The Tree of Life is a massive graphical structure which represents the evolutionary process from single cell organisms into the immense biodiversity of living species in present time. Estimating the Tree of Life would not only represent the greatest accomplishment in evolutionary biology and systematics, but it would also allow us to fully understand the development and evolution of important biological traits in nature, in particular, those related to resilience to extinction when exposed to environmental threats such as climate change. Therefore, the development of statistical and machine-learning theory to reconstruct the Tree of Life, especially those scalable to big data, are paramount in evolutionary biology, systematics, and conservation efforts against mass extinctions. Graphical structures that represent evolutionary processes are denoted phylogenetic trees. A phylogenetic tree is a binary tree whose internal nodes represent ancestral species that over time differentiate into two separate species giving rise to its two children nodes (see Figure 1 left). The evolutionary process is then depicted by this bifurcating tree from the root (the origin of life) to the external nodes of the tree (also denoted leaves) which represent the living organisms today.

It estimates the probability density function of a random variable Fukunaga & Hostetler (1975). The clustering algorithm is applied to a variety of areas, like segmentation images, Tao et al. (2007); Paris & Durand (2007), particularly medical and satellite images Lu et al. (2011); Ai & Xiong (2014); Wu & Luo (2015); Banerjee et al. (2012), videos Wang et al. (2004), and also applied to high dimensional data clustering Saptarshi et al. (2021). An adapted version of mean-shift clustering was applied to short segments speaker clustering Salmun et al. (2016b,a, 2017); Cohen & Lapidot (2021). This algorithm is deterministic and in an iterative procedure estimates the multi-modal probability density function (pdf) via the "climbing" path of each datum to its mode in a multi-modal distribution. All the data points that reached the same mode are grouped to the same cluster.

Knowledge Graphs (KGs) such as Resource Description Framework (RDF) data represent relationships between various entities through the structure of triples (). Knowledge graph embedding (KGE) is crucial in machine learning applications, specifically in node classification and link prediction tasks. KGE remains a vital research topic within the semantic web community. RDF-star introduces the concept of a quoted triple (QT), a specific form of triple employed either as the subject or object within another triple. Moreover, RDF-star permits a QT to act as compositional entities within another QT, thereby enabling the representation of recursive, hyper-relational KGs with nested structures. However, existing KGE models fail to adequately learn the semantics of QTs and entities, primarily because they do not account for RDF-star graphs containing multi-leveled nested QTs and QT-QT relationships. This study introduces RDF-star2Vec, a novel KGE model specifically designed for RDF-star graphs. RDF-star2Vec introduces graph walk techniques that enable probabilistic transitions between a QT and its compositional entities. Feature vectors for QTs, entities, and relations are derived from generated sequences through the structured skip-gram model. Additionally, we provide a dataset and a benchmarking framework for data mining tasks focused on complex RDF-star graphs. Evaluative experiments demonstrated that RDF-star2Vec yielded superior performance compared to recent extensions of RDF2Vec in various tasks including classification, clustering, entity relatedness, and QT similarity.

Traditional clustering algorithms often struggle to capture the complex relationships within graphs and generalise to arbitrary clustering criteria. The emergence of graph neural networks (GNNs) as a powerful framework for learning representations of graph data provides new approaches to solving the problem. Previous work has shown GNNs to be capable of proposing partitionings using a variety of criteria, however, these approaches have not yet been extended to work on Markov chains or kinetic networks. These arise frequently in the study of molecular systems and are of particular interest to the biochemical modelling community. In this work, we propose several GNN-based architectures to tackle the graph partitioning problem for Markov Chains described as kinetic networks. This approach aims to minimize how much a proposed partitioning changes the Kemeny constant. We propose using an encoder-decoder architecture and show how simple GraphSAGE-based GNNs with linear layers can outperform much larger and more expressive attention-based models in this context. As a proof of concept, we first demonstrate the method's ability to cluster randomly connected graphs. We also use a linear chain architecture corresponding to a 1D free energy profile as our kinetic network. Subsequently, we demonstrate the effectiveness of our method through experiments on a data set derived from molecular dynamics. We compare the performance of our method to other partitioning techniques such as PCCA+. We explore the importance of feature and hyperparameter selection and propose a general strategy for large-scale parallel training of GNNs for discovering optimal graph partitionings.

The growth of network-connected devices has led to an exponential increase in data generation, creating significant challenges for efficient data analysis. This data is generated continuously, creating a dynamic flow known as a data stream. The characteristics of a data stream may change dynamically, and this change is known as concept drift. Consequently, a method for handling data streams must efficiently reduce their volume while dynamically adapting to these changing characteristics. This paper proposes a simple online vector quantization method for concept drift. The proposed method identifies and replaces units with low win probability through remove-birth updating, thus achieving a rapid adaptation to concept drift. Furthermore, the results of this study show that the proposed method can generate minimal dead units even in the presence of concept drift. This study also suggests that some metrics calculated from the proposed method will be helpful for drift detection.

Clustering is a fundamental unsupervised representation learning task with wide application in computer vision and pattern recognition. Deep clustering utilizes deep neural networks to learn latent representation, which is suitable for clustering. However, previous deep clustering methods, especially image clustering, focus on the features of the data itself and ignore the relationship between the data, which is crucial for clustering. In this paper, we propose a novel Deep Structure and Attention aware Subspace Clustering (DSASC), which simultaneously considers data content and structure information. We use a vision transformer to extract features, and the extracted features are divided into two parts, structure features, and content features. The two features are used to learn a more efficient subspace structure for spectral clustering. Extensive experimental results demonstrate that our method significantly outperforms state-of-the-art methods. Our code will be available at https://github.com/cs-whh/DSASC

Hyperspectral images (HSIs) provide exceptional spatial and spectral resolution of a scene, crucial for various remote sensing applications. However, the high dimensionality, presence of noise and outliers, and the need for precise labels of HSIs present significant challenges to HSIs analysis, motivating the development of performant HSI clustering algorithms. This paper introduces a novel unsupervised HSI clustering algorithm, Superpixel-based and Spatially-regularized Diffusion Learning (S2DL), which addresses these challenges by incorporating rich spatial information encoded in HSIs into diffusion geometry-based clustering. S2DL employs the Entropy Rate Superpixel (ERS) segmentation technique to partition an image into superpixels, then constructs a spatially-regularized diffusion graph using the most representative high-density pixels. This approach reduces computational burden while preserving accuracy. Cluster modes, serving as exemplars for underlying cluster structure, are identified as the highest-density pixels farthest in diffusion distance from other highest-density pixels. These modes guide the labeling of the remaining representative pixels from ERS superpixels. Finally, majority voting is applied to the labels assigned within each superpixel to propagate labels to the rest of the image. This spatial-spectral approach simultaneously simplifies graph construction, reduces computational cost, and improves clustering performance. S2DL's performance is illustrated with extensive experiments on three publicly available, real-world HSIs: Indian Pines, Salinas, and Salinas A. Additionally, we apply S2DL to landscape-scale, unsupervised mangrove species mapping in the Mai Po Nature Reserve, Hong Kong, using a Gaofen-5 HSI. The success of S2DL in these diverse numerical experiments indicates its efficacy on a wide range of important unsupervised remote sensing analysis tasks.

This study investigates clustered federated learning (FL), one of the formulations of FL with non-i.i.d. data, where the devices are partitioned into clusters and each cluster optimally fits its data with a localized model. We propose a clustered FL framework that incorporates a nonconvex penalty to pairwise differences of parameters. Without a priori knowledge of the set of devices in each cluster and the number of clusters, this framework can autonomously estimate cluster structures. To implement the proposed framework, we introduce a novel clustered FL method called Fusion Penalized Federated Clustering (FPFC). Building upon the standard alternating direction method of multipliers (ADMM), FPFC can perform partial updates at each communication round and allows parallel computation with variable workload. These strategies significantly reduce the communication cost while ensuring privacy, making it practical for FL. We also propose a new warmup strategy for hyperparameter tuning in FL settings and explore the asynchronous variant of FPFC (asyncFPFC). Theoretical analysis provides convergence guarantees for FPFC with general losses and establishes the statistical convergence rate under a linear model with squared loss. Extensive experiments have demonstrated the superiority of FPFC compared to current methods, including robustness and generalization capability.

Phenotypic (or Physical) characteristics of plant species are commonly used to perform clustering. In one of our recent works (Shastri et al. (2021)), we used a probabilistically sampled (using pivotal sampling) and spectrally clustered algorithm to group soybean species. These techniques were used to obtain highly accurate clusterings at a reduced cost. In this work, we extend the earlier algorithm to cluster rice species. We improve the base algorithm in three ways. First, we propose a new function to build the similarity matrix in Spectral Clustering. Commonly, a natural exponential function is used for this purpose. Based upon the spectral graph theory and the involved Cheeger's inequality, we propose the use a base "a" exponential function instead. This gives a similarity matrix spectrum favorable for clustering, which we support via an eigenvalue analysis. Second, the function used to build the similarity matrix in Spectral Clustering was earlier scaled with a fixed factor (called global scaling). Based upon the idea of Zelnik-Manor and Perona (2004), we now use a factor that varies with matrix elements (called local scaling) and works better. Third, to compute the inclusion probability of a specie in the pivotal sampling algorithm, we had earlier used the notion of deviation that captured how far specie's characteristic values were from their respective base values (computed over all species). A maximum function was used before to find the base values. We now use a median function, which is more intuitive. We support this choice using a statistical analysis. With experiments on 1865 rice species, we demonstrate that in terms of silhouette values, our new Sampled Spectral Clustering is 61% better than Hierarchical Clustering (currently prevalent). Also, our new algorithm is significantly faster than Hierarchical Clustering due to the involved sampling.

Latent multi-view subspace clustering has been demonstrated to have desirable clustering performance. However, the original latent representation method vertically concatenates the data matrices from multiple views into a single matrix along the direction of dimensionality to recover the latent representation matrix, which may result in an incomplete information recovery. To fully recover the latent space representation, we in this paper propose an Enhanced Latent Multi-view Subspace Clustering (ELMSC) method. The ELMSC method involves constructing an augmented data matrix that enhances the representation of multi-view data. Specifically, we stack the data matrices from various views into the block-diagonal locations of the augmented matrix to exploit the complementary information. Meanwhile, the non-block-diagonal entries are composed based on the similarity between different views to capture the consistent information. In addition, we enforce a sparse regularization for the non-diagonal blocks of the augmented self-representation matrix to avoid redundant calculations of consistency information. Finally, a novel iterative algorithm based on the framework of Alternating Direction Method of Multipliers (ADMM) is developed to solve the optimization problem for ELMSC. Extensive experiments on real-world datasets demonstrate that our proposed ELMSC is able to achieve higher clustering performance than some state-of-art multi-view clustering methods.