Multiclass Hammersley-Aldous-Diaconis process and multiclass-customer queues

In the Hammersley-Aldous-Diaconis process, infinitely many particles sit in R and at most one particle is allowed at each position. A particle at x, whose nearest neighbor to the right is at y, jumps at rate y - x to a position uniformly distributed in the interval (x, y). The basic coupling between trajectories with different initial configuration induces a process with different classes of particles. We show that the invariant measures for the two-class process can be obtained as follows. First, a stationary M/M/1 queue is constructed as a function of two homogeneous Poisson processes, the arrivals with rate, and the (attempted) services with rate rho > lambda Then put first class particles at the instants of departures (effective services) and second class particles at the instants of unused services. The procedure is generalized for the n-class case by using n - 1 queues in tandem with n - 1 priority types of customers. A multi-line process is introduced; it consists of a coupling (different from Liggett's basic coupling), having as invariant measure the product of Poisson processes. The definition of the multi-line process involves the dual points of the space-time Poisson process used in the graphical construction of the reversed process. The coupled process is a transformation of the multi-line process and its invariant measure is the transformation described above of the product measure.

Mass spectrometry parameters optimization for the 46 multiclass pesticides determination in strawberries with gas chromatography ion-trap tandem mass spectrometry

Multiclass analysis method was optimized in order to analyze pesticides traces by gas chromatography with ion-trap and tandem mass spectrometry (GC-MS/MS). The influence of some analytical parameters on pesticide signal response was explored. Five ion trap mass spectrometry (IT-MS) operating parameters, including isolation time (IT), excitation voltage (EV), excitation time (ET),maximum excitation energy or “q” value (q), and isolationmass window (IMW) were numerically tested in order to maximize the instrument analytical signal response. For this, multiple linear regression was used in data analysis to evaluate the influence of the five parameters on the analytical response in the ion trap mass spectrometer and to predict its response. The assessment of the five parameters based on the regression equations substantially increased the sensitivity of IT-MS/MS in the MS/MS mode. The results obtained show that for most of the pesticides, these parameters have a strong influence on both signal response and detection limit.Using the optimized method, a multiclass pesticide analysis was performed for 46 pesticides in a strawberry matrix. Levels higher than the limit established for strawberries by the European Union were found in some samples.

Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance

We address the problem of scheduling a multiclass $M/M/m$ queue with Bernoulli feedback on $m$ parallel servers to minimize time-average linear holding costs. We analyze the performance of a heuristic priority-index rule, which extends Klimov's optimal solution to the single-server case: servers select preemptively customers with larger Klimov indices. We present closed-form suboptimality bounds (approximate optimality) for Klimov's rule, which imply that its suboptimality gap is uniformly bounded above with respect to (i) external arrival rates, as long as they stay within system capacity;and (ii) the number of servers. It follows that its relativesuboptimality gap vanishes in a heavy-traffic limit, as external arrival rates approach system capacity (heavy-traffic optimality). We obtain simpler expressions for the special no-feedback case, where the heuristic reduces to the classical $c \mu$ rule. Our analysis is based on comparing the expected cost of Klimov's ruleto the value of a strong linear programming (LP) relaxation of the system's region of achievable performance of mean queue lengths. In order to obtain this relaxation, we derive and exploit a new set ofwork decomposition laws for the parallel-server system. We further report on the results of a computational study on the quality of the $c \mu$ rule for parallel scheduling.

Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case

We address the performance optimization problem in a single-stationmulticlass queueing network with changeover times by means of theachievable region approach. This approach seeks to obtainperformance bounds and scheduling policies from the solution of amathematical program over a relaxation of the system's performanceregion. Relaxed formulations (including linear, convex, nonconvexand positive semidefinite constraints) of this region are developedby formulating equilibrium relations satisfied by the system, withthe help of Palm calculus. Our contributions include: (1) newconstraints formulating equilibrium relations on server dynamics;(2) a flow conservation interpretation of the constraintspreviously derived by the potential function method; (3) newpositive semidefinite constraints; (4) new work decomposition lawsfor single-station multiclass queueing networks, which yield newconvex constraints; (5) a unified buffer occupancy method ofperformance analysis obtained from the constraints; (6) heuristicscheduling policies from the solution of the relaxations.

Optimization of multiclass queueing networks with changeover times via the achievable region method: Part II, the multi-station case

We address the problem of scheduling a multi-station multiclassqueueing network (MQNET) with server changeover times to minimizesteady-state mean job holding costs. We present new lower boundson the best achievable cost that emerge as the values ofmathematical programming problems (linear, semidefinite, andconvex) over relaxed formulations of the system's achievableperformance region. The constraints on achievable performancedefining these formulations are obtained by formulatingsystem's equilibrium relations. Our contributions include: (1) aflow conservation interpretation and closed formulae for theconstraints previously derived by the potential function method;(2) new work decomposition laws for MQNETs; (3) new constraints(linear, convex, and semidefinite) on the performance region offirst and second moments of queue lengths for MQNETs; (4) a fastbound for a MQNET with N customer classes computed in N steps; (5)two heuristic scheduling policies: a priority-index policy, anda policy extracted from the solution of a linear programmingrelaxation.

Rapid analysis of multiclass antibiotic residues and some of their metabolites in hospital, urban wastewater and river water by ultra-highperformance liquid chromatography coupled to quadrupole-linear ion trap tandem mass spectrometry

The present work describes the development of a fast and robust analytical method for the determination of 53 antibiotic residues, covering various chemical groups and some of their metabolites, in environmental matrices that are considered important sources of antibiotic pollution, namely hospital and urban wastewaters, as well as in river waters. The method is based on automated off-line solid phase extraction (SPE) followed by ultra-high-performance liquid chromatography coupled to quadrupole linear ion trap tandem mass spectrometry (UHPLC–QqLIT). For unequivocal identification and confirmation, and in order to fulfill EU guidelines, two selected reaction monitoring (SRM) transitions per compound are monitored (the most intense one is used for quantification and the second one for confirmation). Quantification of target antibiotics is performed by the internal standard approach, using one isotopically labeled compound for each chemical group, in order to correct matrix effects. The main advantages of the method are automation and speed-up of sample preparation, by the reduction of extraction volumes for all matrices, the fast separation of a wide spectrum of antibiotics by using ultra-high-performance liquid chromatography, its sensitivity (limits of detection in the low ng/L range) and selectivity (due to the use of tandem mass spectrometry) The inclusion of β-lactam antibiotics (penicillins and cephalosporins), which are compounds difficult to analyze in multi-residue methods due to their instability in water matrices, and some antibiotics metabolites are other important benefits of the method developed. As part of the validation procedure, the method developed was applied to the analysis of antibiotics residues in hospital, urban influent and effluent wastewaters as well as in river water samples

Multiclass Classification of SRBCTs

A novel approach to multiclass tumor classification using Artificial Neural Networks (ANNs) was introduced in a recent paper cite{Khan2001}. The method successfully classified and diagnosed small, round blue cell tumors (SRBCTs) of childhood into four distinct categories, neuroblastoma (NB), rhabdomyosarcoma (RMS), non-Hodgkin lymphoma (NHL) and the Ewing family of tumors (EWS), using cDNA gene expression profiles of samples that included both tumor biopsy material and cell lines. We report that using an approach similar to the one reported by Yeang et al cite{Yeang2001}, i.e. multiclass classification by combining outputs of binary classifiers, we achieved equal accuracy with much fewer features. We report the performances of 3 binary classifiers (k-nearest neighbors (kNN), weighted-voting (WV), and support vector machines (SVM)) with 3 feature selection techniques (Golub's Signal to Noise (SN) ratios cite{Golub99}, Fisher scores (FSc) and Mukherjee's SVM feature selection (SVMFS))cite{Sayan98}.

Improving Multiclass Text Classification with the Support Vector Machine

We compare Naive Bayes and Support Vector Machines on the task of multiclass text classification. Using a variety of approaches to combine the underlying binary classifiers, we find that SVMs substantially outperform Naive Bayes. We present full multiclass results on two well-known text data sets, including the lowest error to date on both data sets. We develop a new indicator of binary performance to show that the SVM's lower multiclass error is a result of its improved binary performance. Furthermore, we demonstrate and explore the surprising result that one-vs-all classification performs favorably compared to other approaches even though it has no error-correcting properties.

Application of complex extreme learning machine to multiclass classification problems with high dimensionality: a THz spectra classification problem

We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

Building binary-tree-based multiclass classifiers using separability measures

Various popular machine learning techniques, like support vector machines, are originally conceived for the solution of two-class (binary) classification problems. However, a large number of real problems present more than two classes. A common approach to generalize binary learning techniques to solve problems with more than two classes, also known as multiclass classification problems, consists of hierarchically decomposing the multiclass problem into multiple binary sub-problems, whose outputs are combined to define the predicted class. This strategy results in a tree of binary classifiers, where each internal node corresponds to a binary classifier distinguishing two groups of classes and the leaf nodes correspond to the problem classes. This paper investigates how measures of the separability between classes can be employed in the construction of binary-tree-based multiclass classifiers, adapting the decompositions performed to each particular multiclass problem. (C) 2010 Elsevier B.V. All rights reserved.

A review on the combination of binary classifiers in multiclass problems

Several real problems involve the classification of data into categories or classes. Given a data set containing data whose classes are known, Machine Learning algorithms can be employed for the induction of a classifier able to predict the class of new data from the same domain, performing the desired discrimination. Some learning techniques are originally conceived for the solution of problems with only two classes, also named binary classification problems. However, many problems require the discrimination of examples into more than two categories or classes. This paper presents a survey on the main strategies for the generalization of binary classifiers to problems with more than two classes, known as multiclass classification problems. The focus is on strategies that decompose the original multiclass problem into multiple binary subtasks, whose outputs are combined to obtain the final prediction.

Evolutionary tuning of SVM parameter values in multiclass problems

Support vector machines (SVMs) were originally formulated for the solution of binary classification problems. In multiclass problems, a decomposition approach is often employed, in which the multiclass problem is divided into multiple binary subproblems, whose results are combined. Generally, the performance of SVM classifiers is affected by the selection of values for their parameters. This paper investigates the use of genetic algorithms (GAs) to tune the parameters of the binary SVMs in common multiclass decompositions. The developed GA may search for a set of parameter values common to all binary classifiers or for differentiated values for each binary classifier. (C) 2008 Elsevier B.V. All rights reserved.

HIERARCHICAL DECOMPOSITION OF MULTICLASS PROBLEMS

Several popular Machine Learning techniques are originally designed for the solution of two-class problems. However, several classification problems have more than two classes. One approach to deal with multiclass problems using binary classifiers is to decompose the multiclass problem into multiple binary sub-problems disposed in a binary tree. This approach requires a binary partition of the classes for each node of the tree, which defines the tree structure. This paper presents two algorithms to determine the tree structure taking into account information collected from the used dataset. This approach allows the tree structure to be determined automatically for any multiclass dataset.

A new and improved strategy combining a dispersive-solid phase extraction-based multiclass method with ultra high pressure liquid chromatography for analysis of low molecular weight polyphenols in vegetables

This paper reports on the development and optimization of a modified Quick, Easy, Cheap Effective, Rugged and Safe (QuEChERS) based extraction technique coupled with a clean-up dispersive-solid phase extraction (dSPE) as a new, reliable and powerful strategy to enhance the extraction efficiency of free low molecular-weight polyphenols in selected species of dietary vegetables. The process involves two simple steps. First, the homogenized samples are extracted and partitioned using an organic solvent and salt solution. Then, the supernatant is further extracted and cleaned using a dSPE technique. Final clear extracts of vegetables were concentrated under vacuum to near dryness and taken up into initial mobile phase (0.1% formic acid and 20% methanol). The separation and quantification of free low molecular weight polyphenols from the vegetable extracts was achieved by ultrahigh pressure liquid chromatography (UHPLC) equipped with a phodiode array (PDA) detection system and a Trifunctional High Strength Silica capillary analytical column (HSS T3), specially designed for polar compounds. The performance of the method was assessed by studying the selectivity, linear dynamic range, the limit of detection (LOD) and limit of quantification (LOQ), precision, trueness, and matrix effects. The validation parameters of the method showed satisfactory figures of merit. Good linearity (View the MathML sourceRvalues2>0.954; (+)-catechin in carrot samples) was achieved at the studied concentration range. Reproducibility was better than 3%. Consistent recoveries of polyphenols ranging from 78.4 to 99.9% were observed when all target vegetable samples were spiked at two concentration levels, with relative standard deviations (RSDs, n = 5) lower than 2.9%. The LODs and the LOQs ranged from 0.005 μg mL−1 (trans-resveratrol, carrot) to 0.62 μg mL−1 (syringic acid, garlic) and from 0.016 μg mL−1 (trans-resveratrol, carrot) to 0.87 μg mL−1 ((+)-catechin, carrot) depending on the compound. The method was applied for studying the occurrence of free low molecular weight polyphenols in eight selected dietary vegetables (broccoli, tomato, carrot, garlic, onion, red pepper, green pepper and beetroot), providing a valuable and promising tool for food quality evaluation.