Algorithm: multi label classification

Question

I am a biologist and I have an algorithm question, I asked on stack exchange but was suggested to come here. Also, I have really tried to explain my problem using simple toy data; note that in real life I have thousands of students/exams; not just the three as in this example.

For example, let's say there are only three students in a class; and from class records, I know their what their #attendance days per year (#), average punctuality (%), class engagement (not good, good, very good) (* = no recorded value)

Over the years:

Student1 = [100, *, not good]
Student2 = [50, 60, good]
Student3 = [200, 100, very good]

These three students only study three subjects: maths, english and history. I can see that the class exam results for maths, english and history are changing throughout the year.

Student1 = [maths increasing, english decreasing, history decreasing]
Student2 = [maths increasing, english stable, *]
Student3 = [maths increasing, english increasing, history increasing]

My question: "What student properties are most strongly correlated with changes in exam results"?

My output: A list of students and their properties that are most strongly correlated with changes in exam results, to identify which traits we woul For this, someone suggested that I look at "multi-label classification methods", since each of the data sets have a number of different class labels to be predicted (where each label is an exam score change in a particular subject?) So my questions are:

Do you agree that multi-label classification is the method to address this problem?

Do you know where I should start (remember that I'm a biologist)? I have found this: http://scikit-learn.org/stable/modules/multiclass.html ; but I'm not sure where to start? Would someone have an example of basic code that I would use to do this correlation for this toy data set? Or should I use a different package/software?

Answer 1

I'm highlighting feature correlation as possible solution to your problem - which is different to multilabel classification, but might be able to give you a simple answer to your question.

I guess that a simple feature correlation between your students attributes (attendance, etc.) and the one-hot encoded labels of their performance on certain exams/subjects (Math increasing, etc.) will answer your question. Here's a short example with some explanation on how this could look like (I'm using R and a dataset from another domain, namely the mtcars dataset, to make everything reproducible):

At first I need to artificially generate fake student records:

d <- data.frame(row.names = 1:nrow(mtcars))
d$engagement <- factor(ifelse(mtcars[,11] %in% c(1,3), 'good', ifelse(mtcars[,11] %in% c(2,6), 'average', 'bad')))
d$attendance <- as.integer(mtcars[,3])
d$punctuality <- mtcars[,5]/max(mtcars[,5])
d$math <- factor(mtcars$cyl, labels = c('increasing', 'decreasing', 'stable'))
d$history <- factor(mtcars$gear, labels = c('increasing', 'decreasing', 'stable'))

This is what our fake student records look like (the data might have a senseless correlation here, but it should serve the purpose):

> print(d)

   engagement attendance punctuality       math    history
1         bad        160   0.7910751 decreasing decreasing
2         bad        160   0.7910751 decreasing decreasing
3        good        108   0.7809331 increasing decreasing
4        good        258   0.6247465 decreasing increasing
5     average        360   0.6389452     stable increasing

We can now one-hot encode students' categorial attributes and performance in exams/subjects:

> library(caret)
> d2 <- data.frame(predict(dummyVars("~ .", data=d), newdata=d))
> print(d2)

   engagement.average engagement.bad engagement.good attendance punctuality math.increasing math.decreasing math.stable
1                   0              1               0        160   0.7910751               0               1           0
2                   0              1               0        160   0.7910751               0               1           0
3                   0              0               1        108   0.7809331               1               0           0
4                   0              0               1        258   0.6247465               0               1           0
5                   1              0               0        360   0.6389452               0               0           1

Having one-hot encoded information allows feature correlation between your students' attributes and the labels:

library(corrplot)
corrplot(cor(d2), type = 'lower')

This gives you the correlation between students' recorded attributes and their performance on certain exams/subjects, and therefore should probably answer your question.

Update:

On a second thought, as your students' attributes and exam performances can be considered to have ordered levels, converting those categorial variables just into (ordered) numeric values instead of one-hot encoding them should work too. This reduces the size of the resulting correlation matrix - and might emphasize the correlation between specific variables a bit better:

d2 <- d
d2$engagement <- as.numeric(as.character(factor(d$engagement, labels = 1:3)))
d2$math <- as.numeric(as.character(factor(d$math, labels = 1:3)))
d2$history <- as.numeric(as.character(factor(d$history, labels = 1:3)))

...which will result in a simpler d2:

> print(d2)

   engagement attendance punctuality math history
1           2        160   0.7910751    2       2
2           2        160   0.7910751    2       2
3           3        108   0.7809331    1       2
4           3        258   0.6247465    2       1
5           1        360   0.6389452    3       1

> library(corrplot)
> corrplot(cor(d2), type = 'lower')