What is the difference between a Confusion Matrix and Contingency Table?

Question

I'm writting a piece of code to evaluate my Clustering Algorithm and I find that every kind of evaluation method needs the basic data from a m*n matrix like A = {aij} where aij is the number of data points that are members of class ci and elements of cluster kj.

But there appear to be two of this type of matrix in Introduction to Data Mining (Pang-Ning Tan et al.), one is the Confusion Matrix, the other is the Contingency Table. I do not fully understand the difference between the two. Which best describes the matrix I want to use?

Mainstream

Just as a side note: I know from a different context that (in many settings, including the popular data sets that you run into everywhere) the geometrical configurations of points and their classes do not correlate all that well. I'm not sure that this gives you a good tool to measure the quality of a clustering, unless of course you make/can make the assumption that classes and point locations are well-correlated. – Pasteurization

I'm pretty sure there is no difference at all. A confusion matrix is just a contingency table of your predictions and the true labels. – Mooned

Answer 1

Wikipedia's definition:

In the field of artificial intelligence, a confusion matrix is a visualization tool typically used in supervised learning (in unsupervised learning it is typically called a matching matrix). Each column of the matrix represents the instances in a predicted class, while each row represents the instances in an actual class.

Confusion matrix should be clear, it basically tells how many actual results match the predicted results. For example, see this confusion matrix

                 predicted class
                        c1  -  c2
  Actual class   c1     15  -   3
                ___________________
                 c2     0   -   2

It tells that:

1. Column1, row 1 means that the classifier has predicted 15 items as belonging to class c1, and actually 15 items belong to class c1 (which is a correct prediction)

2. the second column row 1 tells that the classifier has predicted that 3 items belong to class c2, but they actually belong to class c1 (which is a wrong prediction)

3. Column 1 row 2 means that none of the items that actually belong to class c2 have been predicted to belong to class c1 (which is a wrong prediction)

4. Column 2 row 2 tells that 2 items that belong to class c2 have been predicted to belong to class c2 (which is a correct prediction)

Now see the formula of Accuracy and Error Rate from your book (Chapter 4, 4.2), and you should be able to clearly understand what is a confusion matrix. It is used to test the accuracy of a classifier using data with known results. The K-Fold method (also mentioned in the book) is one of the methods to calculate the accuracy of a classifier that has also been mentioned in your book.

Now, for Contingency table: Wikipedia's definition:

In statistics, a contingency table (also referred to as cross tabulation or cross tab) is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables. It is often used to record and analyze the relation between two or more categorical variables.

In data mining, contingency tables are used to show what items appeared in a reading together, like in a transaction or in the shopping-cart of a sales analysis. For example (this is the example from the book you have mentioned):

       Coffee  !coffee
tea    150       50      200
!tea   650       150     800
       800       200    1000   

It tells that in 1000 responses (responses about do they like Coffee and tea or both or one of them, results of a survey):

1. 150 people like both tea and coffee
2. 50 people like tea but do not like coffee
3. 650 people do not like tea but like coffee
4. 150 people like neither tea nor coffee

Contingency tables are used to find the Support and Confidence of association rules, basically to evaluate association rules (read Chapter 6, 6.7.1).

Now the difference is that Confusion Matrix is used to evaluate the performance of a classifier, and it tells how accurate a classifier is in making predictions about classification, and contingency table is used to evaluate association rules.

Now after reading the answer, google a bit (always use google while you are reading your book), read what is in the book, see a few examples, and don't forget to solve a few exercises given in the book, and you should have a clear concept about both of them, and also what to use in a certain situation and why.

Hope this helps.

Specular

Answer 2

In short, contingency table is used to describe data. and confusion matrix is, as others have pointed out, often used when comparing two hypothesis. One can think of predicted vs actual classification/categorization as two hypothesis, with the ground truth being the null and the model output being the alternative.

Crackerbarrel