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Privacy preserving data mining (PPDM) has been a new research area in the past two decades. The aim of PPDM algorithms is to modify data in the dataset so that sensitive data and confidential knowledge, even after mining data be kept confidential. Association rule hiding is one of the techniques of PPDM to avoid extracting some rules that are recognized as sensitive rules and should be extracted and...
The growth of the web has directly influenced the increase in the availability of relational data. One of the key problems in mining such data is computing the similarity between objects with heterogeneous feature types. For example, publications have many heterogeneous features like text, citations, authorship information, venue information, etc. In most approaches, similarity is estimated using...
A broad class of problems in circuits, electromagnetics, and optics can be expressed as finding some parameters of a linear system with a specific type. This paper is concerned with studying this type of circuit using the available control techniques. It is shown that the underlying problem can be recast as a rank minimization problem that is NP-hard in general. In order to circumvent this difficulty,...
The application of nuclear norm regularization to system identification was recently shown to be a useful method for identifying low order linear models. In this paper, we consider nuclear norm regularization for identification of simulated moving bed processes from data sets with missing entries. The missing data problem is of ongoing interest because the need to analyze incomplete data sets arises...
We propose an algorithm for design of optimal inputs for system identification when amplitude constraints on the input and output are imposed. In contrast to input design with signal power constraints, this problem is non-convex and non-smooth. We propose an iterative solution: in the first step, a convex optimization problem is solved for input design under power constraints. In subsequent steps,...
We consider a network of control systems connected over a graph. Considering the graph structure as constraints on the set of permissible controllers, we show that such systems are simply constrained by a certain sparsity pattern. We provide conditions for which such systems are well-posed, and, under the appropriate assumptions, we show that such systems are quadratically invariant. This allows for...
In the conventional regularized learning, training time increases as the training set expands. Recent work on L2 linear SVM challenges this common sense by proposing the inverse time dependency on the training set size. In this paper, we first put forward a Primal Gradient Solver (PGS) to effectively solve the convex regularized learning problem. This solver is based on the stochastic gradient descent...
Learning to rank is an important area at the interface of machine learning, information retrieval and Web search. The central challenge in optimizing various measures of ranking loss is that the objectives tend to be non-convex and discontinuous. To make such functions amenable to gradient based optimization procedures one needs to design clever bounds. In recent years, boosting, neural networks,...
Quadratic invariance is a condition which has been shown to allow for optimal decentralized control problems to be cast as convex optimization problems. The condition relates the constraints that the decentralization imposes on the controller to the structure of the plant. In this paper, we consider the problem of finding the closest subset and superset of the decentralization constraint which are...
In kernel based regression techniques (such as Support Vector Machines or Least Squares Support Vector Machines) it is hard to analyze the influence of perturbed inputs on the estimates. We show that for a nonlinear black box model a convex problem can be derived if it is linearized with respect to the influence of input perturbations. For this model an explicit prediction equation can be found. The...
The notion of sos-convexity has recently been proposed as a tractable sufficient condition for convexity of polynomials based on a sum of squares decomposition of the Hessian matrix. A multivariate polynomial p(x) = p(x1,...,xn)is said to be sos-convex if its Hessian H(x) can be factored as H(x) = MT(x)M(x) with a possibly nonsquare polynomial matrix M(x). The problem of deciding sos-convexity of...
In this paper we study the problem of robust discrete-time H2 filtering using a Linear Matrix Inequality approach. By assuming that the number of samples available for the identification of the system is large enough, we describe the filter design problem as a semidefinite program. Afterwards, the problem of designing an input signal for the identification of the system, to improve the performance...
This paper considers the worst-case estimation problem in the presence of unknown but bounded noise. Contrary to stochastic approaches, the goal here is to confine the estimation error within a bounded set. Previous work dealing with the problem has shown that the complexity of estimators based upon the idea of constructing the state consistency set (e.g. the set of all states consistent with the...
This paper addresses the problem of robust identification of a class of discrete-time affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and a bound on the number of subsystems, the objective is to identify a suitable set of affine models along with a switching sequence that can explain the available experimental information...
This paper addresses the problem of computing the worst-case expected value of a polynomial function, over a class of admissible distributions. It is shown that this problem, for the class of distributions considered, is equivalent to a convex optimization problem for which efficient linear matrix inequality (LMI) relaxations are available. In case that the performance function is continuous (not...
Classification problems in critical applications such as health care or security often require very high reliability because of the high costs of errors. In order to achieve this reliability, such systems often require the use of sequential inspections, where additional data can be collected to resolve ambiguous test cases. It is impractical or costly to collect this additional data on every sample,...
Multiobjective bilevel programming problem (MBPP) has a wide field of applications and has been proven to be an NP-hard problem. In this paper, a special multiobjective bilevel convex programming problem (MBCPP) is studied, and it is first transformed into an equivalent single objective bilevel convex programming problem by weighted sum of objectives. Then, for the equivalent problem, we design a...
We regard a network of coupled nonlinear dynamical systems that we want to control optimally. The cost function is assumed to be separable and convex. The algorithm we propose to address the numerical solution of this problem is based on two ingredients: first, we exploit the convex problem structure using a sequential convex programming framework that linearizes the nonlinear dynamics in each iteration...
This paper presents a convex approach for parameter estimation problems (PEPs) involving parameter-affine dynamic systems. By using the available state measurements, the nonconvex PEP is modified such that a convex approximation is obtained. The optimum delivered by this approximation is subsequently used to linearize the original PEP such that a refined solution is obtained. An assessment of the...
In this paper a three-stage procedure for set-membership identification of block-structured nonlinear feedback systems is proposed. Nonlinear block parameters bounds are computed in the first stage exploiting steady-state measurements. Then, given the uncertain description of the nonlinear block, bounds on the unmeasurable inner-signal are computed in the second stage. Finally, linear block parameters...
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