Joint dimension reduction and clustering analysis of single-cell RNA-seq and spatial transcriptomics data.

Spatial clustering has been widely used for spatial data mining and knowledge discovery. An ideal multivariate spatial clustering should consider both spatial contiguity and aspatial attributes. Existing spatial clustering approaches may face challenges for discovering repeated geographic patterns with spatial contiguity maintained. In this paper, we propose a Spatial Toeplitz Inverse Covariance-Based Clustering (STICC) method that considers both attributes and spatial relationships of geographic objects for multivariate spatial clustering. A subregion is created for each geographic object serving as the basic unit when performing clustering. A Markov random field is then constructed to characterize the attribute dependencies of subregions. Using a spatial consistency strategy, nearby objects are encouraged to belong to the same cluster. To test the performance of the proposed STICC algorithm, we apply it in two use cases. The comparison results with several baseline methods show that the STICC outperforms others significantly in terms of adjusted rand index and macro-F1 score. Join count statistics is also calculated and shows that the spatial contiguity is well preserved by STICC. Such a spatial clustering method may benefit various applications in the fields of geography, remote sensing, transportation, and urban planning, etc.

In recent years, the application of single-cell transcriptomics and spatial transcriptomics analysis techniques has become increasingly widespread. Whether dealing with single-cell transcriptomic or spatial transcriptomic data, dimensionality reduction and clustering are indispensable. Both single-cell and spatial transcriptomic data are often high-dimensional, making the analysis and visualization of such data challenging. Through dimensionality reduction, it becomes possible to visualize the data in a lower-dimensional space, allowing for the observation of relationships and differences between cell subpopulations. Clustering enables the grouping of similar cells into the same cluster, aiding in the identification of distinct cell subpopulations and revealing cellular diversity, providing guidance for downstream analyses. In this review, we systematically summarized the most widely recognized algorithms employed for the dimensionality reduction and clustering analysis of single-cell transcriptomic and spatial transcriptomic data. This endeavor provides valuable insights and ideas that can contribute to the development of novel tools in this rapidly evolving field.

The hidden Markov random field (HMRF) model is an efficient method for image segmentation. However, it may not accurately segment a poorly defined image like Magnetic Resonance (MR) brain image. The HMRF model uses an initial estimation for tissue segmentation of MR brain image. The initial estimation of an input image has a large role to play to obtain a robust HMRF model. In general, a hard clustering method is used for initial estimation. However, it is not an efficient technique for the segmentation of a complex and irregular shape image like MR brain image. The method of clustering acts as a preprocessing step in improving the performance of HMRF. It aims at producing a set of concise data in the segmentation of brain tissues. In this paper, we propose a new approach to HMRF model, which incorporates the fuzzy C-means (FCM) clustering for the initial estimation of the brain image, which is not found in the literature. This results in efficient segmentation of brain tissues. The results are compared with the spatial FCM clustering algorithm and HMRF model with K-means clustering, using different segmentation evaluation indices. It is seen that the results are better than the other methods.

ABSTRACTThe discovery of spatial clusters formed by proximal spatial units with similar non-spatial attribute values plays an important role in spatial data analysis. Although several spatial contiguity-constrained clustering methods are currently available, almost all of them discover clusters in a geographical dataset, even though the dataset has no natural clustering structure. Statistically evaluating the significance of the degree of homogeneity within a single spatial cluster is difficult. To overcome this limitation, this study develops a permutation test approach Specifically, the homogeneity of a spatial cluster is measured based on the local variance and cluster member permutation, and two-stage permutation tests are developed to determine the significance of the degree of homogeneity within each spatial cluster. The proposed permutation tests can be integrated into the existing spatial clustering algorithms to detect homogeneous spatial clusters. The proposed tests are compared with four existing tests (i.e., Park’s test, the contiguity-constrained nonparametric analysis of variance (COCOPAN) method, spatial scan statistic, and q-statistic) using two simulated and two meteorological datasets. The comparison shows that the proposed two-stage permutation tests are more effective to identify homogeneous spatial clusters and to determine homogeneous clustering structures in practical applications.

Spatial clustering is frequently used in Spatial Data Mining. Spatial clustering methods in presently available literature have obvious limitations in solving spatial clustering problems. On the basis of comparing and analyzing the capability of each spatial clustering method, a new one based on field model is put forward according to the particularity of spatial clustering (complexity in cluster shape and multi-scale-property in cluster structure), so as to solve all kinds of problems of presently spatial clustering research which organizes data with object model and represents continuous space with discrete entities, and make it be adapted to representation of complicated spatial clustering structure.

Recent advancements in spatial transcriptomics (ST) technologies offer unprecedented opportunities to unveil the spatial heterogeneity of gene expression and cell states within tissues. Despite these capabilities of the ST data, accurately dissecting spatiotemporal structures (e.g., spatial domains, temporal trajectories, and functional interactions) remains challenging. Here, we introduce a computational framework, PearlST (partial differential equation [PDE]-enhanced adversarial graph autoencoder of ST), for accurate inference of spatiotemporal structures from the ST data using PDE-enhanced adversarial graph autoencoder. PearlST employs contrastive learning to extract histological image features, integrates a PDE-based diffusion model to enhance characterization of spatial features at domain boundaries, and learns the latent low-dimensional embeddings via Wasserstein adversarial regularized graph autoencoders. Comparative analyses across multiple ST datasets with varying resolutions demonstrate that PearlST outperforms existing methods in spatial clustering, trajectory inference, and pseudotime analysis. Furthermore, PearlST elucidates functional regulations of the latent features by linking intercellular ligand-receptor interactions to most contributing genes of the low-dimensional embeddings, as illustrated in a human breast cancer dataset. Overall, PearlST proves to be a powerful tool for extracting interpretable latent features and dissecting intricate spatiotemporal structures in ST data across various biological contexts.

Spatial transcriptomics (ST) technologies enable dissecting the tissue architecture in spatial context. To perceive the global contextual information of gene expression patterns in tissue, the spatial dependence of cells must be fully considered by integrating both local and non-local features by means of spatial-context-aware. However, the current ST integration algorithm ignores for ST dropouts, which impedes the spatial-aware of ST features, resulting in challenges in the accuracy and robustness of microenvironmental heterogeneity detecting, spatial domain clustering, and batch-effects correction. Here, we developed an STMGraph, a universal dual-view dynamic deep learning framework that combines dual-remask (MASK-REMASK) with dynamic graph attention model (DGAT) to exploit ST data outperforming pre-existing tools. The dual-remask mechanism masks the embeddings before encoding and decoding, establishing dual-decoding-view to share features mutually. DGAT leverages self-supervision to update graph linkage relationships from two distinct perspectives, thereby generating a comprehensive representation for each node. Systematic benchmarking against 10 state-of-the-art tools revealed that the STMGraph has the optimal performance with high accuracy and robustness on spatial domain clustering for the datasets of diverse ST platforms from multi- to sub-cellular resolutions. Furthermore, STMGraph aggregates ST information cross regions by dual-remask to realize the batch-effects correction implicitly, allowing for spatial domain clustering of ST multi-slices. STMGraph is platform independent and superior in spatial-context-aware to achieve microenvironmental heterogeneity detection, spatial domain clustering, batch-effects correction, and new biological discovery, and is therefore a desirable novel tool for diverse ST studies

Spatial clustering is an essential method for the comprehensive understanding of a region. Spatial clustering divides all spatial units into different clusters. The attributes of each cluster of the spatial units are similar, and simultaneously, they are as continuous as spatially possible. In spatial clustering, the handling of spatial outliers is important. It is necessary to improve spatial integration so that each cluster is connected as much as possible, while protecting spatial outliers can help avoid the excessive masking of attribute differences This paper proposes a new spatial clustering method for raster data robust to spatial outliers. The method employs a sliding window to scan the entire region to determine spatial outliers. Additionally, a mechanism based on the range and standard deviation of the spatial units in each window is designed to judge whether the spatial integration should be further improved or the spatial outliers should be protected. To demonstrate the usefulness of the proposed method, we applied it in two case study areas, namely, Changping District and Pinggu District in Beijing. The results show that the proposed method can retain the spatial outliers while ensuring that the clusters are roughly contiguous. This method can be used as a simple but powerful and easy-to-interpret alternative to existing geographical spatial clustering methods.

Malaria remains a menace to the existence of humanity in most contexts. Geospatial analysis of malaria mortality is crucial to identifying clusters of high disease burden and areas with limited access to malaria care for targeted control and remedial interventions. This study identified spatial and space-time clusters of malaria mortality in the Kintampo area of central Ghana. We used 1301 malaria deaths archived from 2005 to 2017 and Global Positioning System (GPS) point locations of the sub-districts in which these deaths occurred for our analysis. Mortality risks were smoothed and mapped using the Spatial Empirical Bayesian smoothing technique in Geoda (version 1.12.1.161) whereas spatial and spatio-temporal clustering analysis was done using SaTScan (version 9.6). Malaria mortality risks ranged between 1.2 and 2.4 deaths per 1000 population for persons of all ages and between 3.3 and 6.0 deaths per 1000 population for children under five years of age by sub-district. Two spatial clusters were detected for all-age malaria mortality with only the primary cluster (RR = 1.42, p = 0.001) being statistically significant. Also, two statistically significant space-time clusters were detected for all-age malaria mortality in the study area. The most likely cluster occurred between 2006 and 2011 in five sub-districts with a relative risk of 2.12 (p < 0.001) whilst the secondary cluster which had a relative risk of 2.47 (p < 0.001) occurred between 2005 and 2010 in four sub-districts. Similarly, only the most likely spatial cluster of under-five malaria mortality was statistically significant (RR = 1.36, p = 0.024). Furthermore, three spatio-temporal clusters of under-five malaria mortality were detected in the study area. The primary and second secondary clusters were statistically significant whilst the first secondary cluster had borderline significance. The primary cluster (RR = 4.49, p = 0.002) occurred in two sub-districts between 2006 and 2007. The first secondary cluster (RR = 2.21, P = 0.005) covered four sub-districts and was detected between 2006 and 2011 whereas the second secondary cluster (RR = 2.51, p = 0.003) covered two sub-districts between 2008 and 2013. Ultimately, our analysis identified a number of substantial spatial and apace-time clusters of malaria mortality in the study context, which could aid in the strategic planning, implementation and monitoring of targeted malaria control interventions.

대용량의 공간데이터베이스로부터 암시적이고 유용한 지식을 자동적으로 추출하는 공간데이터 마이닝은 데이타 양이 급격히 증가하면서 필요성이 더욱 증대되고 있다. 공간데이터 마이닝에서 데이타를 분석하여 유사한 그룹으로 분류하는 공간 클러스터링은 매우 중요한 분야이다. 기존 연구에서 공간 클러스터링을 위한 여러 가지 알고리즘들이 제시되었지만, 다음과 같은 문제점들이 있다. 먼저 클러스터링을 위하여 객체들 간의 거리론 기반으로 하므로 데이타 양이 많아질수록 계산 비용이 커진다. 또한, 메모리 상주 데이타를 대상으로 하므로 대용량의 데이타인 경우에 효율이 떨어진다. 본 논문에서는 공간데이터 마이닝을 위하여 그리드 셀을 기반으로 한 효율적인 공간 클러스터링 방법을 제시한다. 이 클러스터링에서는 기존 공간 클러스터링 기법들의 문제점을 해결하는데 중점을 둔다. 세부적으로 공간 클러스터링의 효율성을 높이기 위하여 클러스터링시에 발생하는 비용(계산량)을 감소시키는 것이다. 이를 위해서 공간지역성을 보장하는 대표적인 공간분할 방법인 그리드 셀을 기반으로 한 공간 클러스터링 기법을 제시한다. Spatial data mining, i.e., discovery of interesting characteristics and patterns that may implicitly exists in spatial databases, is a challenging task due to the huge amounts of spatial data. Clustering algorithms are attractive for the task of class identification in spatial databases. Several methods for spatial clustering have been presented in recent years, but have the following several drawbacks increase costs due to computing distance among objects and process only memory-resident data. In this paper, we propose an efficient grid cell based spatial clustering method for spatial data mining. It focuses on resolving disadvantages of existing clustering algorithms. In details, it aims to reduce cost further for good efficiency on large databases. To do this, we devise a spatial clustering algorithm based on grid ceil structures including cell relationships.

GCHL: A grid-clustering algorithm for high-dimensional very large spatial data bases

Spatially resolved transcriptomics involves a set of emerging technologies that enable the transcriptomic profiling of tissues with the physical location of expressions. Although a variety of methods have been developed for data integration, most of them are for single-cell RNA-seq datasets without consideration of spatial information. Thus, methods that can integrate spatial transcriptomics data from multiple tissue slides, possibly from multiple individuals, are needed. Here, we present PRECAST, a data integration method for multiple spatial transcriptomics datasets with complex batch effects and/or biological effects between slides. PRECAST unifies spatial factor analysis simultaneously with spatial clustering and embedding alignment, while requiring only partially shared cell/domain clusters across datasets. Using both simulated and four real datasets, we show improved cell/domain detection with outstanding visualization, and the estimated aligned embeddings and cell/domain labels facilitate many downstream analyses. We demonstrate that PRECAST is computationally scalable and applicable to spatial transcriptomics datasets from different platforms.

Capturing and characterizing collective human activities in a geographic space have become much easier than ever before in the big era. In the past few decades it has been difficult to acquire the spatiotemporal information of human beings. Thanks to the boom in the use of mobile devices integrated with positioning systems and location-based social media data, we can easily acquire the spatial and temporal information of social media users. Previous studies have successfully used street nodes and geo-tagged social media such as Twitter to predict users’ activities. However, whether human activities can be well represented by social media data remains uncertain. On the other hand, buildings or architectures are permanent and reliable representations of human activities collectively through historical footprints. This study aims to use the big data of US building footprints to investigate the reliability of social media users for human activity prediction. We created spatial clusters from 125 million buildings and 1.48 million Twitter points in the US. We further examined and compared the spatial and statistical distribution of clusters at both country and city levels. The result of this study shows that both building and Twitter data spatial clusters show the scaling pattern measured by the scale of spatial clusters, respectively, characterized by the number points inside clusters and the area of clusters. More specifically, at the country level, the statistical distribution of the building spatial clusters fits power law distribution. Inside the four largest cities, the hotspots are power-law-distributed with the power law exponent around 2.0, meaning that they also follow the Zipf’s law. The correlations between the number of buildings and the number of tweets are very plausible, with the r square ranging from 0.53 to 0.74. The high correlation and the similarity of two datasets in terms of spatial and statistical distribution suggest that, although social media users are only a proportion of the entire population, the spatial clusters from geographical big data is a good and accurate representation of overall human activities. This study also indicates that using an improved method for spatial clustering is more suitable for big data analysis than the conventional clustering methods based on Euclidean geometry.

Spatial transcriptomics is a rapidly emerging field that allows for the study of gene expression within a tissue sample. This technology has the potential to provide valuable insights into the molecular mechanisms underlying cancer progression and could be particularly useful in identifying specific regional cancer progression. By studying the regional spatial trajectory of cancer progression, we can develop more targeted therapies and better predict the likelihood of metastasis. Additionally, analyzing gene expression patterns in specific regions of the tissue can reveal the molecular mechanisms driving cancer growth in those areas, potentially uncovering new therapeutic targets. In this study, we created a spatial trajectory analysis method, named as stLearn - PSeudo-Time-Space (PSTS) algorithm, to investigate specific regional cancer progression. Spatial trajectory analysis is a statistical method that allows for the identification of patterns of transitional gene expression over time and space within a tissue sample. In detail, this method incorporates spatial features, such as tissue sub-structure locations and gene expression changes, to model the trajectory from a single snapshot of transcriptomics data. Also, we evaluated the effectiveness of PSTS by utilizing the cancer progression model in human breast cancer samples. Using this approach, we were able to identify specific regions within the breast tissue that displayed distinct progression branching trajectories patterns of transitional gene expression associated with ductal carcinoma in situ and invasive ductal carcinoma. These regions were found to be characterized by a high level of cellular diversity and were associated with aggressive forms of breast cancer. The results of this study suggest that spatial transcriptomics and spatial trajectory analysis could be a powerful tool for identifying specific regional cancer progression and may help to inform the biomarkers for the development of targeted therapies for breast cancer. Overall, this study highlights the potential of spatial transcriptomics and spatial trajectory analysis to provide valuable insights into the molecular mechanisms underlying cancer progression and could have significant implications for the diagnosis and treatment of cancer. Citation Format: Duy Pham, Quan Nguyen. A novel spatial trajectory inference method for detecting regional breast cancer progression from spatial transcriptomics data [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 2 (Clinical Trials and Late-Breaking Research); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(8_Suppl):Abstract nr LB076.

The detection of spatial clusters has been suggested as a potential tool for guiding the delivery of interventions against visceral leishmaniasis; however, little attention has been given to the consistency of results by using different spatial clustering methods. The present study aimed to assess the performance of three different techniques for identifying patterns in the spatial distribution of canine leishmaniasis in the city of Teresina, Brazil. This cross-sectional study was based on a serological survey for canine leishmaniasis in which each dog domicile was georeferenced to the exact location of each animal in space. The spatial analysis was performed using three methods: the Cuzick-Edwards statistic, the Hierarchical Nearest Neighbour analysis, and the Kulldorff Scan statistic. All techniques were able to identify clusters of high prevalences of canine leishmaniasis, but results were not consistent among techniques. The feasibility of the identification and location of clusters of cases in a restricted number of villages in neighborhoods might contribute to the optimization of control measures against visceral leishmaniasis. However, given the relative inconsistency of the results provided by the different methods, protocols for assessing clusters of diseases should always include more than one method of evaluation.