Principal Component Analysis by Optimization of Symmetric Functions has no Spurious Local Optima

2020 ◽  
Vol 30 (1) ◽  
pp. 439-463
Author(s):  
Armin Eftekhari ◽  
Raphael A. Hauser
Keyword(s):  
Principal Component Analysis ◽  
Symmetric Functions ◽  
Principal Component ◽  
Component Analysis ◽  
Local Optima

scholarly journals An Analysis of the Fitness Landscape of Travelling Salesman Problem

2016 ◽  
Vol 24 (2) ◽  
pp. 347-384 ◽  
Author(s):  
Mohammad-H. Tayarani-N. ◽  
Adam Prügel-Bennett
Keyword(s):  
Principal Component Analysis ◽  
Fitness Landscape ◽  
Travelling Salesman Problem ◽  
Principal Component ◽  
Component Analysis ◽  
Global Optimum ◽  
Local Optimum ◽  
Travelling Salesman ◽  
Local Optima ◽  
Expected Fitness

The fitness landscape of the travelling salesman problem is investigated for 11 different types of the problem. The types differ in how the distances between cities are generated. Many different properties of the landscape are studied. The properties chosen are all potentially relevant to choosing an appropriate search algorithm. The analysis includes a scaling study of the time to reach a local optimum, the number of local optima, the expected probability of reaching a local optimum as a function of its fitness, the expected fitness found by local search and the best fitness, the probability of reaching a global optimum, the distance between the local optima and the global optimum, the expected fitness as a function of the distance from an optimum, their basins of attraction and a principal component analysis of the local optima. The principal component analysis shows the correlation of the local optima in the component space. We show how the properties of the principal components of the local optima change from one problem type to another.

A German version of the Intermittent Claudication Questionnaire (ICQ): cultural adaptation and validation

VASA ◽  
2012 ◽  
Vol 41 (5) ◽  
pp. 333-342 ◽  
Author(s):  
Kirchberger ◽  
Finger ◽  
Müller-Bühl
Keyword(s):  
Principal Component Analysis ◽  
Intermittent Claudication ◽  
Completion Time ◽  
Short Form ◽  
Principal Component ◽  
Component Analysis ◽  
German Version ◽  
Average Completion Time ◽  
Sf 36 ◽  
Related Quality

Background: The Intermittent Claudication Questionnaire (ICQ) is a short questionnaire for the assessment of health-related quality of life (HRQOL) in patients with intermittent claudication (IC). The objective of this study was to translate the ICQ into German and to investigate the psychometric properties of the German ICQ version in patients with IC. Patients and methods: The original English version was translated using a forward-backward method. The resulting German version was reviewed by the author of the original version and an experienced clinician. Finally, it was tested for clarity with 5 German patients with IC. A sample of 81 patients were administered the German ICQ. The sample consisted of 58.0 % male patients with a median age of 71 years and a median IC duration of 36 months. Test of feasibility included completeness of questionnaires, completion time, and ratings of clarity, length and relevance. Reliability was assessed through a retest in 13 patients at 14 days, and analysis of Cronbach’s alpha for internal consistency. Construct validity was investigated using principal component analysis. Concurrent validity was assessed by correlating the ICQ scores with the Short Form 36 Health Survey (SF-36) as well as clinical measures. Results: The ICQ was completely filled in by 73 subjects (90.1 %) with an average completion time of 6.3 minutes. Cronbach’s alpha coefficient reached 0.75. Intra-class correlation for test-retest reliability was r = 0.88. Principal component analysis resulted in a 3 factor solution. The first factor explained 51.5 of the total variation and all items had loadings of at least 0.65 on it. The ICQ was significantly associated with the SF-36 and treadmill-walking distances whereas no association was found for resting ABPI. Conclusions: The German version of the ICQ demonstrated good feasibility, satisfactory reliability and good validity. Responsiveness should be investigated in further validation studies.

Multifactorial analysis of clinical laboratory signs, the levels of IL-17A, IL-23, IL-33, IL-35, and specific antibodies in the serum of patients with Lyme borreliosis without erythema migrans

2020 ◽  
Vol 4 (11) ◽  
pp. 676-681
Author(s):  
V.V. Sapozhnikova ◽  
◽  
A.L. Bondarenko ◽  
Keyword(s):  
Principal Component Analysis ◽  
Lyme Borreliosis ◽  
Clinical Laboratory ◽  
Acute Infection ◽  
Erythema Migrans ◽  
Principal Component ◽  
Component Analysis ◽  
Control Group ◽  
Multifactorial Analysis ◽  
Specific Antibodies

Aim: to determine the association between clinical laboratory parameters, the production of cytokines (IL-17A, -23, -33, -35), and specific IgM and IgG in the serum of patients with Lyme borreliosis without erythema migrans. Patients and Methods: complete blood count, the concentrations of IL-17A, -23, -33, -35, and the levels of specific IgM and IgG were measured during acute infection and convalescence (n=30). The control group included age- and sex-matched healthy individuals (n=30). Statistical analysis was performed using the StatSoft Statistica v 10.0 software (parametric and non-parametric methods and multifactorial analysis, i.e., principal component analysis). Results: most (80%) patients with Lyme borreliosis without erythema migrans are the people of working age. In most patients, the combination of the specific antibodies against Borrelia afzelii and Borrelia garinii (76.7%) and severe intoxication and inflammatory process (100%) were detected. Moderate and severe disease associated with meningism was diagnosed in 90% and 10%, respectively. The mean duration of hectic period was 8.3±1.27 days. Abnormal ECG was reported in 40% of patients, i.e., conduction abnormalities in 20%, sinus bradycardia in 16.7%,and sinus tachycardia in 3.3%. The clinical laboratory signs of hepatitis without jaundice were identified in 26.7%. During treatment, the significant reduction in band and segmented neutrophil counts as well as the significant increase in platelet count were revealed compared to these parameters at admission. Abnormal cytokine levels (i.e., the increase in IL-17A, -23, -33 and the deficiency of IL-35) were detected. Conclusions: multifactorial analysis has demonstrated that the severity of immunological abnormalities in patients with Lyme borreliosis without erythema migrans is associated with fever, cardiac and liver disorders, the high levels of IL-23 and IL-33, and the lack of IL-35 and specific IgM and IgG. KEYWORDS: tick-borne borreliosis, Lyme disease without erythema migrans, clinical laboratory signs, cytokines, specific antibodies, multifactorial analysis, principal component analysis. FOR CITATION: Sapozhnikova V.V., Bondarenko A.L. Multifactorial analysis of clinical laboratory signs, the levels of IL-17A, IL-23, IL-33, IL-35, and specific antibodies in the serum of patients with Lyme borreliosis without erythema migrans. Russian Medical Inquiry. 2020;4(11):676–681. DOI: 10.32364/2587-6821-2020-4-11-676-681.

Oxypropylation of Brazilian Pine-Fruit Shell Evaluated by Principal Component Analysis

2018 ◽  
Vol 6 (7) ◽  
pp. 715-723 ◽  
Author(s):  
Stephany C. de Rezende ◽  
Jo鉶 A. Pinto ◽  
Isabel P. Fernandes ◽  
Fernanda V. Leimann and Maria-Filomena Barreiro
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis
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