scholarly journals Efficient Kernel Selection via Spectral Analysis

2017 ◽  
Author(s):  
Jian Li ◽  
Yong Liu ◽  
Hailun Lin ◽  
Yinliang Yue ◽  
Weiping Wang
Keyword(s):  
Spectral Measure ◽  
Fundamental Problem ◽  
Selection Criterion ◽  
Data Sets ◽  
Maximum Mean Discrepancy ◽  
Generalization Bounds ◽  
Kernel Selection ◽  
Special Cases ◽  
High Computational Efficiency ◽  
High Computational Complexity

Kernel selection is a fundamental problem of kernel methods. Existing measures for kernel selection either provide less theoretical guarantee or have high computational complexity. In this paper, we propose a novel kernel selection criterion based on a newly defined spectral measure of a kernel matrix, with sound theoretical foundation and high computational efficiency. We first show that the spectral measure can be used to derive generalization bounds for some kernel-based algorithms. By minimizing the derived generalization bounds, we propose the kernel selection criterion with spectral measure. Moreover, we demonstrate that the popular minimum graph cut and maximum mean discrepancy are two special cases of the proposed criterion. Experimental results on lots of data sets show that our proposed criterion can not only give the comparable results as the state-of-the-art criterion, but also significantly improve the efficiency.

scholarly journals Feature and Language Selection in Temporal Symbolic Regression for Interpretable Air Quality Modelling

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 76
Author(s):  
Estrella Lucena-Sánchez ◽  
Guido Sciavicco ◽  
Ionel Eduard Stan
Keyword(s):  
Air Quality ◽  
Fundamental Problem ◽  
Multivariate Time Series ◽  
Quality Data ◽  
Data Sets ◽  
Air Quality Modelling ◽  
Regression Problem ◽  
Car Traffic ◽  
Pollutant Concentrations ◽  
Language Selection

Air quality modelling that relates meteorological, car traffic, and pollution data is a fundamental problem, approached in several different ways in the recent literature. In particular, a set of such data sampled at a specific location and during a specific period of time can be seen as a multivariate time series, and modelling the values of the pollutant concentrations can be seen as a multivariate temporal regression problem. In this paper, we propose a new method for symbolic multivariate temporal regression, and we apply it to several data sets that contain real air quality data from the city of Wrocław (Poland). Our experiments show that our approach is superior to classical, especially symbolic, ones, both in statistical performances and the interpretability of the results.

The Circular Cylinder With a Band of Uniform Pressure on a Finite Length of the Surface

1941 ◽  
Vol 8 (3) ◽  
pp. A97-A104 ◽  
Author(s):  
M. V. Barton
Keyword(s):  
Circular Cylinder ◽  
Finite Length ◽  
Infinite Series ◽  
Fundamental Problem ◽  
The Other ◽  
Complete Picture ◽  
Uniform Pressure ◽  
Uniform Tension ◽  
Special Cases ◽  
Stress And Deformation

Abstract The solution to the fundamental problem of a cylinder with a uniform pressure over one half its length and a uniform tension on the other half is found by using the Papcovitch-Neuber solution to the general equations. In this paper, the results, given analytically in terms of infinite-series expressions, are exhibited as curves giving a complete picture of the stress and deformation. The case of a cylinder with a band of uniform pressure of any length, with the exception of very small ones, is then solved by the method of superposition. The stresses and displacements are evaluated for the special cases of a cylinder with a uniform pressure load of 1 diam and 1/2 diam in length. The problem of a cylinder heated over one half its length is solved by the same means.

scholarly journals A New Family of Extended Lindley Models: Properties, Estimation and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2146
Author(s):  
Abdulrahman Abouammoh ◽  
Mohamed Kayid
Keyword(s):  
Power Distribution ◽  
Data Sets ◽  
Simulation Studies ◽  
Biological Engineering ◽  
Unified Approach ◽  
Right Censored Data ◽  
New Family ◽  
Special Cases ◽  
Life Distributions ◽  
And Behavior

There are many proposed life models in the literature, based on Lindley distribution. In this paper, a unified approach is used to derive a general form for these life models. The present generalization greatly simplifies the derivation of new life distributions and significantly increases the number of lifetime models available for testing and fitting life data sets for biological, engineering, and other fields of life. Several distributions based on the disparity of the underlying weights of Lindley are shown to be special cases of these forms. Some basic statistical properties and reliability functions are derived for the general forms. In addition, comparisons among various forms are investigated. Moreover, the power distribution of this generalization has also been considered. Maximum likelihood estimator for complete and right-censored data has been discussed and in simulation studies, the efficiency and behavior of it have been investigated. Finally, the proposed models have been fit to some data sets.

A Feature-Based Approach to Market Segmentation via Overlapping K-Centroids Clustering

1997 ◽  
Vol 34 (3) ◽  
pp. 370-377 ◽  
Author(s):  
Anil Chaturvedi ◽  
J. Douglas Carroll ◽  
Paul E. Green ◽  
John A. Rotondo
Keyword(s):  
Market Segmentation ◽  
Marketing Research ◽  
Large Data ◽  
Large Data Sets ◽  
Data Sets ◽  
Suggested Procedure ◽  
Overlapping Clusters ◽  
Special Cases ◽  
Feature Based ◽  
Distinct Partition

Nonhierarchical partitioning techniques are used widely in many marketing applications, particularly in the clustering of consumers, as opposed to brands. These techniques can be extremely sensitive to the presence of outliers, which might result in misinterpretations of the segments, and subsequently to inferring incorrect relationships of segments to independently defined, actionable variables. The authors propose a general approach to market segmentation based on the concept of overlapping clusters (Shepard and Arabie 1979), wherein each pattern of overlap can be interpreted as a distinct partition. Both K-means and K-medians clustering procedures are special cases of the proposed approach. The suggested procedure can handle relatively large data sets (e.g., 2000 entities), is easily programmable, and hence can be gainfully employed in marketing research.

scholarly journals Enhancing Both Efficiency and Representational Capability of Isomap by Extensive Landmark Selection

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Dong Liang ◽  
Chen Qiao ◽  
Zongben Xu
Keyword(s):  
Manifold Learning ◽  
Computational Efficiency ◽  
New Method ◽  
Data Sets ◽  
Learning Approaches ◽  
Real World Data ◽  
Efficiency Property ◽  
Data Points ◽  
Low Dimensional ◽  
High Computational Efficiency

The problems of improving computational efficiency and extending representational capability are the two hottest topics in approaches of global manifold learning. In this paper, a new method called extensive landmark Isomap (EL-Isomap) is presented, addressing both topics simultaneously. On one hand, originated from landmark Isomap (L-Isomap), which is known for its high computational efficiency property, EL-Isomap also possesses high computational efficiency through utilizing a small set of landmarks to embed all data points. On the other hand, EL-Isomap significantly extends the representational capability of L-Isomap and other global manifold learning approaches by utilizing only an available subset from the whole landmark set instead of all to embed each point. Particularly, compared with other manifold learning approaches, the data manifolds with intrinsic low-dimensional concave topologies and essential loops can be unwrapped by the new method more successfully, which are shown by simulation results on a series of synthetic and real-world data sets. Moreover, the accuracy, robustness, and computational complexity of EL-Isomap are analyzed in this paper, and the relation between EL-Isomap and L-Isomap is also discussed theoretically.

scholarly journals INCOMPLETENESS IN THE FINITE DOMAIN

2017 ◽  
Vol 23 (4) ◽  
pp. 405-441 ◽  
Author(s):  
PAVEL PUDLÁK
Keyword(s):  
Computational Complexity ◽  
Proof Complexity ◽  
Finite Domain ◽  
Semantic Concept ◽  
Syntactic Complexity ◽  
Special Cases ◽  
Incompleteness Theorems ◽  
High Computational Complexity

AbstractMotivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyondNP≠coNP. These conjectures formally connect computational complexity with the difficulty of proving some sentences, which means that high computational complexity of a problem associated with a sentence implies that the sentence is not provable in a weak theory, or requires a long proof. Another reason for putting forward these conjectures is that some results in proof complexity seem to be special cases of such general statements and we want to formalize and fully understand these statements. Roughly speaking, we are trying to connect syntactic complexity, by which we mean the complexity of sentences and strengths of the theories in which they are provable, with the semantic concept of complexity of the computational problems represented by these sentences.We have introduced the most fundamental conjectures in our earlier works [27, 33–35]. Our aim in this article is to present them in a more systematic way, along with several new conjectures, and prove new connections between them and some other statements studied before.

scholarly journals Identifying a Dynamic Model for a GE Frame 7 Gas Turbine

1994 ◽  
Author(s):  
Howard Kaufman ◽  
R. Ravi
Keyword(s):  
Gas Turbine ◽  
Linear Models ◽  
Controller Design ◽  
Guide Vane ◽  
Selection Criterion ◽  
Inlet Guide Vane ◽  
Data Sets ◽  
Similar Work ◽  
Identification Techniques ◽  
Vane Angle

Several tests were conducted on a GE Frame 7 gas turbine to determine its dynamic characteristics. The objective is to obtain a model that can be used for controller design. The tests consisted of adding sequences of square waves to the two inputs — the fuel reference and the inlet guide vane angle reference — and recording the inputs and the outputs. This method of exciting the system afforded us with a way of separating the data sets into two categories, the first, in which the fuel reference was changed, and the second, in which the guide vane angle reference was changed. Least-squares system identification techniques were used to obtain linear models using a selection criterion that was a measure of how well a model fit both the sets of data. This brought in a measure of robustness to the models thus making them ideal for use in controller design. This paper summarizes the results from these tests, contains plots that show how well the linear models are able to fit the recorded data, and finally, provides some recommendations for others doing similar work.

scholarly journals An Inferential Aptness of a Weibull Generated Distribution and Application

2021 ◽  
Author(s):  
Brijesh P. Singh ◽  
Utpal Dhar Das
Keyword(s):  
Weibull Distribution ◽  
Continuous Distribution ◽  
Selection Criterion ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Single Parameter ◽  
Parameter Distribution ◽  
Data Sets ◽  
Lifetime Distributions ◽  
Limiting Behavior

In this article an attempt has been made to develop a flexible single parameter continuous distribution using Weibull distribution. The Weibull distribution is most widely used lifetime distributions in both medical and engineering sectors. The exponential and Rayleigh distribution is particular case of Weibull distribution. Here in this study we use these two distributions for developing a new distribution. Important statistical properties of the proposed distribution is discussed such as moments, moment generating and characteristic function. Various entropy measures like Rényi, Shannon and cumulative entropy are also derived. The kthkt⁢h order statistics of pdf and cdf also obtained. The properties of hazard function and their limiting behavior is discussed. The maximum likelihood estimate of the parameter is obtained that is not in closed form, thus iteration procedure is used to obtain the estimate. Simulation study has been done for different sample size and MLE, MSE, Bias for the parameter λλ has been observed. Some real data sets are used to check the suitability of model over some other competent distributions for some data sets from medical and engineering science. In the tail area, the proposed model works better. Various model selection criterion such as -2LL, AIC, AICc, BIC, K-S and A-D test suggests that the proposed distribution perform better than other competent distributions and thus considered this as an alternative distribution. The proposed single parameter distribution is found more flexible as compare to some other two parameter complicated distributions for the data sets considered in the present study.

scholarly journals METHOD FOR ASSESSING THE SYMMETRY OF OBJECTS ON DIGITAL BINARY IMAGES BASED ON FOURIER DESCRIPTOR

2019 ◽  
Vol XLII-2/W12 ◽  
pp. 143-148
Author(s):  
L. Mestetskiy ◽  
A. Zhuravskaya
Keyword(s):  
Symmetry Axis ◽  
Fourier Descriptor ◽  
Earth Remote Sensing ◽  
Discrete Object ◽  
Binary Images ◽  
Special Cases ◽  
Exact Symmetry ◽  
Measure Of Asymmetry ◽  
Axis Of Symmetry ◽  
High Computational Complexity

<p><strong>Abstract.</strong> In this paper we solve the problem of finding the symmetry axis of the object in a digital binary image. A new axial symmetry criterion is formulated for a connected discrete object. The problem of determining the symmetry measure and finding the symmetry axes arises in a variety of applications. In discrete images, exact symmetry is possible only in special cases. The disadvantage of the existing methods solving this problem is the high computational complexity. To improve computational efficiency, it is proposed to use the so-called Fourier descriptor. A new method for estimating the asymmetry of a discrete silhouette is proposed. The described algorithm for calculating the measure of asymmetry and determining the axis of symmetry is quadratic by the number of contour points. Methods for reducing the volume of calculations using a convex hull and taking into account the values of the modules of Fourier coefficients are proposed. Computational experiments are conducted with silhouettes of aircraft extracted from earth remote sensing images. The reliability of the described solution is established.</p>

Estimation of the earthquake recurrence parameters for unequal observation periods for different magnitudes

1980 ◽  
Vol 70 (4) ◽  
pp. 1337-1346
Author(s):  
Dieter H. Weichert
Keyword(s):  
Least Squares ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Chi Square ◽  
Earthquake Parameters ◽  
Large Numbers ◽  
Special Cases ◽  
Weighting Methods ◽  
Asymptotic Forms

abstract Maximum likelihood estimation of the earthquake parameters No and β in the relation N = No exp (−βm) is extended to the case of events grouped in magnitude with each group observed over individual time periods. Asymptotic forms of the equation for β reduce to the estimators given for different special cases by Aki (1965), Utsu (1965, 1966), and Page (1968). The estimates of β are only approximately chi-square distributed. For sufficiently large numbers of events, they can be estimated from the curvature of the log-likelihood function. Sample calculations for three earthquake source zones in western Canada indicate that for well-constrained data sets, the often-used, least-squares estimation procedures lead to compatible results, but for less well-defined data sets, the effect of subjective plotting and weighting methods used for least-squares fitting leads to appreciably different parameters.

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