Balancing Two Classifiers via A Simplex ETF Structure for Model Calibration

As shown in Definition 1, within the general Simplex ETF framework, in addition to β, the term K K-1 in the matrix M serves as a scaling factor, ensuring that each column vector has a fixed length. This scaling ensures that each column vector in M has an equal norm, which is crucial for maintaining the isometric property required by a Simplex ETF. The scaling factor β K K-1 , plays a crucial role in shaping the model's probability distribution, output confidence, and ultimately its classification performance. A detailed analysis of this factor provides a deeper understanding of its adjustment mechanism and core functionality in classification models.