Influence function of the error rate of classification based on clustering

Conference (2009, May 19)

Cluster analysis may be performed when one wishes to group similar objects into a given number of clusters. Several algorithms are available in order to construct these clusters. In this talk, focus will ... [more ▼]

Cluster analysis may be performed when one wishes to group similar objects into a given number of clusters. Several algorithms are available in order to construct these clusters. In this talk, focus will be on two particular cases of the generalized k-means algorithm : the classical k-means procedure as well as the k-medoids algorithm, while the data of interest are assumed to come from an underlying population consisting of a mixture of two groups. Among the outputs of these clustering techniques, a classification rule is provided in order to classify the objects into one of the clusters. When classification is the main objective of the statistical analysis, performance is often measured by means of an error rate. Two types of error rates can be computed: a theoretical one and a more empirical one. The first one can be written as ER(F, Fm) where F is the distribution of the training sample used to set up the classification rule and Fm (model distribution) is the distribution under which the quality of the rule is assessed (via a test sample). The empirical error rate corresponds to ER(F, F), meaning that the classification rule is tested on the same sample as the one used to set up the rule. This talk will present the results concerning the theoretical error rate. In case there are some outliers in the data, the classification rule may be corrupted. Even if it is evaluated at the model distribution, the theoretical error rate may then be contaminated. To measure the robustness of classification based on clustering, influence functions have been computed. Similar results as those derived by Croux et al (2008) and Croux et al (2008) in discriminant analysis were observed. More specifically, under optimality (which happens when the model distribution is FN = 0.5 N(μ1, σ) + 0.5 N(μ2, σ), Qiu and Tamhane 2007), the contaminated error rate can never be smaller than the optimal value, resulting in a first order influence function identically equal to 0. Second order influence functions need then to be computed. When the optimality does not hold, the first order influence function of the theoretical error rate does not vanish anymore and shows that contamination may improve the error rate achieved under the non-optimal model. The first and, when required, second order influence functions of the theoretical error rate are useful in their own right to compare the robustness of the 2-means and 2-medoids classification procedures. They have also other applications. For example, they may be used to derive diagnostic tools in order to detect observations having an unduly large influence on the error rate. Also, under optimality, the second order influence function of the theoretical error rate can yield asymptotic relative classification efficiencies. [less ▲]

The influence function of the TCLUST robust clustering procedure

in Advances in Data Analysis and Classification [=ADAC] (2012), 6(2), 107-130

The TCLUST procedure performs robust clustering with the aim of finding clusters with different scatter structures and proportions. An Eigenvalue Ratio constraint is considered by TCLUST in order to avoid ... [more ▼]

The TCLUST procedure performs robust clustering with the aim of finding clusters with different scatter structures and proportions. An Eigenvalue Ratio constraint is considered by TCLUST in order to avoid finding spurious clusters. In order to guarantee the robustness of the method against the presence of outliers and background noise, the method allows for trimming of a given proportion of observations self determined by the data. This article studies robustness properties of the TCLUST procedure by means of the influence function, obtaining a robustness behavior close to that of the trimmed k-means. [less ▲]

Influence Lianol Solapro on sow colostrums production

in 21 Inter. Pig Vet Society Congress (2010)

Influence of 2D and 3D images on performance and time estimation in minimal invasive surgery

in Ergonomics (2009), 52(11), 13421349

This study aimed to evaluate the impact of 2D and 3D images on time performance and time estimation during a surgical motor task. 60 subjects without any surgical experience (nurses) and 20 expert ... [more ▼]

This study aimed to evaluate the impact of 2D and 3D images on time performance and time estimation during a surgical motor task. 60 subjects without any surgical experience (nurses) and 20 expert surgeons performed a fine surgical task with a new laparoscopic technology (da Vinci robotic system). The 80 subjects were divided into two groups, one using 3D view option and another using 2D view option. We measured time performance and asked subjects to verbally estimate their time performance. Our results showed faster performance in 3D than in 2D view for novice subjects while the performance in 2D and 3D was similar in the expert group. We obtained a significant interaction between time performance and time evaluation: in 2D condition, all subjects accurately estimated their time performance while they overestimated it in the 3D condition. Our results emphasize the role of 3D in improving performance and the contradictory feeling about time evaluation in 2D and 3D. This finding is discussed in regard with the retrospective paradigm and suggests that 2D and 3D images are differently processed and memorised. [less ▲]

Influence of a blend of fructo-oligosaccharides and sugar beet fiber on nutrient digestibility and plasma metabolites concentrations in healthy Beagles

in American Journal of Veterinary Research (1997), 58

Objective-To evaluate effects of a blend of fructo-oligosaccharides and sugar beet fiber (4:1) at 3 incorporation rates on nutrient digestibility and plasma glucose, insulin, alpha-aminonitrogen, urea ... [more ▼]

Objective-To evaluate effects of a blend of fructo-oligosaccharides and sugar beet fiber (4:1) at 3 incorporation rates on nutrient digestibility and plasma glucose, insulin, alpha-aminonitrogen, urea, cholesterol, and triglycerides concentrations measured weekly in nonfed dogs and during a 360-minute period after a meal. Animals-8 castrated 1 to 1.4-year-old young adult male Beagles weighing 10.0 to 13.5 kg. Procedure-Diets containing 2 incorporation rates of a blend of fructo-oligosaccharides and sugar beet fiber (5 and 10% on a dry matter basis [diets B and C, respectively]) were compared with a control diet without additional fiber (diet A). The 3 diets were evaluated for ability to modify digestibility of dry and organic matter, protein, fat, and ash and for effects on plasma glucose, insulin, alpha-aminonitrogen, urea, cholesterol, and triglycerides concentrations. Each diet was fed for 6 weeks; plasma samples were collected weekly before feeding and after feeding on the last day of the period, During 1 week at the end of the 6-week period, dogs were kept in metabolic cages. Each period of the block was followed by a 4-week washout period. Results-Incorporating the blend of fructo-oiigosaccharides and sugar beet fiber in the diet was associated with greater passage of wet feces (diets B and C) and lower protein digestibility (diet C). Postprandial glucose (diet C), urea (diets B and C) and triglyceride (diets B and C) concentrations were significantly (P < 0.01) decreased. Weekly preprandial measurements were characterized by decreased urea (diets B and C), cholesterol (diet C), and triglycerides (diets B and C) concentrations (P < 0.001). Conclusion-Chronic consumption of fermentable fiber is associated with mildly decreased protein digestibility and with metabolic effects in nonfed or fed dogs. Clinical Relevance-A blend of fructo-oligosaccharides and sugar beet fiber should he tested as a dietary aid for treatment of chronic diseases, such as diabetes mellitus or hyperlipidemia, in dogs. [less ▲]

Influence of a hormonal preparation containing glucocorticoids (dexamethasone esters), progestagen (chlormadinone acetate) and oestrogen (ethynyl oestradiol) on testosterone, insulin-like growth factor-1 (IGF-1), IGF binding proteins and spermatogenic cells in finishing bulls.

in Animal Production (1994), 59

Influence of a medication history and a pharmaceutical opinion at admission of geriatric hospitalized patients on inappropriate drug prescribing

in International Journal of Clinical Pharmacy (2011, April), 33(2), 432-433

Influence of a nonlinear reference temperature profile on oscillatory Benard-Marangoni convection.

in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2003), 68(6 Pt 2), 066310

We analyze oscillatory instabilities in a fluid layer of infinite horizontal extent, heated from above or cooled from below, taking into account the nonlinearity of the reference temperature profile ... [more ▼]

We analyze oscillatory instabilities in a fluid layer of infinite horizontal extent, heated from above or cooled from below, taking into account the nonlinearity of the reference temperature profile during the transient state of heat conduction. The linear stability analysis shows that a nonlinear reference temperature profile can have a strong effect on the system, either stabilizing or destabilizing, depending on the relative importance of buoyancy and surface tension forces. For the nonlinear analysis we use a Galerkin-Eckhaus method leading to a finite set of amplitude equations. In the two-dimensional (2D) case, we show the solution of these amplitude equations are standing waves. [less ▲]

Influence of a short time specific strength training on iso-inertial performances

in Abstract Book of the 4th International Conference on Strength Training (Serres, Greece) (2004, November)

Influence of a water purification unit on the contamination level of salmonella in outcoming water and sludge

in Annales de Médecine Vétérinaire (2002), 146(5), 303-310

Foodborne pathogens occasionally harboured in the gastro-intestinal tract of some domestic animals may be retrieved in slaughterhouses waste water and in sludge of water purification units. Salmonella ... [more ▼]

Foodborne pathogens occasionally harboured in the gastro-intestinal tract of some domestic animals may be retrieved in slaughterhouses waste water and in sludge of water purification units. Salmonella, athogen common to man and Animals, is often used as a biological risk indicator. The aim of the present study was to assess effectiveness of a recent water purification unit by rapid and semi-quantitative detection of this micro-organism. The water purification unit collects waste water of seven food-processing industries, including a pig slaughterhouse. This latest was the main source of Salmonella contamination with a level of more 103 colony forming unit (CFU) per ml, that was very close to the average level of contamination of total incoming waste water. The unit, whose principle of action is based on biological purification, has permitted a 4 log10 reduction of Salmonella contamination, with a final contamination level of less than 1 CFU/ml. It was observed only a little decrease of contamination levels during the biological treatment steps, in contrast with the one observed during the clarification step. This was due to adsorption of bacteria by material in suspension. Fresh sludge were harboured an average of 102 CFU of Salmonella per gram. In the beginning of December 1999, two sludge piles were let on the ground along a field and sampled microbiologically every month. Seven month later, no Salmonella were recovered from the piles. 309 [less ▲]