Increasingly, malwares are becoming complex and they are spreading on networks targeting different infrastructures and personal-end devices to collect, modify, and destroy victim information. Malware behaviors are polymorphic, metamorphic, persistent, able to hide to bypass detectors and adapt to new environments, and even leverage machine learning techniques to better damage targets. Thus, it makes them difficult to analyze and detect with traditional endpoint detection and response, intrusion detection and prevention systems. To defend against malwares, recent work has proposed different techniques based on signatures and machine learning. In this paper, we propose to use an algebraic topological approach called topological-based data analysis (TDA) to efficiently analyze and detect complex malware patterns. Next, we compare the different TDA techniques (i.e., persistence homology, tomato, TDA Mapper) and existing techniques (i.e., PCA, UMAP, t-SNE) using different classifiers including random forest, decision tree, xgboost, and lightgbm. We also propose some recommendations to deploy the best-identified models for malware detection at scale. Results show that TDA Mapper (combined with PCA) is better for clustering and for identifying hidden relationships between malware clusters compared to PCA. Persistent diagrams are better to identify overlapping malware clusters with low execution time compared to UMAP and t-SNE. For malware detection, malware analysts can use Random Forest and Decision Tree with t-SNE and Persistent Diagram to achieve better performance and robustness on noised data.