" R. Herbrich, ICANN, 1999.
This work aims to reduce the problem of ordinal regression (ranking) to classification problem.
In ordinal regression, the loss function is defined by the ordering of data in original data space and the mapping space, while in classification problem it's just 0 or 1.
The goal is to find the mapping function that maps the data to it's rank, and the loss function is defined as:
given samples
And the loss is formulated like following:
The idea that this work transformed the problem of ranking to classification can be showed as following:
S is the original data space, and S' is the transformed data that was feed into the SVM for classification learning process.
To derive the linear mapping function,
and to solve the w,
is where zi is the label for training.
And the result will be:
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