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Patterns of interacting amino acids are so preserved within protein families that the sole analysis of evolutionary comutations can identify pairs of contacting residues. It is also known that evolution conserves functional dynamics, i.e., the concerted motion or displacement of large protein regions or domains. Is it, therefore, possible to use a pure sequence-based analysis to identify these dynamical domains? To address this question, we introduce here a general coevolutionary coupling analysis strategy and apply it to a curated sequence database of hundreds of protein families. For most families, the sequence-based method partitions amino acids into a few clusters. When viewed in the context of the native structure, these clusters have the signature characteristics of viable protein domains: They are spatially separated but individually compact. They have a direct functional bearing too, as shown for various reference cases. We conclude that even large-scale structural and functionally related properties can be recovered from inference methods applied to evolutionary-related sequences. The method introduced here is available as a software package and web server (spectrus.sissa.it/spectrusevo webserver).

Immune checkpoint inhibitors (ICIs) have improved outcomes in metastatic urothelial carcinoma (mUC) but clinical responses remain highly heterogenous. Traditional binary classification of response overlooks clinically relevant variability within each group but a more detailed understanding of intra-group heterogeneity may support subclass-specific therapeutic strategies. We developed a novel analysis framework that integrates interpretable feature extraction and spectral clustering to identify patient subclasses associated with heterogeneous responses to ICIs. This method was applied to tumor transcriptomic data from the IMvigor210 cohort (n = 298), comprising mUC patients treated with atezolizumab. Interpretable features based on SHapley Additive exPlanations (SHAP) were computed from a response classification model to quantify patient-level gene contributions, which were then used for spectral clustering. An independent cohort (GSE176307, n = 88) was used for external validation. This approach identified four patient clusters with distinct immune phenotypes and response patterns. Cluster 3 (92.3% responders) showed an inflamed phenotype with high PD-L1 expression, T cell activation, and TP53 mutations. Cluster 1 (100% non-responders) displayed an immune-desert phenotype with FGFR3 mutations and elevated TGF-β signaling. Cluster 2 was more heterogeneous, containing two subgroups (Sub 1 and Sub 2) with differing immune activity and immunosuppressive gene expression, corresponding to response rates of 23.2% and 77.3%, respectively. Similar patterns were observed in the validation cohort. Our framework, which combines SHAP-based interpretable feature extraction with spectral clustering, revealed subclass-level heterogeneity in ICI response, highlighting biologically distinct immune subclasses. This approach may facilitate the development of subclass-specific therapeutic strategies.

Many real-world systems consist of several types of entities, and heterogeneous networks are required to represent such systems. However, the current statistical toolbox for network data can only deal with homogeneous networks, where all nodes are supposed to be of the same type. This article introduces a statistical framework for community detection in heterogeneous networks. For modeling heterogeneous networks, we propose heterogeneous versions of both the classical stochastic blockmodel and the degree-corrected blockmodel. For community detection, we formulate heterogeneous versions of standard spectral clustering and regularized spectral clustering. We demonstrate the theoretical accuracy of the proposed heterogeneous methods for networks generated from the proposed heterogeneous models. Our simulations establish the superiority of proposed heterogeneous methods over existing homogeneous methods in finite networks generated from the models. An analysis of the DBLP four-area data demonstrates the improved accuracy of the heterogeneous method over the homogeneous method in identifying research areas for authors.

Intentional controlled islanding (ICI) is a final resort for preventing a cascading failure and catastrophic power system blackouts. This paper proposes a controlled islanding algorithm that uses spectral clustering over multi-layer graphs to find a suitable islanding solution. The multi-criteria objective function used in this controlled islanding algorithm involves the correlation coefficients between bus frequency components and minimum active and reactive power flow disruptions. Similar to the previous studies, the algorithm is applied in two stages. In the first stage, groups of coherent buses are identified with the help of modularity clustering using correlation coefficients between bus frequency components. In the second stage, the ICI solution satisfying bus coherency with minimum active and reactive power flow disruptions is determined by grouping all nodes using spectral clustering on the multi-layer graph. Simulation studies on the IEEE 39-bus test system demonstrate the effectiveness of the method in determining an islanding solution in real time while addressing the generator coherency problem.

Spectral Clustering is a graph clustering algorithm that makes use of eigenvector obtained from a matrix describing pairwise similarity between data points. It provides a dimensionality reduction for clustering in lower dimensions. One example of spectral clustering application is the clustering of protein-protein interaction (PPI) network. PPI networks are usually represented as a graph network with proteins and interactions as vertices and edges respectively. However, this spectral clustering only produces a hard clustering of proteins, whereas there may be some relationship between each protein clusters, and possibly multiple functionality for each proteins that has not been detected before. Fuzzy Random Walk is a fuzzy clustering method based on transition probability from a random walk on a dataset. In this paper, we combine both Spectral Clustering and Fuzzy Random Walk to cluster PPI network of protein TP53, a protein thatplays an important role in managing cell cycle, especially in tumor cell suppression. Using PPI dataset of TP53 obtained from the STRING database, we found the combined algorithm is proven to produce both robust and fuzzy clusters with each cluster explains one of TP53 protein's functionality related to the tumor cell.

We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as log n, with n the number of nodes. This result applies to some popular polynomial time spectral clustering algorithms and is further extended to degree corrected stochastic block models using a spherical k-median spectral clustering method. A key component of our analysis is a combinatorial bound on the spectrum of binary random matrices, which is sharper than the conventional matrix Bernstein inequality and may be of independent interest.

Aspergillus series Versicolores are molds distributed among 17 species, commonly found in our environment, and responsible for infections. Since 2022, a new taxonomy has grouped them into 4 major lineages: A. versicolor, A. subversicolor, A. sydowii, and A. creber. Matrix-Assisted Laser Desorption/Ionization Time-Of-Flight Mass Spectrometry (MALDI-TOF MS) could be a faster and more cost-effective alternative to molecular techniques for identifying them by developing a local database. To evaluate this technique, 30 isolates from Aspergillus series Versicolores were used. A total of 59 main spectra profiles (MSPs) were created in the local database. This protocol enabled accurate identification of 100% of the extracted isolates, of which 97% (29/30) were correctly identified with a log score ≥ 2.00. Some MSPs recorded as Aspergillus versicolor in the supplier’s database could lead to false identifications as they did not match with the correct lineages. Although the local database is still limited in the number and diversity of species of Aspergillus series Versicolores, it is sufficiently effective for correct lineage identification according to the latest taxonomic revision, and better than the MALDI-TOF MS supplier’s database. This technology could improve the speed and accuracy of routine fungal identification for these species.

Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCBMs). We first derive asymptotic minimax risks of the problem for a misclassification proportion loss under appropriate conditions. The minimax risks are shown to depend on degree-correction parameters, community sizes and average within and between community connectivities in an intuitive and interpretable way. In addition, we propose a polynomial time algorithm to adaptively perform consistent and even asymptotically optimal community detection in DCBMs.

Spectral clustering is one of the most popular algorithms to group high-dimensional data. It is easy to implement and computationally efficient. Despite its popularity and successful applications, its theoretical properties have not been fully understood. In this paper, we show that spectral clustering is minimax optimal in the Gaussian mixture model with isotropic covariance matrix, when the number of clusters is fixed and the signal-to-noise ratio is large enough. Spectral gap conditions are widely assumed in the literature to analyze spectral clustering. On the contrary, these conditions are not needed to establish optimality of spectral clustering in this paper.

The Shipboard Automatic Identification System (AIS) is crucial for navigation safety and maritime surveillance, data mining and pattern analysis of AIS information have attracted considerable attention in terms of both basic research and practical applications. Clustering of spatio-temporal AIS trajectories can be used to identify abnormal patterns and mine customary route data for transportation safety. Thus, the capacities of navigation safety and maritime traffic monitoring could be enhanced correspondingly. However, trajectory clustering is often sensitive to undesirable outliers and is essentially more complex compared with traditional point clustering. To overcome this limitation, a multi-step trajectory clustering method is proposed in this paper for robust AIS trajectory clustering. In particular, the Dynamic Time Warping (DTW), a similarity measurement method, is introduced in the first step to measure the distances between different trajectories. The calculated distances, inversely proportional to the similarities, constitute a distance matrix in the second step. Furthermore, as a widely-used dimensional reduction method, Principal Component Analysis (PCA) is exploited to decompose the obtained distance matrix. In particular, the top k principal components with above 95% accumulative contribution rate are extracted by PCA, and the number of the centers k is chosen. The k centers are found by the improved center automatically selection algorithm. In the last step, the improved center clustering algorithm with k clusters is implemented on the distance matrix to achieve the final AIS trajectory clustering results. In order to improve the accuracy of the proposed multi-step clustering algorithm, an automatic algorithm for choosing the k clusters is developed according to the similarity distance. Numerous experiments on realistic AIS trajectory datasets in the bridge area waterway and Mississippi River have been implemented to compare our proposed method with traditional spectral clustering and fast affinity propagation clustering. Experimental results have illustrated its superior performance in terms of quantitative and qualitative evaluations.