Traditional image classification often misclassifies unknown samples as known classes during testing, degrading recognition accuracy. Open-set image recognition can simultaneously detect known classes (KCs) and unknown classes (UCs) but still struggles to improve recognition performance caused by open space risk. Therefore, we introduce a cosine distance loss function (CDLoss), which exploits the orthogonality of one-hot encoding vectors to align known samples with their corresponding one-hot encoder directions. This reduces the overlap between the feature spaces of KCs and UCs, mitigating open space risk. CDLoss was incorporated into both Softmax-based and prototype-learning-based frameworks to evaluate its effectiveness. Experimental results show that CDLoss improves AUROC, OSCR, and accuracy across both frameworks and different datasets. Furthermore, various weight combinations of the ARPL and CDLoss were explored, revealing optimal performance with a 1:2 ratio. T-SNE analysis confirms that CDLoss reduces the overlap between the feature spaces of KCs and UCs. These results demonstrate that CDLoss helps mitigate open space risk, enhancing recognition performance in open-set image classification tasks.