  Thermography has been used extensively as a complementary diagnostic tool in
breast cancer detection. Among thermographic methods matrix factorization (MF)
techniques show an unequivocal capability to detect thermal patterns
corresponding to vasodilation in cancer cases. One of the biggest challenges in
such techniques is selecting the best representation of the thermal basis. In
this study, an embedding method is proposed to address this problem and
Deep-semi-nonnegative matrix factorization (Deep-SemiNMF) for thermography is
introduced, then tested for 208 breast cancer screening cases. First, we apply
Deep-SemiNMF to infrared images to extract low-rank thermal representations for
each case. Then, we embed low-rank bases to obtain one basis for each patient.
After that, we extract 300 thermal imaging features, called thermomics, to
decode imaging information for the automatic diagnostic model. We reduced the
dimensionality of thermomics by spanning them onto Hilbert space using RBF
kernel and select the three most efficient features using the block Hilbert
Schmidt Independence Criterion Lasso (block HSIC Lasso). The preserved thermal
heterogeneity successfully classified asymptomatic versus symptomatic patients
applying a random forest model (cross-validated accuracy of 71.36%
(69.42%-73.3%)).
