  Convolutional Neural Network (CNN) struggle to capture the multi-dimensional
structural information of complex high-dimensional data, which limits their
feature learning capability. This paper proposes a feature fusion method based
on Topological Data Analysis (TDA) and CNN, named TDA-CNN. This method combines
numerical distribution features captured by CNN with topological structure
features captured by TDA to improve the feature learning and representation
ability of CNN. TDA-CNN divides feature extraction into a CNN channel and a TDA
channel. CNN channel extracts numerical distribution features, and the TDA
channel extracts topological structure features. The two types of features are
fused to form a combined feature representation, with the importance weights of
each feature adaptively learned through an attention mechanism. Experimental
validation on datasets such as Intel Image, Gender Images, and Chinese
Calligraphy Styles by Calligraphers demonstrates that TDA-CNN improves the
performance of VGG16, DenseNet121, and GoogleNet networks by 17.5%, 7.11%, and
4.45%, respectively. TDA-CNN demonstrates improved feature clustering and the
ability to recognize important features. This effectively enhances the model's
decision-making ability.
