Python: Confusion Matrix

What is a confusion matrix?

A confusion matrix is a supervised machine learning evaluation tool that provides more insight into the overall effectiveness of a machine learning classifier. Unlike a simple accuracy metric, which is calculated by dividing the number of correctly predicted records by the total number of records, confusion matrices return 4 unique metrics for you to work with.

While I am not saying accuracy is always misleading, there are times, especially when working with examples of imbalanced data,  that accuracy can be all but useless.

Let’s consider credit card fraud. It is not uncommon that given a list of credit card transactions, that a fraud event might make up a little as 1 in 10,000 records. This is referred to a severely imbalanced data.  Now imaging a simple machine learning classifier running through that data and simply labeling everything as not fraudulent. When you checked the accuracy, it would come back as 99.99% accurate. Sounds great right? Except you missed the fraud event, the only reason to try to create the model in the first place.

A confusion matrix will show you more details, letting you know that you completely missed the fraud event. Instead of a single number result, a confusion matrix provides you will 4 metrics to evaluate. (note: the minority class – (in the case of fraud – the fraudulent events) – are labeled positive by confusion matrices. So a non-fraud event is a negative. This is not a judgement between the classes, only a naming convention)

TP = true positive – minority class (fraud) is correctly predicted as positive

FP = false positive – majority class (not fraud) is incorrectly predicted

FN = false negative – minority class (fraud) incorrectly predicted

TN = true negative – majority class (not fraud) correctly predicted

In matrix form:


To run a confusion matrix in Python, Sklearn provides a method called confusion_matrix(y_test, y_pred)

y_test = actual results from the test data set

y_pred = predictions made by model on test data set

so in a pseudocode example:,y)
y_pred = model.predict(X_test)

If this is at all confusing, refer to my Python SVM lesson where I create the training and testing set and run a confusion matrix (Python: Support Vector Machine (SVM))

To run a confusion matrix in Python, first run a model, then run predictions (as shown above) and then follow the code below:

from sklearn.metrics import confusion_matrix
confusion_matrix(y_test, y_pred)

Output looks like this:


Now, if you want to capture the TP, TN, FP, FN into individual variables to work with, you can add the ravel() function to your confusion matrix:

TN,FP,FN,TP = confusion_matrix(y_test, y_pred).ravel()

Thank you for taking the time to read this, and good luck on your analytics journey.

Python: Support Vector Machine (SVM)

Support Vector Machine (SVM):

A Support Vector Machine, or SVM, is a popular binary classifier machine learning algorithm. For those who may not know, a binary classifier is a predictive tool that returns one of two values as the result, (YES – NO), (TRUE – FALSE), (1 – 0).  Think of it as a simple decision maker:

Should this applicant be accepted to college? (Yes – No)

Is this credit card transaction fraudulent? (Yes – No)

An SVM predictive model is built by feeding a labeled data set to the algorithm, making this a supervised machine learning model. Remember, when the training data contains the answer you are looking for, you are using a supervised learning model. The goal, of course, of a supervised learning model is that once built, you can feed the model new data which you do not know the answer to, and the model will give you the answer.

Brief explanation of an SVM:

An SVM is a discriminative classifier. It is actually an adaptation of a previously designed classifier called perceptron. (The perceptron algorithm also helped to inform the development of artificial neural networks).

The SVM works by finding the optimal hyperplane that can be used to discriminate between classes in the data set. (Classes refers to the label or “answer” column of each record.  The true/false, yes/no column in a binary set). When considering a two dimensional model, the hyperplane simply becomes a line that divides to the classes of data.

The hyperplane (or line in 2 dimensions) is informed by what are known as Support Vectors. A record from the data set is converted into a vector when fed through the algorithm (this is where a basic understanding of linear algebra comes in handy). Vectors (data records) closest to the decision boundary are called Support Vectors. It is on either side of this decision boundary that a vector is labeled by the classifier.

The focus on the support vectors and where they deem the decision boundary to be, is what informs the SVM as to where to place the optimal hyperplane. It is this focus on the support vectors as opposed to the data set as a whole, that gives SVM an advantage over a simple learner like a linear regression, when dealing with complex data sets.

Coding Exercise:

Libraries needed:



This is the main reason I recommend the Anaconda distribution of Python, because it comes prepackaged with the most popular data science libraries.

from sklearn.model_selection import train_test_split
from sklearn.svm import SVC
from sklearn.metrics import metrics
from sklearn.metrics import confusion_matrix
import pandas as pd

Next, let’s look at the data set. This is the Pima Indians Diabetes data set. It is a publicly available data set consisting of 768 records. Columns are as follows:

  1. Number of times pregnant.
  2. Plasma glucose concentration a 2 hours in an oral glucose tolerance test.
  3. Diastolic blood pressure (mm Hg).
  4. Triceps skinfold thickness (mm).
  5. 2-Hour serum insulin (mu U/ml).
  6. Body mass index (weight in kg/(height in m)^2).
  7. Diabetes pedigree function.
  8. Age (years).
  9. Class variable (0 or 1).

Data can be downloaded with the link below


Once you download the file, load it into python (you’re file path will be different)

df = pd.read_excel(‘C:\\Users\\blars\\Documents\\pima_indians.xlsx’)

now look at the data:



Now keep in mind, class is our target. That is what we want to predict.

So let us start by separating the target class.

We use the pandas command .pop() to remove the Class column to the y variable, and the remained of the dataframe is now in the X

Let’s now split the data into training and test sets:

X_train, X_test, y_train, y_test = train_test_split(X,y, test_size=0.33)

Now we will train (fit) the model. This example I am using Sklearns SVC() model for an SVM example. There are a lot of SVMs available to try if you would like to explore deeper.

Code for fitting the model:

model =SVC(), y_train)

Now using the testing subset we withheld, we will test our model

y_pred = model.predict(X_test)

Now to see how good the model is, we will perform an accuracy test.  This simply takes all the correct guess and divides them by total guesses.

As, you can seen below, we compare the y_pred (predicted values) against y_test (actual values) and we get .7677 or 77% accuracy. Which is not a bad model for simply using defaults.


Let’s look at a confusion matrix to get just a little more in-depth info


For those not familiar with a confusion matrix, this will help you to interpret results:

First number 151 = True Negatives — this would be the number of 0’s or not diabetics correctly predicted

Second number 15 = False Positives — the number of 0’s (non-diabetics) falsely predicted to be a 1

Third number 44 = False negatives — the number of 1’s (diabetics) falsely predicted to be a 0

Fourth number 44 = True Positives — the number of 1 (diabetics) correctly predicted.

So, the model correctly identified 44 out of the 59 diabetics in the test data, and misdiagnoses 44 out the 195 non diabetics in the data sample.

To see a video version of this lesson, click the link here: Python: Build an SVM

Python: Simulate Blockchain Mining

In my earlier tutorial, I demonstrated how to use the Python library hashlib to create a sha256 hash function. Now, using Python, I am going to demonstrate the principle of blockchain mining. Again using BitCoin as my model, I will be trying to find a nonce value that will result in a hash value below a predetermined target.

We will start by simply enumerating an integer through our sha 256 hash function until we find a hash with 4 leading zeros.

I used a while loop, passing the variable “y” through my hashing function each time the loop runs. I then inspect the first 4 digits [:4] of my hash value. If the first four digits equal 0000 then I exit the loop by setting the found variable to 1

(*note, a hash value is a string – hence the need for quotes around ‘0000’)


As you can see in the version above, it took 88445 iterations to find an acceptable hash value

Now, using the basic example of a blockchain I gave in an earlier lesson, let’s simulate mining a block


You’ll see, I am now combining the block number, nonce, data, and previous hash of my simulated block and passing it through my encryption function.  Just like in BitCoin, the only value I change per iteration is the Nonce. I keep passing my block through the hashing function until I find the Nonce that gives me a hash below the target.


Now, let’s lower the target value to 6 leading zeros. This should result in a longer runtime to get your hash


To measure the run time difference, let’s add some time stamps to our code


So, I am using the timestamp function twice. D1 will be our start time, d2 will be our end time, and I am subtracting d1 from d2 to get our elapsed time. In the example below, my elapsed time was 5 secs


Now, let’s bump the target down to 7 leading zeros. Now this brings my elapsed computing time to 20 minutes. That is a considerable commitment of resources. You can see why they call it a “proof of work” now.



Python 2.xx VS 3.xx

If you are trying to learn Python, especially for Data Science, you are going to come across a bunch a people (myself included) who have been very hesitant to move from Python 2.xx to Python 3.xx.

The reason?

Not Backwards Compatible

Well, when Python 3 first came out, it was made very clear that it was not backwards compatible. While most of the code remained the same, there were some changes that made programs coded in Python fail. A prime example is Print. In Python 2,

Print ‘Hello World!’

was perfectly acceptable, but in Python 3, it fails and throws up an exception. Python 3 had added the requirement for () with print statements

Print(‘Hello World’)   — Python 3 friendly

Well I have a whole bunch of code sitting on my hard drive I like to refer to, and having to go through it cleaning up all the new changes did not exactly seem like the best use of my time, since I am able to just continue using Python


Python is so great for Data Science because of the community of libraries out there providing the data horsepower we all love. (Pandas, Numpy, SciKit Learn, ect).  Well guess what, the changes to Python 3 made some of these libraries unstable. Strike 2, another reason not to waste my time with this new version.

Moving On

Well, it appears that enough time has passed and some people tell me all the bugs have been worked out with Python 3. While Python 2.7 will be supported til 2020 (those who love it, just keep using it I say), I have decided to try putting Python 3 through it’s paces.

My lessons will be reviewed one by one, with the 2.7 code being tested in a 3.4 environment. I will note any changes that need to made to the code to make it 3.4 compatible and add them to the  lesson. Each lesson that has been reviewed will have the following heading.

*Note: This lesson was written using Python 2.xx. If you are using Python any changes to the code will be annotated under headings: Python


If you love 2, just keep using it. You’ve got 3 more years. By that point, whatever revision of 3 we are on may not even look like the current version. But if you want to look ahead, follow along with me as I update my code. (Note, all the original 2.7 code will remain on my site until the time that it is no longer supported)

Python: Pivot Tables with Pandas

Pandas provides Python with lots of advanced data management tools. Being able to create pivots tables is one of the cooler tools.

You can download the data set I will be working with here: KMeans1

First, let’s upload our data into Python

import pandas as pd
df = pd.read_excel("C:\Users\Benjamin\Documents\KMeans1.xlsx")


Let’s create our first pivot table.

The syntax is = pd.pivot_table(dataframe, index = Columns you want to group by, values = Columns you want to aggregate, aggfunc = type of aggregation)

pd.pivot_table(df, index='Department', values = 'AVG Labor', aggfunc = 'sum')


We can group by more than one column

pd.pivot_table(df, index=['Department','Model'], values = 'AVG Labor',  
aggfunc= 'mean')


You can also have multiple value columns

 pd.pivot_table(df, index='Department', values = ['AVG Labor','Labor Cost'],
  aggfunc= 'sum')


Now, one catch is, what if you want to have different aggregate functions. What if I want to get the mean of AVG Labor, but I want the sum of Labor Cost columns.

In this case we are going to use the groupby().aggregate()

import numpy as np
df.groupby('Department').aggregate({'AVG Labor':np.mean, 'Labor Cost': np.sum})


Python: An Interesting Problem with Pandas

I was writing a little tongue and cheek article for LinkedIn on fraud detection using frequency distributions (you can read the article here: LinkedIn). While this was a non-technical article, I wanted to use some histograms from a real data set, so I uploaded a spread sheet into Python and went to work.

While working with the data I ran into an interesting problem that had me chasing my tail for about 10 minutes before I figured it out. It is a fun little problem involving Series and Dataframes.

As always, you can upload the data set here: FraudCheck1

Upload the data.

import pandas as pd
df = pd.read_excel


The data is pretty simple here. We are concerned with our answer column and the CreatedBy (which is the employee ID).  What I am trying to do is see if the “answer”  (a reading from an electric meter) are really random or if they have been contrived by someone trying to fake the data.

First, I want to get the readings for all the employees, so I used pop() to place the answer column into a separate list.

df1 = df

y = df1.pop("answer")


Then, to make my histogram more pleasant looking, I decided to only use the last digit before the decimal. That way I will have 10 bars (0-9). (Remember, this is solely for making charts for an article. So I was not concerned with any more stringent methods of normalization)

What I am doing below is int(199.7%10). Remember % is the modulus – leaves you with the remainder and int converts your float to an integers. So 199.7 is cut to 199. The 199/10 remainder = 9.

a= []
i = 0 
while i < len(y):
     i += 1


Then I created my histogram.

%matplotlib inline
from matplotlib import pyplot as plt


Now my problem

Now I want graph only the answers from employee 619, so first I filter out all rows but the ones for employee 619.

df2 = df.query('CreatedBy == 619')
y1 =df2.pop("answer")

Then I ran my loop to turn my answers into a single digit.

And I get an error.  Why?


Well the answer lies in the datatypes we are working with. Pandas read_excel function creates a Dataframe.

When you pop a column from a dataframe, you end up with a Series. And remember a series is an indexed listing of values.

Let’s look at our Series. Check out the point my line is pointing to below. Notice how my index jumps from 31 to 62. My while loop counts by 1, so after 31, I went looking for y1[32] and it doesn’t exist.


Using .tolist() converts our Series to a list and now our while loop works.


And now we can build another histogram.


The Code

import pandas as pd
df = pd.read_excel

df1 = df
y =df1.pop("answer")

a= []
i = 0 
while i < len(y):
   i += 1

%matplotlib inline
from matplotlib import pyplot as plta1 = []
i = 0
while i < len(y2):
 i = i+1


df2 = df.query('CreatedBy == 619')
y1 =df2.pop("answer")

y2= y1.tolist()

a1 = []
i = 0
while i < len(y2):
    i = i+1



Python: Naive Bayes’

Naive Bayes’ is a supervised machine learning classification algorithm based off of Bayes’ Theorem. If you don’t remember Bayes’ Theorem, here it is:


Seriously though, if you need a refresher, I have a lesson on it here: Bayes’ Theorem

The naive part comes from the idea that the probability of each column is computed alone. They are “naive” to what the other columns contain.

You can download the data file here: logi2

Import the Data

import pandas as pd
df = pd.read_excel("C:\Users\Benjamin\Documents\logi2.xlsx")


Let’s look at the data. We have 3 columns – Score, ExtraCir, Accepted. These represent:

  • Score – Student Test Score
  • ExtraCir – Was Student in an Extra Circular Activity
  • Accepted – Was the Student Accepted

Now the Accepted column is our result column – or the column we are trying to predict. Having a result in your data set makes this a supervised machine learning algorithm.

Split the Data

Next split the data into input(score and extracir) and results (accepted).

y = df.pop('Accepted')
X = df




Fit Naive Bayes

Lucky for us, scikitlearn has a bit in Naive Bayes algorithm – (MultinomialNB)

Import MultinomialNB and fit our split columns to it (X,y)

from sklearn.naive_bayes import MultinomialNB
classifier = MultinomialNB(),y)


Run the some predictions

Let’s run the predictions below. The results show 1 (Accepted) 0 (Not Accepted)

#--score of 1200, ExtraCir = 1

#--score of 1000, ExtraCir = 0


The Code

import pandas as pd
df = pd.read_excel("C:\Users\Benjamin\Documents\logi2.xlsx")

y = df.pop('Accepted')
X = df


from sklearn.naive_bayes import MultinomialNB
classifier = MultinomialNB(),y)

#--score of 1200, ExtraCir = 1

#--score of 1000, ExtraCir = 0


Python: K Means Clustering Part 2

In part 2 we are going focus on checking our assumptions. So far we have learned how to perform a K Means Cluster. When running a K Means Cluster, you first have to choose how many clusters you want. But what is the optimal number of clusters? This is  the “art” part of an algorithm like this.

One thing you can do is check the distance from you points to the cluster center. We can measure this using the interia_ function from scikit learn.

Let’s start by building our K Means Cluster:

Import the data

import pandas as pd

df = pd.read_excel("C:\Users\Benjamin\Documents\KMeans1.xlsx")


Drop unneeded columns

df1 = df.drop(["ID Tag", "Model", "Department"], axis = 1)


Create the model – here I set clusters to 4

from sklearn.cluster import KMeans
km = KMeans(n_clusters=4, init='k-means++', n_init=10)

Now fit the model and run the interia_ function


Now the answer you get is the sum of distances from your sample points to the cluster center.

What does the number mean? Well, on its own, not much. What you need to do is look at a list of interia_ for a range of cluster choices.

To do so, I am set up a for loop.

n = int(raw_input("Enter Starting Cluster: "))
n1 = int(raw_input("Enter Ending Cluster: "))
for i in range(n,n1):
 km = KMeans(n_clusters=i, init='k-means++', n_init=10)
 print i, km.inertia_


The trick to reading the results is look for the point of diminishing returns. The area I am pointing to with the arrow is where I would look. The changes in values start slowing down here.

I am using this example because I feel it is more real world. Working with real data takes time to a get a feeling for. If you are having trouble seeing why I chose this point, consider the following textbook example:

See how at this highlight part, the drop in number goes from hundreds to 25. That is a diminished return. The new result is not that much better than the earlier result. As opposed to 1 and 2 where 2 clusters perform 1000 units better.



Python: K Means Cluster

K Means Cluster will be our introduction to Unsupervised Machine Learning. What is Unsupervised Machine Learning exactly? Well, the simplest explanation I can offer is that unlike supervised where our data set contains a result, unsupervised does not.

Think of a simple regression where I have the square footage and selling prices (result) of 100 houses. Taking that data, I can easily create a prediction model that will predict the selling price of a house based off of square footage. – This is supervised machine learning

Now, take a data set containing 100 houses with the following data: square footage, house style, garage/no garage, but no selling price. We can’t create a prediction model since we have no knowledge of prices, but we can group the houses together based on commonalities. These groupings (clusters) can be used to gain knowledge of your data set.

I think seeing it in action will help.

If you want to play along, download the data set here: KMeans1

The data set contains a 1 year repair history of 197 Ultrasound medical devices.

Data dictionary (ID Tag – asset number assigned device, Model – model name of device, WO Count – count of repair work orders, AVG Labor – average labor minutes per repair, Labor Cost – average labor cost per repair, No Problem-  count of repairs where no problem was found, Avg Cost -average cost of parts, Travel – average travel hours per repair, Travel Cost – average travel cost per repair, Department – department that owns the ultrasound device)


We want to see what kind of information we can extract from this data.

To do so, we are going to use K Means Clustering.

How does K Means Clustering work? Each row in the table is converted to a vector. Imagine the vectors now graphed in N-dimension space. Next pick the number of clusters you want to create. For each cluster, you will place a  point(a centroid) in space and the vectors are grouped based on their proximity to their nearest centroid.

The calculation to tell proximity is made using geometric means (not arithmetic)- hence the name K-Means Cluster

(each dot below is a row in your table, the colors represent a cluster)


Let’s do it in Python

Import the data.

import pandas as pd

df = pd.read_excel("C:\Users\Benjamin\Documents\KMeans1.xlsx")


Now, we are going to drop a few columns: ID Tag – is a random number, has no value in clustering. Then Model and Department,as they are text and while there are ways to work with the text, it is more complicated so for now, we are just going to drop the columns

df1 = df.drop(["ID Tag", "Model", "Department"], axis = 1)


Now lets import KMeans from sklearn.cluster

We then initialize KMeans (n_clusters= 4 -no of clusters you want, init=’k-means++’ -sets how the centroids are places. k-means++ is one of the faster methods of centroid placement, n_init=10 – number times the algorithm with run placing new centroids each iteration)

from sklearn.cluster import KMeans
km = KMeans(n_clusters=4, init='k-means++', n_init=10)


Choosing number of clusters is a bit of an art. Play with it a bit and see how different values play out for you.

Now fit the model


Now, export the cluster identifiers to a list. Notice my values are 0 -3. One value for each cluster.

x = km.fit_predict(df1)


Create a new column on the original dataframe called Cluster and place your results (x) in that column

df["Cluster"]= x


Sort your dataframe by cluster

df1 = df.sort(['Cluster'])


Now as you start to examine the data in each cluster, you show start to see patterns emerge.

Below is an example of the patterns I found in the clusters.


Now remember, this is just an INTRODUCTION to unsupervised learning. We will learn more tricks to help you discover the patterns as we move forward.

Python: K Nearest Neighbor

K Nearest Neighbor (Knn) is a classification algorithm. It falls under the category of supervised machine learning. It is supervised machine learning because the data set we are using to “train” with contains results (outcomes). It is easier to show you what I mean.

Here is our training set: logi

Let’s import our set into Python


This data set contains 42 student test score (Score) and whether or not they were accepted (Accepted) in a college program.  It is the presence of the Accepted column that makes supervised machine learning possible. Knowing the outcomes of past events, we can create a prediction model for future events. So you could use the finished model to predict whether someone will be accepted based on their test score.

So how does Knn work?

Look at the chart below. Imagine this represents our data set. Each blue dot is accepted (1) while each red dot is not(0).


What if I want to know about my new data point (green star)? Is it a 1 or a 0?


I start by choosing a neighbor count – in this example I will choose 3, and I find the 3 nearest neighbors to my new point.

Let’s look at the results, I have 2 red(0) and 1 blue(1). Using basic probability, I am 67% (2/3) certain that you will not get in.


Now, let’s code it!

First we need to separate our data into 2 dataframes: Our training set X (Score) and our target set y (Accepted)

df.pop() removes the Accepted column from your dataframe and places it in a newly created one.



Import sklearn

sklearn is a massive library of machine learning algorithms available for Python. Today we are going to use KNeighborsClassfier

So below imported KNeighborsClassifier from sklearn.neighbors

Next I set my neighbor count to 5. You can experiment with other numbers and see how works out for you. Setting the neighbor count is something you kind of have to develop a feel for.


Now let’s fit the model with our training set(X) and target set(y)


Now we can use our model to make predictions.

ne.predict() will return 1 or 0 – (Accepted or Not)

while ne.predict_proba() will return a probability range. Results below read as (40% change of not Accepted(0), 60% chance of Accepted(1))


So there you go, you have now built a prediction model using K Nearest Neighbor.