Related papers: Using Constraints to Discover Sparse and Alternati…
Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…
We build on a recently proposed method for stepwise explaining solutions of Constraint Satisfaction Problems (CSP) in a human-understandable way. An explanation here is a sequence of simple inference steps where simplicity is quantified…
Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard…
Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all…
Cluster analysis methods are used to identify homogeneous subgroups in a data set. In biomedical applications, one frequently applies cluster analysis in order to identify biologically interesting subgroups. In particular, one may wish to…
Semi-supervised clustering methods incorporate a limited amount of supervision into the clustering process. Typically, this supervision is provided by the user in the form of pairwise constraints. Existing methods use such constraints in…
This paper studies high-dimensional sparse clustering, a combinatorial NP-hard problem arising from the bilinear coupling between cluster assignment and feature selection. We analyze semidefinite programming (SDP) relaxations of $K$-means…
When searching for communities in networks, domain experts may have some prior expectations about the size of communities. Yet, community detection methods normally do not optimize communities under cluster size constraints.…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
In this paper we present efficient algorithmic solutions for several constrained resource allocation, management and discovery problems. We consider new types of resource allocation models and constraints, and we present new geometric…
The aim of this paper is twofold. First, we introduce "resource constraints" as a general concept that covers many practical restrictions on experimental design. Second, for computing efficient exact designs of experiments under any…
This paper considers extractive summarisation in a comparative setting: given two or more document groups (e.g., separated by publication time), the goal is to select a small number of documents that are representative of each group, and…
State-of-the-art subspace clustering methods are based on self-expressive model, which represents each data point as a linear combination of other data points. By enforcing such representation to be sparse, sparse subspace clustering is…
Feature selection is an important preprocessing step in machine learning and data mining. In real-world applications, costs, including money, time and other resources, are required to acquire the features. In some cases, there is a test…
Discovering pattern sets or global patterns is an attractive issue from the pattern mining community in order to provide useful information. By combining local patterns satisfying a joint meaning, this approach produces patterns of higher…
We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on…
Current subgroup identification methods typically follow a two-step approach: first estimate conditional average treatment effects and then apply thresholding or rule-based procedures to define subgroups. While intuitive, this decoupled…
This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of…
Peer-grouping is used in many sectors for organisational learning, policy implementation, and benchmarking. Clustering provides a statistical, data-driven method for constructing meaningful peer groups, but peer groups must be compatible…
Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…