Run demo.m. This can reproduce the results in Fig.4A for the following TWO clustering methods on 30 test datasets.

1. ND-Ward-E(KT): the proposed clustering method (Title: "Enhancing In-Tree-based Clustering via Distance Ensemble and Kernelization" by Qiu and Li, in Pattern Recognition, 2020.);

2. ND-K: a compared method (Qiu, et al. "Nearest descent, in-tree, and clustering",arXiv:1412.5902v2, 2014).

Note: a) ND-K is the basis of ND-Ward-E(KT); b) for ND.m, function "maxk" may not exist in low-version Matlab; in this case, the following code behind it in ND.m can be used instead (we have highlighted it in ND.m). c) you can also choose to directly run the code in my code ocean: https://codeocean.com/capsule/6383011/tree/v1

Recently, we have proposed a novel physically-inspired method, called the Nearest Descent (ND), which plays the role of organizing all the samples into an effective Graph, called the in-tree (Fig. 1A). Due to its effective characteristics, this in-tree proves very suitable for data clustering. Nevertheless, this in-tree-based clustering still has some non-trivial limitations in terms of robustness, capability, etc. In this study, we first propose a distance-ensemble-based framework for the in-tree-based clustering, which proves a very convenient way to overcome the robustness limitation in our previous in-tree-based clustering. To enhance the capability of the in-tree-based clustering in handling extremely linearly-inseparable clusters, we kernelize the proposed ensemble-based clustering via the so-called kernel trick. As a result (Fig. 4), the improved in-tree-based clustering method achieves high robustness and accuracy on diverse challenging synthetic and real-world datasets, showing a certain degree of practical value.

Fig.1: Comparison between the in-tree (A) and the MST (B) of the same dataset. In (A), the inter-cluster edges are highlighted in red (the rest edges are the intra-cluster ones). MST: minimal spanning tree.

Fig.4: Results of the 1st group of experiments. (A) The scores (NMI) of different methods (columns) with fixed empirical parameter values across all synthetic and real-world datasets (rows). See cluster structures of all the 2-dimensional synthetic datasets in Fig. 2 (in the following). The methods in bold are the density-peak-based methods; the rest are the level-set-based ones. The highest score (on NMI) for each row is marked in bold (Note: for the evaluation index NMI, a higher value means better performance and a value of 1 means the best result). (B) and (C) show the mean and variance of the scores of each method on all the datasets, respectively.

Fig.2: The cluster structures of all the 2-dimensional synthetic datasets.