  Breast cancer is the most widespread neoplasm among women and early detection
of this disease is critical. Deep learning techniques have become of great
interest to improve diagnostic performance. However, distinguishing between
malignant and benign masses in whole mammograms poses a challenge, as they
appear nearly identical to an untrained eye, and the region of interest (ROI)
constitutes only a small fraction of the entire image. In this paper, we
propose a framework, parameterized hypercomplex attention maps (PHAM), to
overcome these problems. Specifically, we deploy an augmentation step based on
computing attention maps. Then, the attention maps are used to condition the
classification step by constructing a multi-dimensional input comprised of the
original breast cancer image and the corresponding attention map. In this step,
a parameterized hypercomplex neural network (PHNN) is employed to perform
breast cancer classification. The framework offers two main advantages. First,
attention maps provide critical information regarding the ROI and allow the
neural model to concentrate on it. Second, the hypercomplex architecture has
the ability to model local relations between input dimensions thanks to
hypercomplex algebra rules, thus properly exploiting the information provided
by the attention map. We demonstrate the efficacy of the proposed framework on
both mammography images as well as histopathological ones. We surpass
attention-based state-of-the-art networks and the real-valued counterpart of
our approach. The code of our work is available at
https://github.com/ispamm/AttentionBCS.
