# IFF-Net: Irregular Feature Fusion Network for Multimodal Remote Sensing Image Classification
## 1 Introduction
This shared subspace can better convey and interact information from different modalities and is suitable for multimodal and cross-modal remote sensing data classification tasks. Regularization is a widely employed technique in the fields of machine learning and statistics to effectively manage model complexity and fitting. During model training, regularization imposes a penalty on the model's complexity by incorporating a regularization term into the loss function. Subsequently, the researchers conducted a study on regression and regularization problems in the context of HSI-MSI feature fusion, aiming to predict the target variable or map it based on input features while employing regression methods to establish the relationship between HSI and MSI data. Various regression regularization conditions were explored, including _L2_ regularization and _L1_ regularization, with an emphasis on highlighting the superiority of _L1_-regularized regression for multimodal feature extraction [20]. Later, [PERSON] et al. [21] further expanded their investigation and introduced a framework known as learnable manifold alignment (LeMA) cross-modal learning within the domain of land use classification. [PERSON] et al. [22] conducted an in-depth investigation into the theory of topological analysis and proposed a semi-supervised fusion algorithm based on the mapper framework, which is a cutting-edge technology for topological data analysis enabling comprehensive examination and visualization of complex structures within high-dimensional datasets. The primary objective of their proposed algorithm is to effectively integrate multiple data modalities for accurate land cover and land use classification. However, the utilization of shallow feature classification models in these approaches poses challenges in effectively handling intricate sample data and nonlinearities. Furthermore, enhancing classification accuracy is hindered by the heavy reliance on a priori information within these methods. With the use and advantages of deep learning networks in remote sensing image classification, researchers have proposed various multimodal remote sensing data classification methods. These methods have been gradually used in the field of remote sensing image classification, and their classification accuracy is better than that of single-modal remote sensing image classification to a certain extent, and good classification results have been achieved [23; 24]. The performance of the multichannel network in classification tasks within remote sensing data heavily relies on the pivotal role played by the strategy for fusing multichannel data. It should be emphasized that the fusion strategy is indeed the crucial factor influencing the performance of multimodal networks [25]. [PERSON] et al. [26] introduced a CNN that incorporates feature-level fusion and decision-level fusion strategies to enhance classification accuracy. [PERSON] et al. [27] proposed an encoder-decoder network named EndNet, which proves to be a straightforward and efficient approach for classifying HSI and LiDAR data. In their study, [PERSON] et al. [28] introduced a multimodal deep learning approach that combines multispectral and multi-temporal satellite images to classify crops with remarkable precision. The research conducted by [PERSON] et al. [29] utilized diverse deep learning methods to assess urban traffic congestion, estimate the economic status of cities, and forecast potential ecological harm through the integration of remote sensing data and street view imagery. [PERSON] et al. [30] introduced a novel cross-aware CNN model for integrating diverse data types and enhancing the accuracy of joint classification. Despite the considerable advancements achieved by these deep learning techniques in CNNs, they have greatly enhanced the classification performance of HSI and LiDAR datasets, the limited training data and feature redundancy lead to a relatively high computational cost.