Abstract Spectral clustering algorithms typically require a priori selection of input parameters such as the number of clusters, a scaling parameter for the affinity measure, or ranges of these values for parameter tuning. Despite efforts for automating the process of spectral clustering, the task of grouping data in multi-scale and higher dimensional spaces is yet to be explored. This study presents a spectral clustering heuristic algorithm that obviates the need for any input by estimating the parameters from the data itself. Specifically, it introduces the heuristic of iterative eigengap search with (1) global scaling and (2) local scaling. These approaches estimate the scaling parameter and implement iterative eigengap quantification along a search tree to reveal dissimilarities at different scales of a feature space and identify clusters. The performance of these approaches has been tested on various real-world datasets of power variation with multi-scale nature and gene expression. Our findings show that iterative eigengap search with a PCA-based global scaling scheme can discover different patterns with an accuracy of higher than 90 in most cases without asking for a priori input information.
Unlike the aforementioned efforts that have proposed solutions for challenging 2D datasets and image segmentation, @cite_46 proposed a kernel spectral clustering for a large-scale network without parameter input. To this end, entropy was used to detect the block-diagonal of the affinity matrix that was created by the projections in the eigenspace. The efficacy of the proposed approach was studied through synthetic data and real-world network datasets. While these existing approaches @cite_30 @cite_23 @cite_12 @cite_46 were developed to tackle spectral clustering in an automated manner, they are either designed to solve the problem for multi-scale 2D and image segmentation or network data, which is different in nature from data with multi-scale higher dimensional attributes as sought here.
@cite_30 @cite_46 @cite_12 @cite_23
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We propose a parameter-free kernel spectral clustering model for large scale complex networks. The kernel spectral clustering (KSC) method works by creating a model on a subgraph of the complex network. The model requires a kernel function which can have parameters and the number of communities k has be detected in the large scale network. We exploit the structure of the projections in the eigenspace to automatically identify the number of clusters. We use the concept of entropy and balanced clusters for this purpose. We show the effectiveness of the proposed approach by comparing the cluster memberships w.r.t. several large scale community detection techniques like Louvain, Infomap and Bigclam methods. We conducted experiments on several synthetic networks of varying size and mixing parameter along with large scale real world experiments to show the efficiency of the proposed approach. Spectral clustering has become an increasingly adopted tool and an active area of research in the machine learning community over the last decade. A common challenge with image segmentation methods based on spectral clustering is scalability, since the computation can become intractable for large images. Down-sizing the image, however, will cause a loss of finer details and can lead to less accurate segmentation results. A combination of blockwise processing and stochastic ensemble consensus are used to address this challenge. Experimental results indicate that this approach can preserve details with higher accuracy than comparable spectral clustering image segmentation methods and without significant computational demands. We introduce a novel spectral clustering algorithm that allows us to automatically determine the number of clusters in a dataset. The algorithm is based on a theoretical analysis of the spectral properties of block diagonal affinity matrices; in contrast to established methods, we do not normalise the rows of the matrix of eigenvectors, and argue that the non-normalised data contains key information that allows the automatic determination of the number of clusters present. We present several examples of datasets successfully clustered by our algorithm, both artificial and real, obtaining good results even without employing refined feature extraction techniques