Constrained Spectral Clustering Research Articles

Systemic risk mitigation strategy for power grid cascade failures using constrained spectral clustering

Power grids are prone to damage induced by natural or anthropogenic hazard events that might disrupt the functionality of key/multiple grid components concurrently, resulting in a chain of cascade failures spreading throughout the grid. Through integrating grid operation-guided with structure-driven modeling strategies, the current study proposes an approach to manage the risks of such cascade failure (known as systemic-risks) to minimize the possibility of large-scale catastrophic blackouts. The operation-guided modeling strategy is implemented through dispatch and load shedding to rebalance power demand and supply after disruptive events. On the other hand, the grid structure-driven modeling strategy adopted intentional controlled islanding approach through employing a constrained spectral clustering algorithm. Introducing the latter algorithm within the integrated (operation + structure) cascade failure model facilitated identifying the optimal cut-set lines to separate the grid into a group of functioning sub-grids following initial failure and prior to cascade propagation. To demonstrate the utility of the developed systemic risk management strategy, an actual power grid was simulated using a high-fidelity physics-based model under different disruption scenarios to compare the cascade failure size with and without strategy implementation, considering different numbers of sub-grids. The simulations demonstrate that the integrated (dispatch & load shedding-controlled islanding) strategy can effectively boost the overall grid robustness, and subsequently its resilience, and effectively manage catastrophic blackout systemic risks.

State space partitioning based on constrained spectral clustering for block particle filtering

To overcome the curse of dimensionality of particle filter (PF), the block PF (BPF) partitions the state space into several blocks of smaller dimension so that the correction and resampling steps can be performed independently on each block. Despite its potential performance, this approach has a practical limitation. BPF requires an additional input compared to classical PF: the partition from which blocks are defined. A poor choice will not offer the expected performance gain.In this paper, we formulate the partitioning problem as a clustering problem and propose a data-driven partitioning method based on constrained spectral clustering (CSC) to automatically provide an appropriate partition.We design a generalized BPF that contains two new steps: (i) estimation of the state vector correlation matrix from particles, (ii) CSC using this estimate to determine blocks. The proposed method succeeds in providing an online partition into blocks restricted in size and grouping the most correlated state variables. This partition allows the BPF to escape the curse of dimensionality by reducing the variance of the filtering distribution estimate while limiting the level of bias. Since our approach relies on particles that are already necessary to generate as part of BPF, the computation overhead is limited.

Auto-weighted multi-view constrained spectral clustering

Constrained clustering is a new fashion of semi-supervised learning which focused on enhancing the quality of the partition by utilizing pairwise constraints. Though many constrained clustering methods have an excellent performance in single-view clustering, they can’t be directly applied to multi-view scenario. In this paper, we propose a novel constrained spectral clustering approach for multi-view data, which explicitly imposes pairwise constraints as a series of linear constraints on the unified indicator matrix. To our best knowledge, this is the first work on multi-view constrained spectral clustering. Our approach can differ the importance of different views via the auto-weight learning strategy. Simultaneously, the views which contain much noisy or irrelevant information are also automatically eliminated, thereby improving the prediction performance. Extensive experiments conducted on various multi-view datasets demonstrate that the proposed approach can efficiently utilize pairwise constraints and outperforms the state-of-the-art approaches.

Constrained spectral clustering via multi–layer graph embeddings on a grassmann manifold

Abstract We present two algorithms in which constrained spectral clustering is implemented as unconstrained spectral clustering on a multi-layer graph where constraints are represented as graph layers. By using the Nystrom approximation in one of the algorithms, we obtain time and memory complexities which are linear in the number of data points regardless of the number of constraints. Our algorithms achieve superior or comparative accuracy on real world data sets, compared with the existing state-of-the-art solutions. However, the complexity of these algorithms is squared with the number of vertices, while our technique, based on the Nyström approximation method, has linear time complexity. The proposed algorithms efficiently use both soft and hard constraints since the time complexity of the algorithms does not depend on the size of the set of constraints.

Functional Connectivity Analysis of Cerebellum Using Spatially Constrained Spectral Clustering.

The human cerebellum contains almost 50% of the neurons in the brain, although its volume does not exceed 10% of the total brain volume. The goal of this study is to derive the functional network of the cerebellum during the resting-state and then compare the ensuing group networks between males and females. Toward this direction, a spatially constrained version of the classic spectral clustering algorithm is proposed and then compared against conventional spectral graph theory approaches, such as spectral clustering, and N-cut, on synthetic data as well as on resting-state fMRI data obtained from the Human Connectome Project (HCP). The extracted atlas was combined with the anatomical atlas of the cerebellum resulting in a functional atlas with 46 regions of interest. As a final step, a gender-based network analysis of the cerebellum was performed using the data-driven atlas along with the concept of the minimum spanning trees. The simulation analysis results confirm the dominance of the spatially constrained spectral clustering approach in discriminating activation patterns under noisy conditions. The network analysis results reveal statistically significant differences in the optimal tree organization between males and females. In addition, the dominance of the left VI lobule in both genders supports the results reported in a previous study of ours. To our knowledge, the extracted atlas comprises the first resting-state atlas of the cerebellum based on HCP data.

Compressed constrained spectral clustering framework for large-scale data sets

The method of incorporating constraint information into spectral clustering, i.e., \\constrained spectral clustering (CSC), can greatly improve clustering accuracy, and thus has been widely employed in the machine learning literature. In this paper, we propose a compressed CSC framework by combining specific graph constructions with a recently introduced CSC model. Particularly, our framework has ability to avoid losing the main partition information in the compression process. By presenting a theoretical analysis and empirical results, we demonstrate that our new framework can achieve the same clustering solution as that of the original model with the specific graph structure. In addition, because our framework utilizes landmark-based graph construction and the approximate matrix decomposition simultaneously, it can be applied to both feature and graph data in a more general way. Moreover, the parameter setting in our framework is rather simple, and therefore it is very practical. Experimental results indicate that our framework has advantages in terms of efficiency and effectiveness.

Graph Spectra Based Controlled Islanding for Low Inertia Power Systems

The inertia of modern power systems is decreasing and becoming more variable as more inverter-connected renewable energy sources and loads are integrated. This leads to a low and time-varied inertia power system that is more sensitive to disturbances and may not be robust enough to survive large disturbances. How to protect such a low and time-varied inertia system from blackouts is in question. This paper tries to answer this question using a graph spectra-based controlled islanding method. Eigenvector sensitivity, with respect to inertia, is used to identify the impact of reduced inertia on the spectral properties of power system graphs and, thus, coherent generator grouping. Constrained spectral clustering is then used to find the islanding boundary with minimal power-flow disruption to island low inertia systems. Simulation results, obtained using the IEEE 9-bus and 118-bus test systems, validate the effectiveness of the proposed algorithm in the case of low inertia systems.

Fast Constrained Spectral Clustering and Cluster Ensemble with Random Projection.

Constrained spectral clustering (CSC) method can greatly improve the clustering accuracy with the incorporation of constraint information into spectral clustering and thus has been paid academic attention widely. In this paper, we propose a fast CSC algorithm via encoding landmark-based graph construction into a new CSC model and applying random sampling to decrease the data size after spectral embedding. Compared with the original model, the new algorithm has the similar results with the increase of its model size asymptotically; compared with the most efficient CSC algorithm known, the new algorithm runs faster and has a wider range of suitable data sets. Meanwhile, a scalable semisupervised cluster ensemble algorithm is also proposed via the combination of our fast CSC algorithm and dimensionality reduction with random projection in the process of spectral ensemble clustering. We demonstrate by presenting theoretical analysis and empirical results that the new cluster ensemble algorithm has advantages in terms of efficiency and effectiveness. Furthermore, the approximate preservation of random projection in clustering accuracy proved in the stage of consensus clustering is also suitable for the weighted k-means clustering and thus gives the theoretical guarantee to this special kind of k-means clustering where each point has its corresponding weight.

Affinity and Penalty Jointly Constrained Spectral Clustering With All-Compatibility, Flexibility, and Robustness.

The existing, semisupervised, spectral clustering approaches have two major drawbacks, i.e., either they cannot cope with multiple categories of supervision or they sometimes exhibit unstable effectiveness. To address these issues, two normalized affinity and penalty jointly constrained spectral clustering frameworks as well as their corresponding algorithms, referred to as type-I affinity and penalty jointly constrained spectral clustering (TI-APJCSC) and type-II affinity and penalty jointly constrained spectral clustering (TII-APJCSC), respectively, are proposed in this paper. TI refers to type-I and TII to type-II. The significance of this paper is fourfold. First, benefiting from the distinctive affinity and penalty jointly constrained strategies, both TI-APJCSC and TII-APJCSC are substantially more effective than the existing methods. Second, both TI-APJCSC and TII-APJCSC are fully compatible with the three well-known categories of supervision, i.e., class labels, pairwise constraints, and grouping information. Third, owing to the delicate framework normalization, both TI-APJCSC and TII-APJCSC are quite flexible. With a simple tradeoff factor varying in the small fixed interval (0, 1], they can self-adapt to any semisupervised scenario. Finally, both TI-APJCSC and TII-APJCSC demonstrate strong robustness, not only to the number of pairwise constraints but also to the parameter for affinity measurement. As such, the novel TI-APJCSC and TII-APJCSC algorithms are very practical for medium- and small-scale semisupervised data sets. The experimental studies thoroughly evaluated and demonstrated these advantages on both synthetic and real-life semisupervised data sets.

Portfolio Decisions and Brain Reactions via the CEAD method.

Decision making can be a complex process requiring the integration of several attributes of choice options. Understanding the neural processes underlying (uncertain) investment decisions is an important topic in neuroeconomics. We analyzed functional magnetic resonance imaging (fMRI) data from an investment decision study for stimulus-related effects. We propose a new technique for identifying activated brain regions: cluster, estimation, activation, and decision method. Our analysis is focused on clusters of voxels rather than voxel units. Thus, we achieve a higher signal-to-noise ratio within the unit tested and a smaller number of hypothesis tests compared with the often used General Linear Model (GLM). We propose to first conduct the brain parcellation by applying spatially constrained spectral clustering. The information within each cluster can then be extracted by the flexible dynamic semiparametric factor model (DSFM) dimension reduction technique and finally be tested for differences in activation between conditions. This sequence of Cluster, Estimation, Activation, and Decision admits a model-free analysis of the local fMRI signal. Applying a GLM on the DSFM-based time series resulted in a significant correlation between the risk of choice options and changes in fMRI signal in the anterior insula and dorsomedial prefrontal cortex. Additionally, individual differences in decision-related reactions within the DSFM time series predicted individual differences in risk attitudes as modeled with the framework of the mean-variance model.

Scalable Constrained Spectral Clustering

Constrained spectral clustering (CSC) algorithms have shown great promise in significantly improving clustering accuracy by encoding side information into spectral clustering algorithms. However, existing CSC algorithms are inefficient in handling moderate and large datasets. In this paper, we aim to develop a scalable and efficient CSC algorithm by integrating sparse coding based graph construction into a framework called constrained normalized cuts . To this end, we formulate a scalable constrained normalized-cuts problem and solve it based on a closed-form mathematical analysis. We demonstrate that this problem can be reduced to a generalized eigenvalue problem that can be solved very efficiently. We also describe a principled $k$ -way CSC algorithm for handling moderate and large datasets. Experimental results over benchmark datasets demonstrate that the proposed algorithm is greatly cost-effective, in the sense that (1) with less side information, it can obtain significant improvements in accuracy compared to the unsupervised baseline; (2) with less computational time, it can achieve high clustering accuracies close to those of the state-of-the-art.

Constrained spectral clustering based controlled islanding

Controlled islanding, which splits the whole power system into islands, is an effective way of limiting blackouts during severe disturbances. Calculating islanding solutions in real time is difficult because of the combinatorial explosion of the solution space occurs for large power system. This paper proposes a computationally efficient controlled islanding algorithm that uses constrained spectral clustering. An undirected edge-weighted graph is constructed based on absolute values of active power flow and constraints related to transmission line availability and coherent generator groups are included by modifying the edge weights of the graph and using a subspace projection. Spectral clustering is then applied to the constrained solution subspace to find the islanding solution. To improve the clustering quality, a pre-processing procedure is used to detect and eliminate outliers in the eigenvectors of the graph before clustering. A robust k-medoids algorithm, which is less sensitive to outliers than the traditional k-means algorithm, is then used for clustering. Simulation results show that the proposed algorithm is computationally efficient when solving a controlled islanding problem in real-time.

Two-Step Spectral Clustering Controlled Islanding Algorithm

<?Pub Dtl=""?> Controlled islanding is an active and effective way of avoiding catastrophic wide area blackouts. It is usually considered as a constrained combinatorial optimization problem. However, the combinatorial explosion of the solution space that occurs for large power systems increases the complexity of solving it. This paper proposes a two-step controlled islanding algorithm that uses spectral clustering to find a suitable islanding solution for preventing the initiation of wide area blackouts by un-damped electromechanical oscillations. The objective function used in this controlled islanding algorithm is the minimal power-flow disruption. The sole constraint applied to this solution is related to generator coherency. In the first step of the algorithm, the generator nodes are grouped using normalized spectral clustering, based on their dynamic models, to produce groups of coherent generators. In the second step of the algorithm, the islanding solution that provides the minimum power-flow disruption while satisfying the constraint of coherent generator groups is determined by grouping all nodes using constrained spectral clustering. Simulation results, obtained using the IEEE 9-, 39-, and 118-bus test systems, show that the proposed algorithm is computationally efficient when solving the controlled islanding problem, particularly in the case of a large power system.

3D human posture segmentation by spectral clustering with surface normal constraint

In this paper, we propose a new algorithm for partitioning human posture represented by 3D point clouds sampled from the surface of human body. The algorithm is formed as a constrained extension of the recently developed segmentation method, spectral clustering (SC). Two folds of merits are offered by the algorithm: (1) as a nonlinear method, it is able to deal with the situation that data (point cloud) are sampled from a manifold (the surface of human body) rather than the embedded entire 3D space; (2) by using constraints, it facilitates the integration of multiple similarities for human posture partitioning, and it also helps to reduce the limitations of spectral clustering. We show that the constrained spectral clustering (CSC) still can be solved by generalized eigen-decomposition. Experimental results confirm the effectiveness of the proposed algorithm.