clustering

Mixed-Integer Quadratic Optimization and Iterative Clustering Techniques for Semi-Supervised Support Vector Machines

  • Martin Schmidt
  • Jan Pablo Burgard
  • Maria Eduarda Pinheiro
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Algorithms, Data Science Applications Tags , , ,

    Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a subset of points. Furthermore, this subset can be non-representative, e.g., due to self-selection in a survey. Semi-supervised SVMs tackle … Read more

    Machine Learning for K-adaptability in Two-stage Robust Optimization

  • Esther Julien
  • Krzysztof Postek
  • Ş. İlker Birbil
    • Categories Robust Optimization Tags , , , , ,

    Two-stage robust optimization problems constitute one of the hardest optimization problem classes.One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the uncertainty set of scenarios into K subsets, and optimizesdecisions corresponding to each of these subsets. In general case, it is solved using the … Read more

    Statistical performance of subgradient step-size update rules in Lagrangian relaxations of chance-constrained optimization models

  • Charlotte Ritter
  • Bismark Singh
    • Categories Stochastic Programming Tags , , , ,

    Lagrangian relaxation schemes, coupled with a subgradient procedure, are frequently employed to solve chance-constrained optimization models. The subgradient procedure typically relies on a step-size update rule. Although there is extensive research on the properties of these step-size update rules, there is little consensus on which rules are most suited in practice. This is especially so … Read more

    Time-series aggregation for the optimization of energy systems: goals, challenges, approaches, and opportunities

  • Holger Teichgraeber
  • Adam R. Brandt
    • Categories Data-Mining, Facility Planning and Design, Smart Grids Tags , , , , ,

    The rising significance of renewable energy increases the importance of representing time-varying input data in energy system optimization studies. Time-series aggregation, which reduces temporal model complexity, has emerged in recent years to address this challenge. We provide a comprehensive review of time-series aggregation for the optimization of energy systems. We show where time series affect … Read more

    On the Cluster-aware Supervised Learning (CluSL): Frameworks, Convergent Algorithms, and Applications

  • Shutong Chen
  • Weijun Xie
    • Categories Data-Mining Tags , , , , ,

    This paper proposes a cluster-aware supervised learning (CluSL) framework, which integrates the clustering analysis with supervised learning (SL). The objective of CluSL is to simultaneously find the best clusters of the data points and minimize the sum of loss functions within each cluster. This framework has many potential applications in healthcare, operations management, manufacturing, and … Read more

    Clustering methods to find representative periods for the optimization of energy systems: an initial framework and comparison

  • Adam R. Brandt
  • Holger Teichgraeber
    • Categories Applications - Science and Engineering, Chemical Engineering, Smart Grids Tags , , , , ,

    Modeling time-varying operations in complex energy systems optimization problems is often computationally intractable, and time-series input data are thus often aggregated to representative periods. In this work, we introduce a framework for using clustering methods for this purpose, and we compare both conventionally-used methods (k-means, k-medoids, and hierarchical clustering), and shape-based clustering methods (dynamic time … Read more

    Clustering and Multifacility Location with Constraints via Distance Function Penalty Method and DC Programming

  • Nguyen Thai An
  • Nguyen Mau Nam
  • Sam Reynolds
  • Tuyen Tran
    • Categories Nonsmooth Optimization Tags , , ,

    This paper is a continuation of our effort in using mathematical optimization involving DC programming in clustering and multifacility location. We study a penalty method based on distance functions and apply it particularly to a number of problems in clustering and multifacility location in which the centers to be found must lie in some given … Read more

    Divisive heuristic for modularity density maximization

  • Alberto Costa
  • Leo Liberti
  • Sergey Kushnarev
  • Zeyu Sun
    • Categories (Mixed) Integer Linear Programming, Network Optimization Tags , , , ,

    In this paper we consider a particular method of clustering for graphs, namely the modularity density maximization. We propose a hierarchical divisive heuristic which works by splitting recursively a cluster into two new clusters by maximizing the modularity density, and we derive four reformulations for the mathematical programming model used to obtain the optimal splitting. … Read more

    Clustering Categories in Support Vector Machines

  • Emilio Carrizosa
  • Dolores Romero Morales
  • Amaya Nogales-Gómez
    • Categories Applications - OR and Management Sciences Tags , , , , ,

    Support Vector Machines (SVM) is the state-of-the-art in Supervised Classification. In this paper the Cluster Support Vector Machines (CLSVM) methodology is proposed with the aim to reduce the complexity of the SVM classifier in the presence of categorical features. The CLSVM methodology lets categories cluster around their peers and builds an SVM classifier using the … Read more