Wafer map defect pattern classification is a critical step in semiconductor manufacturing, significantly impacting product yield and production efficiency. To address the limitations of existing deep learning-based wafer map defect pattern classification methods, such as poor interpretability and high computational resource consumption, this study proposes an improved feature extraction method based on topological data analysis (TDA). By leveraging persistent homology theory, the method constructs Alpha complexes to characterize topological structures in wafer maps and quantifies them into discriminative features. Experimental results on a synthetic wafer map dataset, generated by emulating the geometric distribution characteristics of the WM-811K dataset, demonstrate that replacing the conventional vietoris-rips (VR) complex with the Alpha complex reduces the average complex construction time by approximately 82% and decreases memory usage by 10.09%. Compared to state-of-the-art models including DenseNet121, Swin Transformer, and ConvNeXt, the TDA-based method achieves superior clustering performance, as evidenced by t-SNE visualizations, with a 17.24% improvement in Silhouette Coefficient over the suboptimal ConvNeXt model, along with a 75% reduction in feature extraction time and a 95% reduction in peak memory consumption. When integrated with a support vector machine (SVM) classifier, the TDA-based framework attains an overall classification accuracy of 0.992, outperforming DenseNet (0.989 3) and Swin Transformer (0.982 0).