can sort this list using the itemgetter class as our key, which allows for the sorting of nested lists such as this one. Using itemgetter(1) allows us to sort based on the values. Setting reverse=True gives us the highest values first:

from operator import itemgetter 
sorted_support = sorted(support.items(), key=itemgetter(1), reverse=True)

We can then print out the top five rules:

sorted_confidence = sorted(confidence.items(), key=itemgetter(1),
                           reverse=True)
for index in range(5):
    print("Rule #{0}".format(index + 1))
    premise, conclusion = sorted_confidence[index][0]
    print_rule(premise, conclusion, support, confidence, features)

The result will look like the following:

Rule #1 
Rule: If a person buys bananas they will also buy milk 
 - Support: 27 
 - Confidence: 0.474 
Rule #2 
Rule: If a person buys milk they will also buy bananas 
 - Support: 27 
 - Confidence: 0.519 
Rule #3 
Rule: If a person buys bananas they will also buy apples 
 - Support: 27 
 - Confidence: 0.474 
Rule #4 
Rule: If a person buys apples they will also buy bananas 
 - Support: 27 
 - Confidence: 0.628 
Rule #5 
Rule: If a person buys apples they will also buy cheese 
 - Support: 22 
 - Confidence: 0.512

Similarly, we can print the top rules based on confidence. First, compute the sorted confidence list and then print them out using the same method as before.

sorted_confidence = sorted(confidence.items(), key=itemgetter(1),
                           reverse=True)
for index in range(5):
    print("Rule #{0}".format(index + 1))
    premise, conclusion = sorted_confidence[index][0]
    print_rule(premise, conclusion, support, confidence, features)

Two rules are near the top of both lists. The first is If a person buys apples, they will also buy cheese, and the second is If a person buys cheese, they will also buy bananas. A store manager can use rules like these to organize their store. For example, if apples are on sale this week, put a display of cheeses nearby. Similarly, it would make little sense to put both bananas on sale at the same time as cheese, as nearly 66 percent of people buying cheese will probably buy bananas -our sale won't increase banana purchases all that much.

We can visualize the results using a library called matplotlib.

We are going to start with a simple line plot showing the confidence values of the rules, in order of confidence. matplotlib makes this easy - we just pass in the numbers, and it will draw up a simple but effective plot:

from matplotlib import pyplot as plt 
plt.plot([confidence[rule[0]] for rule in sorted_confidence])

Using the previous graph, we can see that the first five rules have decent confidence, but the efficacy drops quite quickly after that. Using this information, we might decide to use just the first five rules to drive business decisions. Ultimately with exploration techniques like this, the result is up to the user.

Data mining has great exploratory power in examples like this. A person can use data mining techniques to explore relationships within their datasets to find new insights. In the next section, we will use data mining for a different purpose: prediction and classification.

The dataset we are going to use for this example is the famous Iris database of plant classification. In this dataset, we have 150 plant samples and four measurements of each: sepal length, sepal width, petal length, and petal width (all in centimeters). This classic dataset (first used in 1936!) is one of the classic datasets for data mining. There are three classes: Iris Setosa, Iris Versicolour, and Iris Virginica. The aim is to determine which type of plant a sample is, by examining its measurements.

The scikit-learn library contains this dataset built-in, making the loading of the dataset straightforward:

from sklearn.datasets import load_iris 
dataset = load_iris() 
X = dataset.data 
y = dataset.target

You can also print(dataset.DESCR) to see an outline of the dataset, including some details about the features.

The features in this dataset are continuous values, meaning they can take any range of values. Measurements are a good example of this type of feature, where a measurement can take the value of 1, 1.2, or 1.25 and so on. Another aspect of continuous features is that feature values that are close to each other indicate similarity. A plant with a sepal length of 1.2 cm is like a plant with a Sepal width of 1.25 cm.

In contrast are categorical features. These features, while often represented as numbers, cannot be compared in the same way. In the Iris dataset, the class values are an example of a categorical feature. The class 0 represents Iris Setosa; class 1 represents Iris Versicolour, and class 2 represents Iris Virginica. The numbering doesn't mean that Iris Setosa is more similar to Iris Versicolour than it is to Iris Virginica-despite the class value being more similar. The numbers here represent categories. All we can say is whether categories are the same or different.

There are other types of features too, which we will cover in later chapters. These include pixel intensity, word frequency and n-gram analysis.

While the features in this dataset are continuous, the algorithm we will use in this example requires categorical features. Turning a continuous feature into a categorical feature is a process called discretization.

A simple discretization algorithm is to choose some threshold, and any values below this threshold are given a value 0. Meanwhile, any above this are given the value 1. For our threshold, we will compute the mean (average) value for that feature. To start with, we compute the mean for each feature:

attribute_means = X.mean(axis=0)

The result from this code will be an array of length 4, which is the number of features we have. The first value is the mean of the values for the first feature and so on. Next, we use this to transform our dataset from one with continuous features to one with discrete categorical features:

assert attribute_means.shape == (n_features,)
X_d = np.array(X >= attribute_means, dtype='int')

We will use this new X_d dataset (for X discretized) for our training and testing, rather than the original dataset (X).

OneR is a simple algorithm that simply predicts the class of a sample by finding the most frequent class for the feature values. OneR is shorthand for One Rule, indicating we only use a single rule for this classification by choosing the feature with the best performance. While some of the later algorithms are significantly more complex, this simple algorithm has been shown to have good performance in some real-world datasets.

The algorithm starts by iterating over every value of every feature. For that value, count the number of samples from each class that has that feature value. Record the most frequent class of the feature value, and the error of that prediction.

For example, if a feature has two values, 0 and 1, we first check all samples that have the value 0. For that value, we may have 20 in Class A, 60 in Class B, and a further 20 in Class C. The most frequent class for this value is B, and there are 40 instances that have different classes. The prediction for this feature value is B with an error of 40, as there are 40 samples that have a different class from the prediction. We then do the same procedure for the value 1 for this feature, and then for all other feature value combinations.

Once these combinations are computed, we compute the error for each feature by summing up the errors for all values for that feature. The feature with the lowest total error is chosen as the One Rule and then used to classify other instances.

In code, we will first create a function that computes the class prediction and error for a specific feature value. We have two necessary imports, defaultdict and itemgetter, that we used in earlier code:

from collections import defaultdict 
from operator import itemgetter

Next, we create the function definition, which needs the dataset, classes, the index of the feature we are interested in, and the value we are computing. It loops over each sample, and counts the number of time each feature value corresponds to a specific class. We then choose the most frequent class for the current feature/value pair:

def train_feature_value(X, y_true, feature, value):
# Create a simple dictionary to count how frequency they give certain
predictions
 class_counts = defaultdict(int)
# Iterate through each sample and count the frequency of each
class/value pair
 for sample, y in zip(X, y_true):
    if sample[feature] == value: 
        class_counts[y] += 1
# Now get the best one by sorting (highest first) and choosing the
first item
sorted_class_counts = sorted(class_counts.items(), key=itemgetter(1),
                             reverse=True)
most_frequent_class = sorted_class_counts[0][0]
 # The error is the number of samples that do not classify as the most
frequent class
 # *and* have the feature value.
    n_samples = X.shape[1]
    error = sum([class_count for class_value, class_count in
                 class_counts.items()
 if class_value != most_frequent_class])
    return most_frequent_class, error

As a final step, we also compute the error of this rule. In the OneR algorithm, any sample with this feature value would be predicted as being the most frequent class. Therefore, we compute the error by summing up the counts for the other classes (not the most frequent). These represent training samples that result in error or an incorrect classification.

With this function, we can now compute the error for an entire feature by looping over all the values for that feature, summing the errors, and recording the predicted classes for each value.

The function needs the dataset, classes, and feature index we are interested in. It then iterates through the different values and finds the most accurate feature value to use for this specific feature, as the rule in OneR:

def train(X, y_true, feature): 
    # Check that variable is a valid number 
    n_samples, n_features = X.shape 
    assert 0 <= feature < n_features 
    # Get all of the unique values that this variable has 
    values = set(X[:,feature]) 
    # Stores the predictors array that is returned 
    predictors = dict() 
    errors = [] 
    for current_value in values: 
        most_frequent_class, error = train_feature_value
        (X, y_true, feature, current_value) 
        predictors[current_value] = most_frequent_class 
        errors.append(error) 
    # Compute the total error of using this feature to classify on 
    total_error = sum(errors) 
    return predictors, total_error

Let's have a look at this function in a little more detail.

After some initial tests, we then find all the unique values that the given feature takes. The indexing in the next line looks at the whole column for the given feature and returns it as an array. We then use the set function to find only the unique values:

    values = set(X[:,feature_index])

Next, we create our dictionary that will store the predictors. This dictionary will have feature values as the keys and classification as the value. An entry with key 1.5 and value 2 would mean that, when the feature has a value set to 1.5, classify it as belonging to class 2. We also create a list storing the errors for each feature value:

predictors = {} 
    errors = []

As the main section of this function, we iterate over all the unique values for this feature and use our previously defined train_feature_value function to find the most frequent class and the error for a given feature value. We store the results as outlined earlier:

Finally, we compute the total errors of this rule and return the predictors along with this value:

total_error = sum(errors)
return predictors, total_error

When we evaluated the affinity analysis algorithm of the earlier section, our aim was to explore the current dataset. With this classification, our problem is different. We want to build a model that will allow us to classify previously unseen samples by comparing them to what we know about the problem.

For this reason, we split our machine-learning workflow into two stages: training and testing. In training, we take a portion of the dataset and create our model. In testing, we apply that model and evaluate how effectively it worked on the dataset. As our goal is to create a model that can classify previously unseen samples, we cannot use our testing data for training the model. If we do, we run the risk of overfitting.

Overfitting is the problem of creating a model that classifies our training dataset very well but performs poorly on new samples. The solution is quite simple: never use training data to test your algorithm. This simple rule has some complex variants, which we will cover in later chapters; but, for now, we can evaluate our OneR implementation by simply splitting our dataset into two small datasets: a training one and a testing one. This workflow is given in this section.

The scikit-learn library contains a function to split data into training and testing components:

from sklearn.cross_validation import train_test_split

This function will split the dataset into two sub-datasets, per a given ratio (which by default uses 25 percent of the dataset for testing). It does this randomly, which improves the confidence that the algorithm will perform as expected in real world environments (where we expect data to come in from a random distribution):

Xd_train, Xd_test, y_train, y_test = train_test_split(X_d, y, 
    random_state=14)

We now have two smaller datasets: Xd_train contains our data for training and Xd_test contains our data for testing. y_train and y_test give the corresponding class values for these datasets.

We also specify a random_state. Setting the random state will give the same split every time the same value is entered. It will look random, but the algorithm used is deterministic, and the output will be consistent. For this book, I recommend setting the random state to the same value that I do, as it will give you the same results that I get, allowing you to verify your results. To get truly random results that change every time you run it, set random_state to None.

Next, we compute the predictors for all the features for our dataset. Remember to only use the training data for this process. We iterate over all the features in the dataset and use our previously defined functions to train the predictors and compute the errors:

all_predictors = {} 
errors = {} 
for feature_index in range(Xd_train.shape[1]): 
    predictors, total_error = train(Xd_train,
                                    y_train,
                                    feature_index) 
    all_predictors[feature_index] = predictors 
    errors[feature_index] = total_error

Next, we find the best feature to use as our One Rule, by finding the feature with the lowest error:

best_feature, best_error = sorted(errors.items(), key=itemgetter(1))[0]

We then create our model by storing the predictors for the best feature:

model = {'feature': best_feature,
         'predictor': all_predictors[best_feature]}

Our model is a dictionary that tells us which feature to use for our One Rule and the predictions that are made based on the values it has. Given this model, we can predict the class of a previously unseen sample by finding the value of the specific feature and using the appropriate predictor. The following code does this for a given sample:

variable = model['feature'] 
predictor = model['predictor'] 
prediction = predictor[int(sample[variable])]

Often we want to predict several new samples at one time, which we can do using the following function. It simply uses the above code, but iterate over all the samples in a dataset, obtaining the prediction for each sample:

def predict(X_test, model):
variable = model['feature']
predictor = model['predictor']
y_predicted = np.array([predictor
                        [int(sample[variable])] for sample
                        in X_test])
return y_predicted

For our testing dataset, we get the predictions by calling the following function:

y_predicted = predict(Xd_test, model)

We can then compute the accuracy of this by comparing it to the known classes:

accuracy = np.mean(y_predicted == y_test) * 100 
print("The test accuracy is {:.1f}%".format(accuracy))

This algorithm gives an accuracy of 65.8 percent, which is not bad for a single rule!