Spectral Clustering Joint Deep Embedding Learning by Autoencoder

A robust adaptive clustering analysis method for automatic identification of clusters

Cluster analysis seeks to assign objects with similar characteristics into groups called clusters so that objects within a group are similar to each other and dissimilar to objects in other groups. Spectral clustering has been shown to perform well in different scenarios on continuous data: it can detect convex and non-convex clusters, and can detect overlapping clusters. However, the constraint on continuous data can be limiting in real applications where data are often of mixed-type, i.e., data that contains both continuous and categorical features. This paper looks at extending spectral clustering to mixed-type data. The new method replaces the Euclidean-based similarity distance used in conventional spectral clustering with different dissimilarity measures for continuous and categorical variables. A global dissimilarity measure is than computed using a weighted sum, and a Gaussian kernel is used to convert the dissimilarity matrix into a similarity matrix. The new method includes an automatic tuning of the variable weight and kernel parameter. The performance of spectral clustering in different scenarios is compared with that of two state-of-the-art mixed-type data clustering methods, k-prototypes and KAMILA, using several simulated and real data sets.

Simulated annealing spectral clustering algorithm for image segmentation

Spectral clustering has become a typical and efficient clustering method used in a variety of applications. The critical step of spectral clustering is the similarity measurement, which largely determines the performance of the spectral clustering method. In this paper, we propose a novel spectral clustering algorithm based on the local similarity measure of shared neighbors. This similarity measurement exploits the local density information between data points based on the weight of the shared neighbors in a directed k $$ k $$ -nearest neighbor graph with only one parameter k $$ k $$ , that is, the number of nearest neighbors. Numerical experiments on synthetic and real-world datasets demonstrate that our proposed algorithm outperforms other existing spectral clustering algorithms in terms of the clustering performance measured via the normalized mutual information, clustering accuracy, and F $$ F $$ -measure. As an example, the proposed method can provide an improvement of 15.82% in the clustering performance for the Soybean dataset.

Machine learning, particularly classification algorithms, has been widely employed for diagnosing COVID-19 cases. However, these methods typically rely on labeled datasets and analyze a single data view. With the vast amount of patient data available without labels, this paper addresses the novel challenge of unsupervised COVID-19 diagnosis. The goal is to harness the abundant data without labels effectively. In recent times, multi-view clustering has garnered considerable attention in the research community. Spectral clustering, known for its robust theoretical framework, is a key focus. However, traditional spectral clustering methods generate only nonlinear data projections, necessitating additional clustering steps. The quality of these post-processing steps can be influenced by various factors, such as initialization procedures and outliers. This paper introduces an enhanced version of the recent “Multiview Spectral Clustering via integrating Nonnegative Embedding and Spectral Embedding” method. While retaining the benefits of the original technique, the proposed model integrates two essential constraints: (1) a constraint for ensuring the consistent smoothness of the nonnegative embedding across all views and (2) an orthogonality constraint imposed on the columns of the nonnegative embedding matrix. The effectiveness of this approach is demonstrated using COVIDx datasets. Additionally, the method is evaluated on other image datasets to validate its suitability for this study.

Spectral Clustering (SC) is an effective clustering method for its excellent performance in partitioning non-linearly distributed data. On the other hand, Ensemble Clustering (EC), a different clustering technology, can promote cluster quality by ensembling the results of base clusterings. In this work, we concentrate on an EC framework that utilizes SC as the base method. Nevertheless, SC suffers from scalability due to its high computational complexity in constructing the Laplacian graph and computing the corresponding eigendecomposition. In the past decades, many efforts have been made to it. However, SC suffers from the scalability issue in processing extensive data, especially in web-scale scenarios. Additionally, EC requires multiple clustering results as the ensemble bases, which further aggravates resource consumption. To address this issue, LiteWSEC, a simple yet efficient Lightweight Framework for Web-scale Spectral Ensemble Clustering, is proposed to cluster web-scale data with limited resource requirements. It adopts the Web-scale Spectral Clustering (WSC) as the base method, which has minimal space overhead without computing overall embedding explicitly. LiteWSEC is highly flexible in the memory requirement, which is adaptive to the available resource. It can partition web-scale data (e.g., <inline-formula><tex-math notation="LaTeX">$n $</tex-math></inline-formula> = 8,000 k) in an resource-limited host (e.g., memory is restricted to 1 GB). Experiments on real-world, large-scale, and web-scale datasets demonstrate both the efficiency and effectiveness of LiteWSEC over state-of-the-art SC and EC methods.

Spectral clustering has been shown to be more effective than most of the traditional clustering algorithms. However, the heavy computational cost of spectral clustering limits its applicability to large-scale clustering problems. To perform spectral clustering on large datasets, in this paper, we propose an accelerated spectral clustering method based on sparse presentation where each data point is presented as sparse linear combinations of a part of representative data points. The hubs that appear frequently in the nearest neighbor lists of other data points are selected as the representative data points, by which a proper spectral embedding is constructed. Taking advantage of the topological property of hubs, the proposed method is able to achieve scalable and accurate clustering results. We evaluated the proposed method on both synthetic and real-world datasets to show its effectiveness in comparison to the existing related methods.

Brain tumour segmentation from MRI using superpixels based spectral clustering

Human activity recognition has many valuable applications in computer vision. Unlike existing works, the challenging problem of the similarity degree of skeleton-based human postures is addressed. In this paper, the Relation Matrix of 3D Rigid Bodies (RMRB3D), which is a compact representation of postures, makes a powerful way to compute the similarity degree between postures. Then representative postures are built through Spectral Clustering (SC) on sample data and action sequences of discrete symbols will be generated according to a global linear eigenfunction constructed by Spectral Embedding (SE). Finally, action classifier can be modeled as temporal order by using Dynamic Time Warping (DTW) and Hidden Markov Model (HMM). The experimental evaluations of the proposed method on challenging 3D action datasets show that our approach achieves promising results.

Multi-view spectral clustering, which exploits the complementary information among graphs of diverse views to obtain superior clustering results, has attracted intensive attention recently. However, most existing multi-view spectral clustering methods obtain the clustering partitions in a two-step scheme, i.e., spectral embedding and subsequent k-means. This two-step scheme inevitably seeks sub-optimal clustering results due to the information loss during the two-steps processes. Besides, existing multi-view spectral clustering methods do not jointly utilize the information of graphs and embedding matrices, which also degrades final clustering results. To solve these issues, we propose a unified one-step multi-view spectral clustering method, which integrates the spectral embedding and <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$k$</tex></formula> -means into a unified framework to obtain discrete clustering labels with a one-step strategy. Under the observation that the inner product of the embedding matrix is a low-rank approximation of the graph, we combine graphs and embedding matrices of different views to obtain a unified graph. Then, we directly capture the discrete clustering indicator matrix from the unified graph. Furthermore, we design an effective optimization algorithm to solve the resultant problem. Finally, a set of experiments on various datasets are conducted to verify the effectiveness of the proposed method. The demo code of this work is publicly available at https://github.com/guanyuezhen/UOMvSC.

Weighted adaptively ensemble clustering method based on fuzzy Co-association matrix

Spectral clustering (SC) is one of the most popular clustering methods and often outperforms traditional clustering methods. SC uses the eigenvectors of a Laplacian matrix calculated from a similarity matrix of a dataset. SC has serious drawbacks: the significant increases in the time complexity derived from the computation of eigenvectors and the memory space complexity to store the similarity matrix. To address the issues, I develop a new approximate spectral clustering using the network generated by growing neural gas (GNG), called ASC with GNG in this study. ASC with GNG uses not only reference vectors for vector quantization but also the topology of the network for extraction of the topological relationship between data points in a dataset. ASC with GNG calculates the similarity matrix from both the reference vectors and the topology of the network generated by GNG. Using the network generated from a dataset by GNG, ASC with GNG achieves to reduce the computational and space complexities and improve clustering quality. In this study, I demonstrate that ASC with GNG effectively reduces the computational time. Moreover, this study shows that ASC with GNG provides equal to or better clustering performance than SC.

A fast spectral clustering technique using MST based proximity graph for diversified datasets

A fundamental task in single-cell RNA-seq (scRNA-seq) analysis is the identification of transcriptionally distinct groups of cells. Numerous methods have been proposed for this problem, with a recent focus on methods for the cluster analysis of ultralarge scRNA-seq data sets produced by droplet-based sequencing technologies. Most existing methods rely on a sampling step to bridge the gap between algorithm scalability and volume of the data. Ignoring large parts of the data, however, often yields inaccurate groupings of cells and risks overlooking rare cell types. We propose method Specter that adopts and extends recent algorithmic advances in (fast) spectral clustering. In contrast to methods that cluster a (random) subsample of the data, we adopt the idea of landmarks that are used to create a sparse representation of the full data from which a spectral embedding can then be computed in linear time. We exploit Specter's speed in a cluster ensemble scheme that achieves a substantial improvement in accuracy over existing methods and identifies rare cell types with high sensitivity. Its linear-time complexity allows Specter to scale to millions of cells and leads to fast computation times in practice. Furthermore, on CITE-seq data that simultaneously measures gene and protein marker expression, we show that Specter is able to use multimodal omics measurements to resolve subtle transcriptomic differences between subpopulations of cells.

Analyzing cancers using microarray gene expression datasets is currently an active research in medical community. There are many tasks related to this research, e.g., clustering and classifcation, data compression, and samples characterization. In this paper, we discuss the task of cancer clustering. The spectral clustering is one of the most commonly used methods in cancer clustering. As the gene expression datasets usually are highly imbalanced, i.e., containing only a few tissue samples (hundreds at most) but each is expressed by thousands of genes, filtering out some irrelevant and potentially misleading gene expressions is a necessary step to improve the performance of the method. In this paper, we propose an unsupervised gene selection algorithm based on the nonnegative matrix factorization (NMF). Our algorithm is designed by making use of the clustering capability of the NMF to select the most informative genes. Clustering performance of the spectral method is then evaluated by comparing the results using the original datasets with the results using the pruned datasets. Our results suggest that the proposed algorithm can be used to improve clustering performance of the spectral method.