We discuss two intrinsic weaknesses of the spectral graph partitioning method, both of which have practical consequences. The first is that spectral embeddings tend to hide the best cuts from the commonly used hyperplane rounding method. Rather than cleaning up the resulting suboptimal cuts with local search, we recommend the adoption of flow-based rounding. The second weakness is that for many "power law" graphs, the spectral method produces cuts that are highly unbalanced, thus decreasing the usefulness of the method for visualization (see figure 4(b)) or as a basis for divide-and-conquer algorithms. These balance problems, which occur even though the spectral method's quotient-style objective function does encourage balance, can be fixed with a stricter balance constraint that turns the spectral mathematical program into an SDP that can be solved for million-node graphs by a method of Burer and Monteiro.

In this paper we consider the problem of finding sets of points that conform to a given underlying model from within a dense, noisy set of observations. This problem is motivated by the task of efficiently linking faint asteroid detections, but is applicable to a range of spatial queries. We survey current tree-based approaches, showing a tradeoff exists between single tree and multiple tree algorithms. To this end, we present a new type of multiple tree algorithm that uses a variable number of trees to exploit the advantages of both approaches. We empirically show that this algorithm performs well using both simulated and astronomical data.

We discuss two intrinsic weaknesses of the spectral graph partitioning method, both of which have practical consequences. The first is that spectral embeddings tend to hide the best cuts from the commonly used hyperplane rounding method. Rather than cleaning up the resulting suboptimal cuts with local search, we recommend the adoption of flow-based rounding. The second weakness is that for many "power law" graphs, the spectral method produces cuts that are highly unbalanced, thus decreasing the usefulness of the method for visualization (see figure 4(b)) or as a basis for divide-and-conquer algorithms. These balance problems, which occur even though the spectral method's quotient-style objective function does encourage balance, can be fixed with a stricter balance constraint that turns the spectral mathematical program into an SDP that can be solved for million-node graphs by a method of Burer and Monteiro.

Sparse PCA seeks approximate sparse "eigenvectors" whose projections capture the maximal variance of data. As a cardinality-constrained and non-convex optimization problem, it is NPhard and is encountered in a wide range of applied fields, from bio-informatics to finance. Recent progress has focused mainly on continuous approximation and convex relaxation of the hard cardinality constraint. In contrast, we consider an alternative discrete spectral formulation based on variational eigenvalue bounds and provide an effective greedy strategy as well as provably optimal solutions using branch-and-bound search. Moreover, the exact methodology used reveals a simple renormalization step that improves approximate solutions obtained by any continuous method. The resulting performance gain of discrete algorithms is demonstrated on real-world benchmark data and in extensive Monte Carlo evaluation trials.

In this paper we consider the problem of finding sets of points that conform to a given underlying model from within a dense, noisy set of observations. This problem is motivated by the task of efficiently linking faint asteroid detections, but is applicable to a range of spatial queries. We survey current tree-based approaches, showing a tradeoff exists between single tree and multiple tree algorithms. To this end, we present a new type of multiple tree algorithm that uses a variable number of trees to exploit the advantages of both approaches. We empirically show that this algorithm performs well using both simulated and astronomical data.

Sparse PCA seeks approximate sparse "eigenvectors" whose projections capture the maximal variance of data. As a cardinality-constrained and non-convex optimization problem, it is NPhard and is encountered in a wide range of applied fields, from bio-informatics to finance. Recent progress has focused mainly on continuous approximation and convex relaxation of the hard cardinality constraint. In contrast, we consider an alternative discrete spectral formulation based on variational eigenvalue bounds and provide an effective greedy strategy as well as provably optimal solutions using branch-and-bound search. Moreover, the exact methodology used reveals a simple renormalization step that improves approximate solutions obtained by any continuous method. The resulting performance gain of discrete algorithms is demonstrated on real-world benchmark data and in extensive Monte Carlo evaluation trials.

We discuss two intrinsic weaknesses of the spectral graph partitioning method, both of which have practical consequences. The first is that spectral embeddings tend to hide the best cuts from the commonly used hyperplane rounding method. Rather than cleaning up the resulting suboptimal cutswith local search, we recommend the adoption of flow-based rounding. The second weakness is that for many "power law" graphs, the spectral method produces cuts that are highly unbalanced, thus decreasing theusefulness of the method for visualization (see figure 4(b)) or as a basis for divide-and-conquer algorithms. These balance problems, which occur even though the spectral method's quotient-style objective function does encourage balance, can be fixed with a stricter balance constraint thatturns the spectral mathematical program into an SDP that can be solved for million-node graphs by a method of Burer and Monteiro.

In this paper we consider the problem of finding sets of points that conform toa given underlying model from within a dense, noisy set of observations. Thisproblem is motivated by the task of efficiently linking faint asteroid detections, but is applicable to a range of spatial queries. We survey current tree-based approaches, showing a tradeoff exists between singletree and multiple tree algorithms. To this end, we present a new type of multiple tree algorithm that uses a variable number of trees to exploit the advantages of both approaches. We empirically show that this algorithm performs well using both simulated and astronomical data.

The Workshop program of the Twenty-First Conference on Artificial Intelligence was held July 16-17, 2006 in Boston, Massachusetts. The program was chaired by Joyce Chai and Keith Decker. The titles of the 17 workshops were AIDriven Technologies for Service-Oriented Computing; Auction Mechanisms for Robot Coordination; Cognitive Modeling and Agent-Based Social Simulations, Cognitive Robotics; Computational Aesthetics: Artificial Intelligence Approaches to Beauty and Happiness; Educational Data Mining; Evaluation Methods for Machine Learning; Event Extraction and Synthesis; Heuristic Search, Memory- Based Heuristics, and Their Applications; Human Implications of Human-Robot Interaction; Intelligent Techniques in Web Personalization; Learning for Search; Modeling and Retrieval of Context; Modeling Others from Observations; and Statistical and Empirical Approaches for Spoken Dialogue Systems.

We present a heuristic search algorithm for solving first-order Markov Decision Processes (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, in contrast to existing systems, which start with propositionalizing the FOMDP and then perform state abstraction on its propositionalized version we apply state abstraction directly on the FOMDP avoiding propositionalization. This kind of abstraction is referred to as first-order state abstraction. Secondly, guided by an admissible heuristic, the search is restricted to those states that are reachable from the initial state. We demonstrate the usefulness of the above techniques for solving FOMDPs with a system, referred to as FluCaP (formerly, FCPlanner), that entered the probabilistic track of the 2004 International Planning Competition (IPC'2004) and demonstrated an advantage over other planners on the problems represented in first-order terms.