The increasing volume of data in modern business and science calls for more complex and sophisticated tools. Although advances in data mining technology have made extensive data collection much easier, it's still always evolving and there is a constant need for new techniques and tools that can help us transform this data into useful information and knowledge. Since the previous edition's publication, great advances have been made in the field of data mining. Not only does the third of edition of Data Mining: Concepts and Techniques continue the tradition of equipping you with an understanding and application of the theory and practice of discovering patterns hidden in large data sets, it also focuses on new, important topics in the field: data warehouses and data cube technology, mining stream, mining social networks, and mining spatial, multimedia and other complex data. Each chapter is a stand-alone guide to a critical topic, presenting proven algorithms and sound implementations ready to be used directly or with strategic modification against live data. This is the resource you need if you want to apply today's most powerful data mining techniques to meet real business challenges. * Presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects. * Addresses advanced topics such as mining object-relational databases, spatial databases, multimedia databases, time-series databases, text databases, the World Wide Web, and applications in several fields. *Provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data

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Data Mining: Concepts and Techniques

We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging.

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Normalized cuts and image segmentation

We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We have applied this approach to segmenting static images and found results very encouraging.

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In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.

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Consensus problems in networks of agents with switching topology and time-delays

Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

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Linear Matrix Inequalities in System and Control Theory

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Algebraic connectivity of graphs

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A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory

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On matrices with non-positive off-diagonal elements and positive principal minors

1. Basic Concepts of the Theory of Matrices.- Matrices.- Determinants.- Nonsingular matrices. Inverse matrices.- Schur complement. Factorization.- Vector spaces. Rank.- Eigenvectors, eigenvalues. Characteristic polynomial.- Similarity. Jordan normal form.- Exercises.- 2. Symmetric Matrices. Positive Definite and Semidefinite Matrices.- Euclidean and unitary spaces.- Symmetric and Hermitian matrices.- Orthogonal and unitary matrices.- Gram-Schmidt orthonormalization. Schur's theorem.- Positive definite and positive semidefinite matrices.- Sylvester's law of inertia.- Singular value decomposition.- Exercises.- 3. Graphs and Matrices.- Digraphs.- Digraph of a matrix.- Undirected graphs. Trees.- Bigraphs.- Exercises.- 4. Nonnegative Matrices. Stochastic and Doubly Stochastic Matrices.- Nonnegative matrices.- The Perron-Frobenius theorem.- Cyclic matrices.- Stochastic matrices.- Doubly stochastic matrices.- Exercises.- 5. M-Matrices (Matrices of Classes K and K0).- Class K.- Class K0.- Diagonally dominant matrices.- Monotone matrices.- Class P.- Exercises.- 6. Tensor Product of Matrices. Compound Matrices.- Tensor product.- Compound matrices.- Exercises.- 7. Matrices and Polynomials. Stable matrices.- Characteristic polynomial.- Matrices associated with polynomials.- Bezout matrices.- Hankel matrices.- Toeplitz and Lowner matrices.- Stable matrices.- Exercises.- 8. Band Matrices.- Band matrices and graphs.- Eigenvalues and eigenvectors of tridiagonal matrices.- Exercises.- 9. Norms and Their Use for Estimation of Eigenvalues.- Norms.- Measure of nonsingularity. Dual norms.- Bounds for eigenvalues.- Exercises.- 10. Direct Methods for Solving Linear Systems.- Nonsingular case.- General case.- Exercises.- 11. Iterative Methods for Solving Linear Systems.- The Jacobi method.- The Gauss-Seidel method.- The SOR method.- Exercises.- 12. Matrix Inversion.- Inversion of special matrices.- The pseudoinverse.- Exercises.- 13. Numerical Methods for Computing Eigenvalues of Matrices.- Computation of selected eigenvalues.- Computation of all the eigenvalues.- Exercises.- 14. Sparse matrices.- Storing. Elimination ordering.- Envelopes. Profile.- Exercises.

Special matrices and their applications in numerical mathematics

Matrices.- Solvability of systems of interval linear equations and inequalities.- Interval linear programming.- Linear programming with set coefficients.- Fuzzy linear optimization.- Interval linear systems and optimization problems over max-algebras.

Miroslav Fiedler

Papers

Algebraic connectivity of graphs

A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory

On matrices with non-positive off-diagonal elements and positive principal minors

Special matrices and their applications in numerical mathematics

Linear Optimization Problems with Inexact Data