Tensor Decomposition for Multiple-Instance Classification of High-Order Medical Data
Algorithm 1
TensMIL (training)
Input: training and test instances’ features Utrain and Utest, subjects’ training labels Ytrain, percentage of variance retained by PCA , the number of bins used for the histograms
Output: prediction model
1. Concatenate Utrain and Utest along the first dimension into a matrix U.
2. Perform PCA for decorrelation and dimensionality reduction on the concatenated matrix U and get the scores T, using the m-leading singular values that preserve of data variance.
3. Split the truncated scores matrix T into the corresponding Ttrain and Ttest (will be used in the testing phase) scores matrix.
4. Train a robust full quadratic regression model (Equation (10)) using Ttrain and ytrain (the instance labels inherited by the corresponding bag labels) and get the instance labels predictions Predtrain for each instance
5. Split the vector Predtrain into subsets of equal sizes and store the cutting points to be used as histogram bin edges in the testing phase
6. For each of the training bags calculate the normalized cumulative histogram and construct the feature matrix Atrain
7. Fit a QDA model to map Atrain to Ytrain (Equation (12)).
