We propose a nested ensemble learning framework that utilizes Topological Data Analysis (TDA) to extract and integrate topological features from graph data, with the goal of improving performance on classification and regression tasks. Our approach computes persistence diagrams (PDs) using lower-star filtrations induced by three filter functions: closeness, betweenness, and degree2 centrality. To overcome the limitation of relying on a single filter, these PDs are integrated through a data-driven, three-level architecture. At Level-0, diverse base models are independently trained on the topological features extracted for each filter function. At Level-1, a meta-learner combines the predictions of these base models for each filter to form filter-specific ensembles. Finally, at Level-2, a meta-learner integrates the outputs of these filter-specific ensembles to produce the final prediction. We evaluate our method on both simulated and real-world graph datasets. Experimental results demonstrate that our framework consistently outperforms base models and standard stacking methods, achieving higher classification accuracy and lower regression error. It also surpasses existing state-of-the-art approaches, ranking among the top three models across all benchmarks.
In the lower-star filtration (LSF), simplices are assigned filtration values according to the maximum-vertex rule, with each simplex entering the filtration when its highest-valued vertex appears. A limitation of this construction is that some higher-dimensional simplices may enter simultaneously with their boundary faces, causing certain topological features to be filled immediately upon formation and thus not appear in the resulting persistence diagram. To address this limitation, we propose three alternative filtration methods: the \(\varepsilon\)-lower-star filtration (ELSF), the \(L_p\) filtration (LpF), and the softmax filtration (SMF). {ELSF introduces a dimension-dependent delay to the maximum-vertex rule,} allowing higher-dimensional simplices to enter the filtration after their boundary faces, whereas {LpF and SMF use aggregation functions that depend on all vertex values rather} than solely on their maximum. By modifying how filtration values are assigned, these methods allow simplices to enter the filtration more progressively, so that topological features such as loops and voids may persist over longer filtration intervals rather than being filled immediately. Consequently, the resulting persistence diagrams may include persistence features that are not observed under LSF, potentially providing useful information for distinguishing data populations. Experimental results on simulated and real-world datasets demonstrate that the proposed filtration methods are computationally efficient and can provide greater sensitivity to structural differences in the data than LSF.