Assessing the Multi-labelness of Multi-label Data

Before constructing a classifier, we should examine the data to gain an understanding of the relationships between the variables, to assist with the design of the classifier. Using multi-label data requires us to examine the association between labels: its multi-labelness. We cannot directly measure association between two labels, since the labels’ relationships are confounded with the set of observation variables. A better approach is to fit an analytical model to a label with respect to the observations and remaining labels, but this might present false relationships due to the problem of multicollinearity between the observations and labels. In this article, we examine the utility of regularised logistic regression and a new form of split logistic regression for assessing the multi-labelness of data. We find that a split analytical model using regularisation is able to provide fewer label relationships when no relationships exist, or if the labels can be partitioned. We also find that if label relationships do exist, logistic regression with \(l_1\) regularisation provides the better measurement of multi-labelness.