ABSTRACT: An overview of some of the classification **techniques** appearing in this paper for Diabetes diagnoses and treatment. Hybrid **optimization** **techniques** are in the form Artificial Neural networks, Genetic Algorithm, Fuzzy classifier, Support Vector Machine, **Least** **Squares** Support Vector Machine, Particle Swarm **Optimization**. All the **techniques** are analyzed using Pima Indians Diabetes Data set from UCI repository of machine learning databases. This review aims to conclude best **optimization** technique for Diabetes Mellitus Diagnosis

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Heuristic **optimization** **techniques** have been successfully applied to a vari- ety of problems in statistics and economics for well over a decade (see Gilli et al. (2008) and Gilli and Winker (2008) for recent overviews). However, appli- cations to estimation problems are still rare. Fitzenberger and Winker (2007) consider Threshold Accepting (TA) for censored quantile regression, a prob- lem similar to the LMS estimator. 2 Maringer and Meyer (2008) and Yang et al. (2007) also use TA for model selection and estimation of smooth transi- tion autoregressive models. In contrast, several **optimization** heuristics have been used in other ﬁelds of research in ﬁnance, e.g., portfolio **optimization** (Dueck and Winker (1992), Maringer (2005), Winker and Maringer (2007a), Specht and Winker (2008)) or credit risk bucketing (Krink et al. 2007).

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In order to improve the accuracy of traffic flow prediction, scholars and practitioners have proposed many methods over the past several decades, such as time series **techniques** and regression models [2–6]. In recent years, many artificial intelligence forecasting **techniques** have been applied to traffic flow forecasting to improve the accuracy of forecasting. Yan Chen et al. [7] proposed a kind of intelligent forecasting method based on particle swarm **optimization** algorithm, which improves the stability and reliability of the forecast. Wei-Chiang Hong et al. [8] proposed a hybrid model combined with differential evolution algorithm for traffic flow, which was shown to outperform the SVR default parameter prediction support vector regression, regression forecast model and BP artificial neural network (BPNN). Li et al. [9] implemented a method for chaotic time series of optimized BP neural network based on particle swarm **optimization** (PSO), and the practical application of this method is indicated. Xu et al. [10] presented a short-term traffic forecasting model which combines support vector regression (SVR) model with continuous ant colony **optimization** (SVRCACO) to forecast traffic flow. These methods improve the accuracy of traffic flow forecast to a certain extent.

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Unlike the methods mentioned above, which solve the STLS problem in its original for- mulation (4), the proposed methods solve an equivalent **optimization** problem, derived by analytically minimizing (4) over p , for a xed X . A similar approach, using a dierent parameterization of the structure, is taken in the derivation of the so-called constrained total **least** **squares** (CTLS) problem [17]. However, Reference [17] is restricted to univariate prob- lems and does not use the best **optimization** **techniques** in terms of computational eciency and robustness (very good initial estimates are needed). Another STLS problem formulation is based on the Riemannian singular value decomposition [18], where the derived equivalent problem is interpreted as a non-linear singular value decomposition problem.

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The next-generation wireless networks are expected to produce broadband transmission services like voice, internet browsing, video conference, etc. With numerous Quality of Service (Quos) necessities. Multicast service over wireless networks is a very important and difficult goal destined to several transmission applications like audio/video clips, Mobile TV and interactive game There are 2 key traffics, namely, unit forged traffics and multicast traffics, in wireless transmission communications. Current studies principally target unit-cast traffics. particularly, dynamic resource allocation has been known together of the foremost economical **techniques** to realize higher Quos and better system spectral potency in uncast wireless networks. moreover, a lot of attention is paid to the uncast OFDM systems. Orthogonal Frequency

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From (20) we can conclude that the optimal value, if it exists, of problem (7) is bounded be- low by the optimal value, if it exists, of the one given in (21). Our strategy is to demonstrate that **optimization** problem (21) admits a solution, and we shall furnish a feasible solution of (7) that achieves a value of the objective function that is equal to the optimal value of the problem (21). This will solve (7).

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Remark 12 Corollary 11 shows that distributed learning with the **least** **squares** regulariza- tion scheme in a RKHS can achieve the optimal learning rates in expectation, provided that m satisfies the restriction (13). It should be pointed out that our error analysis is carried out under regularity condition (9) with 1/2 < r ≤ 1 while the work in (Zhang et al., 2015) focused on the case with r = 1/2. When r approaches 1/2, the number m of local proces- sors under the restriction (13) reduces to 1, which corresponds to the non-distributed case. In our follow-up work, we will consider to relax the restriction (13) in a semi-supervised learning framework by using additional unlabelled data, as done in (Caponnetto and Yao, 2010). The main contribution of our analysis for distributed learning in this paper is to remove an eigenfunction assumption in (Zhang et al., 2015) by using a novel second order decomposition for a difference of operator inverses.

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Even though the resulting estimates are not sparse, prediction accuracy is improved by shrinking the coefficients, and the computational issues with high-dimensional robust estimators are overcome due to the regularization. Another possible choice for the penalty function is the smoothly clipped absolute deviation penalty (SCAD) proposed by Fan and Li (2001). It sat- isfies the mathematical conditions for sparsity but results in a more difficult **optimization** problem than the lasso. Still, a robust version of SCAD can be obtained by optimizing the associated objective function over trimmed samples, instead of over the full sample.

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the first ten PLS factors, for both the factors and the responses. Notice that the first five PLS factors ac- count for almost all of the variation in the responses, with the fifth factor accounting for a sizable proportion. This gives a strong indication that five PLS factors are appropriate for modeling the five component amounts. The cross-validation analysis confirms this: although the model with nine PLS factors achieves the absolute minimum predicted residual sum of **squares** (PRESS), it is insignificantly better than the model with only five factors.

Theory of errors and **least** **squares** adjustment is an important subject within the geomatics programme o¤ered at KTH. This is due to the fact that surveying and mapping (or production of spatial data) often requires mathematical processing of measurement data. Furthermore, the general methodology of spatial data processing is essentially the same as that for data processing in other science and engineering …elds, even though data collection procedures and data types can be di¤erent. Theory of errors is related to and comparable with what is called estimation theory used in automatic control and signal processing. Therefore, studying theory of errors can be helpful for solving general data processing problems in other scienti…c and engineering …elds.

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The **least** **squares** method, a fundamental piece of knowledge for students of all scientific tracks, is often introduced considering the simple linear regression with only two parameters to be determined. However, the availability of ever more large data sets prompts even undergraduate students to a sounder and wider knowledge of linear regression. Here, we have used the linear algebra formal- ism to compact the main results of the **least** **squares** method, encompassing ordi- nary and weighted **least** **squares**, goodness of fit indicators, and eventually a basic equation of re-sampling, which could be used to stimulate interested students in an even broader knowledge of data analysis. The compactness of the equations reported above allow their introduction at the undergraduate level, provided that basic linear algebra has been previously introduced.

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RLScore is implemented as a Python module that depends on NumPy (van der Walt et al., 2011) for basic data structures and linear algebra, SciPy (Jones et al., 2001–) for sparse matrices and **optimization** methods, and Cython (Behnel et al., 2011) for implementing low-level routines in C-language. The aim of the software is to provide high quality im- plementations of algorithms developed by the authors that combine efficient training with automated performance evaluation and model selection methods.

Least squares means, least squares deviations of sire groups from the means, least squares differences due to birthrank and sex, and partial regression coefficients for the characteristi[r]

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In this paper we obtain analogs to (1.4) and (1.6) for power series f defined on the open interval ( − 1, 1). Such functions f (especially without closed forms) arise, for ex- ample, in solutions to diﬀerential equations. It will be necessary to first extend the above **least** **squares** polynomial. This is accomplished in Section 2 by replacing the integral in (1.3) by a sum in terms of Maclaurin coeﬃcients of f and inversion coeﬃcients of expan- sions of monomials as linear combinations of ultraspherical polynomials. After proving key properties of the latter coe ﬃ cients in Section 3, we then derive uniform or pointwise estimates to f with these **least** **squares** extensions.

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We show that the well-known least squares LS solution of an overdetermined system of linear equations is a convex combination of all the non-trivial solutions weighed by the squares of t[r]

This paper continues as follows. In the second part, quadratic surfaces and the theory of **least** **squares** will be discussed. In the third part, the **least** square planes, suggested algorithms, and evaluation parameters will be proposed. The fourth section compares the results of implementation by other methods. In the last section, conclusions and recommendations will be presented.

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Maximum Likelihood and Least Squares Geometry of Least Squares Sequential Learning Regularized Least Squares Multiple Outputs Loss Function for Regression The Bias-Variance Decomposition[r]

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In our work, we explore an alternative “local” approach to- wards feature preserving deformation. Our work mainly builds upon the 2d image deformation technique introduced by Schae- fer et al. [Schaefer et al. 2006], which solves for the optimal rigid transformation that maps a set of weighted point handles to their deformed positions, at each image domain point. The image do- main point is than transformed by the optimal rigid transformation at that point. Because an optimal transformation is calculated for every point to be deformed, it is called Moving **Least** Square. The work-flow of deforming a model using our method is as follow- ing. The user first defines a set of point handles around the model that he wants to deform. He can then drag the point handles around, and the model will deform in a smooth and realistic manner such that the region close to a handle will move to the new position of the handle.

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Despite their statistical virtues and all their nice axiomatic properties as spectral risk measures and concave distortion risk measures, extremiles have an apparent limitation when applied to distributions with infinite mean. This should not be considered to be a serious disadvantage however, at **least** in financial and actuarial applications, since the definition of a coherent risk measure for distributions with an infinite first moment is not clear, see the discussion in Section 3 of Neˇslehov´ a et al. (2006). Whether operational risk models in which losses have an infinite mean make sense in the first place has also recently been questioned by Cirillo and Taleb (2016).

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Apply finally Theorem 2.3.9 in de Haan and Ferreira 2006, p.48 to construct by induction an increasing sequence ptp q tending to infinity such that for any positive integer p:.. rn q as [r]

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