Knee OsteoArthritis (KOA) is a prevalent musculoskeletal disorder that causes decreased mobility in seniors. The diagnosis provided by physicians is subjective, however, as it relies on personal experience and the semi-quantitative Kellgren-Lawrence (KL) scoring system. KOA has been successfully diagnosed by Computer-Aided Diagnostic (CAD) systems that use deep learning techniques like Convolutional Neural Networks (CNN). In this paper, we propose a novel Siamese-based network, and we introduce a new hybrid loss strategy for the early detection of KOA. The model extends the classical Siamese network by integrating a collection of Global Average Pooling (GAP) layers for feature extraction at each level. Then, to improve the classification performance, a novel training strategy that partitions each training batch into low-, medium- and high-confidence subsets, and a specific hybrid loss function are used for each new label attributed to each sample. The final loss function is then derived by combining the latter loss functions with optimized weights. Our test results demonstrate that our proposed approach significantly improves the detection performance.