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`0-Motivated Low-Rank Sparse Subspace Clustering

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arXiv 2018年

作者： Brbić, Maria Kopriva, Ivica Laboratory for Machine Learning and Knowledge Representation Division of Electronics Rudjer Boskovic Institute

In many applications, high-dimensional data points can be well represented by low-dimensional subspaces. To identify the subspaces, it is important to capture a global and local structure of the data which is achieved by imposing low-rank and sparseness constraints on the data representation matrix. In low-rank sparse subspace clustering (LRSSC), nuclear and 1 norms are used to measure rank and sparsity. However, the use of nuclear and 1 norms leads to an overpenalized problem and only approximates the original problem. In this paper, we propose two 0 quasi-norm based regularizations. First, the paper presents regularization based on multivariate generalization of minimax-concave penalty (GMC-LRSSC), which contains the global minimizers of 0 quasi-norm regularized objective. Afterward, we introduce the Schatten-0 (S0) and 0 regularized objective and approximate the proximal map of the joint solution using a proximal average method (S0/0-LRSSC). The resulting nonconvex optimization problems are solved using alternating direction method of multipliers with established convergence conditions of both algorithms. Results obtained on synthetic and four real-world datasets show the effectiveness of GMC-LRSSC and S0/0-LRSSC when compared to state-of-the-art methods. Copyright © 2018, The Authors. All rights reserved.

关键词： Clustering algorithms

0-Motivated Low-Rank Sparse Subspace Clustering

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IEEE Transactions on Cybernetics 2020年第4期50卷 1711-1725页

作者： Brbić, Maria Kopriva, Ivica Laboratory for Machine Learning and Knowledge Representation Division of Electronics Ruder Bošković Institute Zagreb10000 Croatia

In many applications, high-dimensional data points can be well represented by low-dimensional subspaces. To identify the subspaces, it is important to capture a global and local structure of the data which is achieved by imposing low-rank and sparseness constraints on the data representation matrix. In low-rank sparse subspace clustering (LRSSC), nuclear and 1-norms are used to measure rank and sparsity. However, the use of nuclear and 1-norms leads to an overpenalized problem and only approximates the original problem. In this paper, we propose two 0 quasi-norm-based regularizations. First, this paper presents regularization based on multivariate generalization of minimax-concave penalty (GMC-LRSSC), which contains the global minimizers of a 0 quasi-norm regularized objective. Afterward, we introduce the Schatten-0 (S0) and 0-regularized objective and approximate the proximal map of the joint solution using a proximal average method (S00-LRSSC). The resulting nonconvex optimization problems are solved using an alternating direction method of multipliers with established convergence conditions of both algorithms. Results obtained on synthetic and four real-world datasets show the effectiveness of GMC-LRSSC and S00 -LRSSC when compared to state-of-the-art methods. © 2013 IEEE.

关键词： Clustering algorithms

ROBUST SELF-SUPERVISED CONVOLUTIONAL NEURAL NETWORK FOR SUBSPACE CLUSTERING AND CLASSIFICATION

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arXiv 2020年

作者： Sitnik, Dario Kopriva, Ivica Laboratory for Machine Learning and Knowledge Representation Division of Electronics Ruder ¯ Bošković Institute Bijenička cesta 54 Zagreb10000 Croatia

Insufficient capability of existing subspace clustering methods to handle data coming from nonlinear manifolds, data corruptions, and out-of-sample data hinders their applicability to address real-world clustering and classification problems. This paper proposes the robust formulation of the self-supervised convolutional subspace clustering network (S2ConvSCN) that incorporates the fully connected (FC) layer and, thus, it is capable for handling out-of-sample data by classifying them using a softmax classifier. S2ConvSCN clusters data coming from nonlinear manifolds by learning the linear self-representation model in the feature space. Robustness to data corruptions is achieved by using the correntropy induced metric (CIM) of the error. Furthermore, the block-diagonal (BD) structure of the representation matrix is enforced explicitly through BD regularization. In a truly unsupervised training environment, Robust S2ConvSCN outperforms its baseline version by a significant amount for both seen and unseen data on four well-known datasets. Arguably, such an ablation study has not been reported before. Copyright © 2020, The Authors. All rights reserved.

关键词： Clustering algorithms

CLUSTERING AND CLASSIFICATION OF LOW-DIMENSIONAL DATA IN EXPLICIT FEATURE MAP DOMAIN: INTRAOPERATIVE PIXEL-WISE DIAGNOSIS OF ADENOCARCINOMA OF A COLON IN A LIVER

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arXiv 2022年

作者： Sitnik, Dario Kopriva, Ivica Laboratory For Machine Learning And Knowledge Representation Division of Electronics Ruder Bošković Institute Bijenička cesta 54 Zagreb10000 Croatia

Application of artificial intelligence in medicine brings in highly accurate predictions achieved by complex models, the reasoning of which is hard to interpret. Their generalization ability can be reduced because of the lack of pixel wise annotated images that occurs in frozen section tissue analysis. To partially overcome this gap, this paper explores the approximate explicit feature map (aEFM) transform of low-dimensional data into a low-dimensional subspace in Hilbert space. There, with a modest increase in computational complexity, linear algorithms yield improved performance and keep interpretability. They remain amenable to incremental learning that is not a trivial issue for some nonlinear algorithms. We demonstrate proposed methodology on a very large-scale problem related to intraoperative pixel-wise semantic segmentation and clustering of adenocarcinoma of a colon in a liver. Compared to the results in the input space, logistic classifier achieved statistically significant performance improvements in micro balanced accuracy and F1 score in the amounts of 12.04% and 12.58%, respectively. Support vector machine classifier yielded the increase of 8.04% and 9.41%. For clustering, increases of 0.79% and 0.85% are obtained with ultra large-scale spectral clustering algorithm. Results are supported by a discussion of interpretability using Shapely additive explanation values for predictions of linear classifier in input space and aEFM induced space. © 2022, CC BY.

关键词： Pixels

Computational analysis of laminar structure of the human cortex based on local neuron features

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arXiv 2019年

作者： Stajduhar, Andrija Lipic, Tomislav Sedmak, Goran Loncaric, Sven Judaš, Milos Croatian Institute for Brain Research University of Zagreb School of Medicine Šalata 12 Zagreb10000 Croatia Laboratory for Machine Learning and Knowledge Representation Rud-er Boškovic Institute Faculty of Electrical Engineering and Computing University of Zagreb

In this paper, we present a novel method for analysis and segmentation of laminar structure of the cortex based on tissue characteristics whose change across the gray matter facilitates distinction between cortical layers. We develop and analyze features of individual neurons to investigate changes in architectonic differentiation and present a novel high-performance, automated tree-ensemble method trained on data manually labeled by three human investigators. From the location and basic measures of neurons, more complex features are developed and used in machine learning models for automatic segmentation of cortical layers. Tree ensembles are used on data manually labeled by three human experts. The most accurate classification results were obtained by training three models separately and creating another ensemble by combining probability outputs for final neuron layer classification. Measurement of importances of developed neuron features on both global model level and individual prediction level are obtained. Copyright © 2019, The Authors. All rights reserved.

关键词： Neurons

Front Cover: Inhibitory Effect of DMSO on Halohydrin Dehalogenase: Experimental and Computational Insights into the Influence of an Organic Co-solvent on the Structural and Catalytic Properties of a Biocatalyst (Chem. Eur. J. 56/2022)

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Chemistry – A European Journal 2022年第56期28卷

作者： Nevena Milčić Dr. Višnja Stepanić Dr. Ivo Crnolatac Prof. Zvjezdana Findrik Blažević Dr. Zlatko Brkljača Dr. Maja Majerić Elenkov Faculty of Chemical Engineering and Technology University of Zagreb Savska c. 16 10000 Zagreb Croatia Laboratory for Machine Learning and Knowledge Representation Ruđer Bošković Institute Bijenička c. 54 10000 Zagreb Croatia Division of Organic Chemistry and Biochemistry Ruđer Bošković Institute Bijenička c. 54 10000 Zagreb Croatia Present Address: Selvita Ltd. 10000 Zagreb Croatia