Unsupervised Learning with Mini Free Energy

摘要

In this paper, we present an unsupervised learning with mini free energy for early breast cancer detection. Although an early malignant tumor must be small in size, the abnormal cells reveal themselves physiologically by emitting spontaneously thermal radiation due to the rapid cell growth, the so-called angiogenesis effect. This forms the underlying principle of Thermal Infrared (TIR) imaging in breast cancer study. Thermal breast scanning has been employed for a number of years, which however is limited to a single infrared band. In this research, we deploy two satellite-grade dual-color (at middle wavelength IR (3 — 5μm) and long wavelength IR (8 — 12μm)) IR imaging cameras equipped with smart subpixel automatic target detection algorithms. According to physics, the radiation of high/low temperature bodies will shift toward a shorter/longer IR wavelength band. Thus, the measured vector data x per pixel can be used to invert the matrix-vector equation x = As pixel-by-pixel independently, known as a single pixel blind sources separation (BSS). We impose the universal constraint of equilibrium physics governing the blackbody Planck radiation distribution, i.e., the minimum Helmholtz free energy, H = E — T-oS. To stabilize the solution of Lagrange constrained neural network (LCNN) proposed by Szu et al., we incorporate the second order approximation of free energy, which corresponds to the second order constraint in the method of multipliers. For the subpixel target, we assume the constant ground state energy E-o can be determined by those normal neighborhood tissue, and then the excited state can be computed by means of Taylor series expansion in terms of the pixel I/O data. We propose an adaptive method to determine the neighborhood to find the free energy locally. The proposed methods enhance both the sensitivity and the accuracy of traditional breast cancer diagnosis techniques. It can be used as a first line supplement to traditional mammography to reduce the unwanted X-rays during the chemotherapy recovery. More important, the single pixel BSS method renders information on the tumor stage and tumor degree during the recovery process, which is not available using the popular independent component analysis (ICA) techniques.