Semidefinite Programming-Based Method for Implementing Linear Fitting to Interval-Valued Data

2011 ◽  
Vol 1 (3) ◽  
pp. 32-46 ◽  
Author(s):  
Minghuang Li ◽  
Fusheng Yu
Keyword(s):  
Lower Bound ◽  
Semidefinite Programming ◽  
Large Scale ◽  
Experimental Studies ◽  
Optimal Solution ◽  
Data Set ◽  
Linear Fitting ◽  
Optimal Value ◽  
Fitting Model ◽  
Interval Valued

Building a linear fitting model for a given interval-valued data set is challenging since the minimization of the residue function leads to a huge combinatorial problem. To overcome such a difficulty, this article proposes a new semidefinite programming-based method for implementing linear fitting to interval-valued data. First, the fitting model is cast to a problem of quadratically constrained quadratic programming (QCQP), and then two formulae are derived to develop the lower bound on the optimal value of the nonconvex QCQP by semidefinite relaxation and Lagrangian relaxation. In many cases, this method can solve the fitting problem by giving the exact optimal solution. Even though the lower bound is not the optimal value, it is still a good approximation of the global optimal solution. Experimental studies on different fitting problems of different scales demonstrate the good performance and stability of our method. Furthermore, the proposed method performs very well in solving relatively large-scale interval-fitting problems.

Semidefinite Programming-Based Method for Implementing Linear Fitting to Interval-Valued Data

2013 ◽  
pp. 172-187
Author(s):  
Minghuang Li ◽  
Fusheng Yu
Keyword(s):  
Lower Bound ◽  
Semidefinite Programming ◽  
Large Scale ◽  
Experimental Studies ◽  
Optimal Solution ◽  
Combinatorial Problem ◽  
Linear Fitting ◽  
Optimal Value ◽  
Fitting Model ◽  
Interval Valued

Building a linear fitting model for a given interval-valued data set is challenging since the minimization of the residue function leads to a huge combinatorial problem. To overcome such a difficulty, this article proposes a new semidefinite programming-based method for implementing linear fitting to interval-valued data. First, the fitting model is cast to a problem of quadratically constrained quadratic programming (QCQP), and then two formulae are derived to develop the lower bound on the optimal value of the nonconvex QCQP by semidefinite relaxation and Lagrangian relaxation. In many cases, this method can solve the fitting problem by giving the exact optimal solution. Even though the lower bound is not the optimal value, it is still a good approximation of the global optimal solution. Experimental studies on different fitting problems of different scales demonstrate the good performance and stability of our method. Furthermore, the proposed method performs very well in solving relatively large-scale interval-fitting problems.

Semidefinite Programming-Based Method for Implementing Linear Fitting to Interval-Valued Data

2012 ◽  
pp. 297-312
Author(s):  
Minghuang Li ◽  
Fusheng Yu
Keyword(s):  
Lower Bound ◽  
Semidefinite Programming ◽  
Large Scale ◽  
Experimental Studies ◽  
Optimal Solution ◽  
Combinatorial Problem ◽  
Linear Fitting ◽  
Optimal Value ◽  
Fitting Model ◽  
Interval Valued

Building a linear fitting model for a given interval-valued data set is challenging since the minimization of the residue function leads to a huge combinatorial problem. To overcome such a difficulty, this article proposes a new semidefinite programming-based method for implementing linear fitting to interval-valued data. First, the fitting model is cast to a problem of quadratically constrained quadratic programming (QCQP), and then two formulae are derived to develop the lower bound on the optimal value of the nonconvex QCQP by semidefinite relaxation and Lagrangian relaxation. In many cases, this method can solve the fitting problem by giving the exact optimal solution. Even though the lower bound is not the optimal value, it is still a good approximation of the global optimal solution. Experimental studies on different fitting problems of different scales demonstrate the good performance and stability of our method. Furthermore, the proposed method performs very well in solving relatively large-scale interval-fitting problems.

Primary and Referential Horizontal Partitioning Selection Problems

2011 ◽  
pp. 258-286
Author(s):  
Ladjel Bellatreche ◽  
Kamel Boukhalfa ◽  
Pascal Richard
Keyword(s):  
Data Warehouse ◽  
Cost Model ◽  
Experimental Studies ◽  
Optimal Solution ◽  
Hill Climbing ◽  
Data Warehouses ◽  
Data Set ◽  
Primary Fragmentation ◽  
Partition Dimension ◽  
Horizontal Partitioning

Horizontal partitioning has evolved significantly in recent years and widely advocated by the academic and industrial communities. Horizontal Partitioning affects positively query performance, database manageability and availability. Two types of horizontal partitioning are supported: primary and referential. Horizontal fragmentation in the context of relational data warehouses is to partition dimension tables by primary fragmentation then fragmenting the fact table by referential fragmentation. This fragmentation can generate a very large number of fragments which may make the maintenance task very complicated. In this paper, we first focus on the evolution of horizontal partitioning in commercial DBMS motivated by decision support applications. Secondly, we give a formalization of the referential fragmentation schema selection problem in the data warehouse and we study its hardness to select an optimal solution. Due to its high complexity, we develop two algorithms: hill climbing and simulated annealing with several variants to select a near optimal partitioning schema. We present ParAdmin, an advisor tool assisting administrators to use primary and referential partitioning during the physical design of their data warehouses. Finally, extensive experimental studies are conducted using the data set of APB1 benchmark to compare the quality the proposed algorithms using a mathematical cost model. Based on these experiments, some recommendations are given to ensure the well use of horizontal partitioning.

Improved Learning Algorithm Based on Semi-Supervised Support Vector

2011 ◽  
Vol 474-476 ◽  
pp. 1-6
Author(s):  
Guo Xing Peng ◽  
Bei Li
Keyword(s):  
Support Vector Machines ◽  
Lower Bound ◽  
Simulation Analysis ◽  
Learning Algorithm ◽  
Optimal Solution ◽  
Support Vector ◽  
Dual Function ◽  
Data Set ◽  
Vector Machines ◽  
Improved Learning

Improved learning algorithm for branch and bound for semi-supervised support vector machines is proposed, according to the greater difference in the optimal solution in different semi-supervised support vector machines for the same data set caused by the local optimization. The lower bound of node in IBBS3VM algorithm is re-defined, which will be pseudo-dual function value as the lower bound of node to avoid the large amount of calculation of 0-1 quadratic programming, reducing the lower bound of each node calculate the time complexity; at the same time, in determining the branch nodes, only based on the credibility of the unlabeled samples without the need to repeatedly carry out the training of support vector machines to enhance the training speed of the algorithm. Simulation analysis shows that IBBS3VM presented in this paper has faster training speed than BBS3VM algorithms, higher precision and stronger robustness than the other semi-supervised support vector machines.

Referential Horizontal Partitioning Selection Problem in Data Warehouses

2009 ◽  
Vol 5 (4) ◽  
pp. 1-23 ◽  
Author(s):  
Ladjel Bellatreche ◽  
Kamel Boukhalfa ◽  
Pascal Richard ◽  
Komla Yamavo Woameno
Keyword(s):  
Data Warehouse ◽  
Cost Model ◽  
Experimental Studies ◽  
Optimal Solution ◽  
Database Systems ◽  
Selection Problem ◽  
Hill Climbing ◽  
Materialized Views ◽  
Data Set ◽  
Horizontal Partitioning

Horizontal Partitioning has been largely adopted by the database community, where it took a significant part in the physical design process. Actually, it is supported by most commercial database systems (DBMS), where a native Data Definition Language for decomposing tables/materialized views using various modes is proposed. In traditional databases, horizontal partitioning has been largely studied, where several fragmentation algorithms were proposed to partition tables in isolation. In the relational data warehouse environment, horizontal partitioning consists in decomposing the whole warehouse schema into sub schemas, where each schema contains fragments of dimension and fact tables. Dimension tables are fragmented using the primary partitioning mode, whereas the fact table is divided using referential mode. In this article, the authors first focus on the evolution of horizontal partitioning in commercial DBMS motivated by decision support applications. Secondly, they give a formalization of the referential fragmentation schema selection problem in the data warehouse and they study its hardness to select an optimal solution. Due to its high complexity, they develop two algorithms: hill climbing and simulated annealing with several variants to select a near optimal partitioning schema. Finally, extensive experimental studies are conducted using the data set of APB1 benchmark to compare the quality the proposed algorithms using a mathematical cost model. Based on these experiments, some recommendations are given to advise database administrator for well using horizontal partitioning.

scholarly journals 1214 Higher Bedroom Temperature Associated With Poorer Sleep: Data From Over 3.75 Million Nights

SLEEP ◽  
2020 ◽  
Vol 43 (Supplement_1) ◽  
pp. A464-A464
Author(s):  
A Raj ◽  
M Ruder ◽  
H M Rus ◽  
L Gahan ◽  
B O’Mullane ◽  
...  
Keyword(s):  
Large Scale ◽  
Sleep Onset ◽  
Experimental Studies ◽  
Sleep Time ◽  
Sleep Onset Latency ◽  
Multilevel Regression ◽  
Time Duration ◽  
Data Set ◽  
Large Scale Data ◽  
Objectively Measured

Abstract Introduction Bedroom temperature can influence nocturnal thermoregulation and sleep. To date, limited, small experimental studies have shown that bedroom temperatures outside the recommended range of 65 and 70°F can negatively impact sleep. However, this association has not been studied in a large-scale data set. Using over 3.75 million nights of objectively measured data, we analyzed the associations between habitual bedroom temperatures and sleep. Methods Over 3.75 million nights of sleep and bedroom temperature data were collected using S+ by ResMed technology from 34,096 Individuals (57% male, 20-90 years, mean age 48.7 +/-14.5 years, all US residents). Multilevel regression analyses were used to analyze associations between bedroom temperature and sleep. A stricter alpha level of 0.001 was used to account for the large number of observations in the dataset. Results Bedroom temperature was above 70°F for 69% of nights, with the average temperature ranging between 68.8 and 76.2°F. For each 1°F increase in bedroom temperature between 60-85°F, sleep efficiency decreased by 0.06%. Likewise, higher bedroom temperatures were linked to shorter Total Sleep Time duration (-0.45 mins/°F), longer Sleep Onset Latency (+0.04 mins/°F), and longer Wake After Sleep Onset (+0.11 mins/°F), all ps<0.001. Conclusion Analyzing data from over 3.75 million nights, we found that many people sleep in a bedroom warmer than the optimal temperature. Further, higher bedroom temperatures - even within the recommended range for optimal sleep - are associated with poorer sleep and higher wakefulness. Bedroom thermostats and cooling options should be considered to achieve optimal sleeping temperature conditions. Support N/A

scholarly journals A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hongwei Jiao ◽  
Yongqiang Chen
Keyword(s):  
Lower Bound ◽  
Optimal Solution ◽  
Global Optimum ◽  
Initial Problem ◽  
Linear Relaxation ◽  
Feasible Region ◽  
Global Optimal Solution ◽  
Optimal Value ◽  
Global Optimal ◽  
Methods Numerical

A new linearizing method is presented for globally solving sum of linear ratios problem with coefficients. By using the linearizing method, linear relaxation programming (LRP) of the sum of linear ratios problem with coefficients is established, which can provide the reliable lower bound of the optimal value of the initial problem. Thus, a branch and bound algorithm for solving the sum of linear ratios problem with coefficients is put forward. By successively partitioning the linear relaxation of the feasible region and solving a series of the LRP, the proposed algorithm is convergent to the global optimal solution of the initial problem. Compared with the known methods, numerical experimental results show that the proposed method has the higher computational efficiency in finding the global optimum of the sum of linear ratios problem with coefficients.

ProGen:Provenance database generator for large-scale data set

2009 ◽  
Vol 28 (11) ◽  
pp. 2737-2740
Author(s):  
Xiao ZHANG ◽  
Shan WANG ◽  
Na LIAN
Keyword(s):  
Large Scale ◽  
Data Set ◽  
Large Scale Data ◽  
Scale Data

Integrative Data Analysis from a Unifying Research Synthesis Perspective

2018 ◽  
Author(s):  
Eun-Young Mun ◽  
Anne E. Ray
Keyword(s):  
Data Analysis ◽  
Large Scale ◽  
Research Synthesis ◽  
Alcohol Intervention ◽  
Data Set ◽  
Integrative Data Analysis ◽  
Level Data ◽  
Model Complex ◽  
Wide Range ◽  
Individual Participant

Integrative data analysis (IDA) is a promising new approach in psychological research and has been well received in the field of alcohol research. This chapter provides a larger unifying research synthesis framework for IDA. Major advantages of IDA of individual participant-level data include better and more flexible ways to examine subgroups, model complex relationships, deal with methodological and clinical heterogeneity, and examine infrequently occurring behaviors. However, between-study heterogeneity in measures, designs, and samples and systematic study-level missing data are significant barriers to IDA and, more broadly, to large-scale research synthesis. Based on the authors’ experience working on the Project INTEGRATE data set, which combined individual participant-level data from 24 independent college brief alcohol intervention studies, it is also recognized that IDA investigations require a wide range of expertise and considerable resources and that some minimum standards for reporting IDA studies may be needed to improve transparency and quality of evidence.

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