Quality indices for (practical) clustering evaluation

Clustering quality or validation indices allow the evaluation of the quality of clustering in order to support the selection of a specific partition or clustering structure in its natural unsupervised environment, where the real solution is unknown or not available. In this paper, we investigate the use of quality indices mostly based on the concepts of clusters` compactness and separation, for the evaluation of clustering results (partitions in particular). This work intends to offer a general perspective regarding the appropriate use of quality indices for the purpose of clustering evaluation. After presenting some commonly used indices, as well as indices recently proposed in the literature, key issues regarding the practical use of quality indices are addressed. A general methodological approach is presented which considers the identification of appropriate indices thresholds. This general approach is compared with the simple use of quality indices for evaluating a clustering solution.

A study on parallel versus sequential relational fuzzy clustering methods

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

Novos métodos determinísticos para gerar centros iniciais dos grupos no algoritmo fuzzy C-Means e variantes

Data clustering is applied to various fields such as data mining, image processing and pattern recognition technique. Clustering algorithms splits a data set into clusters such that elements within the same cluster have a high degree of similarity, while elements belonging to different clusters have a high degree of dissimilarity. The Fuzzy C-Means Algorithm (FCM) is a fuzzy clustering algorithm most used and discussed in the literature. The performance of the FCM is strongly affected by the selection of the initial centers of the clusters. Therefore, the choice of a good set of initial cluster centers is very important for the performance of the algorithm. However, in FCM, the choice of initial centers is made randomly, making it difficult to find a good set. This paper proposes three new methods to obtain initial cluster centers, deterministically, the FCM algorithm, and can also be used in variants of the FCM. In this work these initialization methods were applied in variant ckMeans.With the proposed methods, we intend to obtain a set of initial centers which are close to the real cluster centers. With these new approaches startup if you want to reduce the number of iterations to converge these algorithms and processing time without affecting the quality of the cluster or even improve the quality in some cases. Accordingly, cluster validation indices were used to measure the quality of the clusters obtained by the modified FCM and ckMeans algorithms with the proposed initialization methods when applied to various data sets

Semi-supervised subspace clustering and applications to neuroscience

Machine learning techniques are used for extracting valuable knowledge from data. Nowa¬days, these techniques are becoming even more important due to the evolution in data ac¬quisition and storage, which is leading to data with different characteristics that must be exploited. Therefore, advances in data collection must be accompanied with advances in machine learning techniques to solve new challenges that might arise, on both academic and real applications. There are several machine learning techniques depending on both data characteristics and purpose. Unsupervised classification or clustering is one of the most known techniques when data lack of supervision (unlabeled data) and the aim is to discover data groups (clusters) according to their similarity. On the other hand, supervised classification needs data with supervision (labeled data) and its aim is to make predictions about labels of new data. The presence of data labels is a very important characteristic that guides not only the learning task but also other related tasks such as validation. When only some of the available data are labeled whereas the others remain unlabeled (partially labeled data), neither clustering nor supervised classification can be used. This scenario, which is becoming common nowadays because of labeling process ignorance or cost, is tackled with semi-supervised learning techniques. This thesis focuses on the branch of semi-supervised learning closest to clustering, i.e., to discover clusters using available labels as support to guide and improve the clustering process. Another important data characteristic, different from the presence of data labels, is the relevance or not of data features. Data are characterized by features, but it is possible that not all of them are relevant, or equally relevant, for the learning process. A recent clustering tendency, related to data relevance and called subspace clustering, claims that different clusters might be described by different feature subsets. This differs from traditional solutions to data relevance problem, where a single feature subset (usually the complete set of original features) is found and used to perform the clustering process. The proximity of this work to clustering leads to the first goal of this thesis. As commented above, clustering validation is a difficult task due to the absence of data labels. Although there are many indices that can be used to assess the quality of clustering solutions, these validations depend on clustering algorithms and data characteristics. Hence, in the first goal three known clustering algorithms are used to cluster data with outliers and noise, to critically study how some of the most known validation indices behave. The main goal of this work is however to combine semi-supervised clustering with subspace clustering to obtain clustering solutions that can be correctly validated by using either known indices or expert opinions. Two different algorithms are proposed from different points of view to discover clusters characterized by different subspaces. For the first algorithm, available data labels are used for searching for subspaces firstly, before searching for clusters. This algorithm assigns each instance to only one cluster (hard clustering) and is based on mapping known labels to subspaces using supervised classification techniques. Subspaces are then used to find clusters using traditional clustering techniques. The second algorithm uses available data labels to search for subspaces and clusters at the same time in an iterative process. This algorithm assigns each instance to each cluster based on a membership probability (soft clustering) and is based on integrating known labels and the search for subspaces into a model-based clustering approach. The different proposals are tested using different real and synthetic databases, and comparisons to other methods are also included when appropriate. Finally, as an example of real and current application, different machine learning tech¬niques, including one of the proposals of this work (the most sophisticated one) are applied to a task of one of the most challenging biological problems nowadays, the human brain model¬ing. Specifically, expert neuroscientists do not agree with a neuron classification for the brain cortex, which makes impossible not only any modeling attempt but also the day-to-day work without a common way to name neurons. Therefore, machine learning techniques may help to get an accepted solution to this problem, which can be an important milestone for future research in neuroscience. Resumen Las técnicas de aprendizaje automático se usan para extraer información valiosa de datos. Hoy en día, la importancia de estas técnicas está siendo incluso mayor, debido a que la evolución en la adquisición y almacenamiento de datos está llevando a datos con diferentes características que deben ser explotadas. Por lo tanto, los avances en la recolección de datos deben ir ligados a avances en las técnicas de aprendizaje automático para resolver nuevos retos que pueden aparecer, tanto en aplicaciones académicas como reales. Existen varias técnicas de aprendizaje automático dependiendo de las características de los datos y del propósito. La clasificación no supervisada o clustering es una de las técnicas más conocidas cuando los datos carecen de supervisión (datos sin etiqueta), siendo el objetivo descubrir nuevos grupos (agrupaciones) dependiendo de la similitud de los datos. Por otra parte, la clasificación supervisada necesita datos con supervisión (datos etiquetados) y su objetivo es realizar predicciones sobre las etiquetas de nuevos datos. La presencia de las etiquetas es una característica muy importante que guía no solo el aprendizaje sino también otras tareas relacionadas como la validación. Cuando solo algunos de los datos disponibles están etiquetados, mientras que el resto permanece sin etiqueta (datos parcialmente etiquetados), ni el clustering ni la clasificación supervisada se pueden utilizar. Este escenario, que está llegando a ser común hoy en día debido a la ignorancia o el coste del proceso de etiquetado, es abordado utilizando técnicas de aprendizaje semi-supervisadas. Esta tesis trata la rama del aprendizaje semi-supervisado más cercana al clustering, es decir, descubrir agrupaciones utilizando las etiquetas disponibles como apoyo para guiar y mejorar el proceso de clustering. Otra característica importante de los datos, distinta de la presencia de etiquetas, es la relevancia o no de los atributos de los datos. Los datos se caracterizan por atributos, pero es posible que no todos ellos sean relevantes, o igualmente relevantes, para el proceso de aprendizaje. Una tendencia reciente en clustering, relacionada con la relevancia de los datos y llamada clustering en subespacios, afirma que agrupaciones diferentes pueden estar descritas por subconjuntos de atributos diferentes. Esto difiere de las soluciones tradicionales para el problema de la relevancia de los datos, en las que se busca un único subconjunto de atributos (normalmente el conjunto original de atributos) y se utiliza para realizar el proceso de clustering. La cercanía de este trabajo con el clustering lleva al primer objetivo de la tesis. Como se ha comentado previamente, la validación en clustering es una tarea difícil debido a la ausencia de etiquetas. Aunque existen muchos índices que pueden usarse para evaluar la calidad de las soluciones de clustering, estas validaciones dependen de los algoritmos de clustering utilizados y de las características de los datos. Por lo tanto, en el primer objetivo tres conocidos algoritmos se usan para agrupar datos con valores atípicos y ruido para estudiar de forma crítica cómo se comportan algunos de los índices de validación más conocidos. El objetivo principal de este trabajo sin embargo es combinar clustering semi-supervisado con clustering en subespacios para obtener soluciones de clustering que puedan ser validadas de forma correcta utilizando índices conocidos u opiniones expertas. Se proponen dos algoritmos desde dos puntos de vista diferentes para descubrir agrupaciones caracterizadas por diferentes subespacios. Para el primer algoritmo, las etiquetas disponibles se usan para bus¬car en primer lugar los subespacios antes de buscar las agrupaciones. Este algoritmo asigna cada instancia a un único cluster (hard clustering) y se basa en mapear las etiquetas cono-cidas a subespacios utilizando técnicas de clasificación supervisada. El segundo algoritmo utiliza las etiquetas disponibles para buscar de forma simultánea los subespacios y las agru¬paciones en un proceso iterativo. Este algoritmo asigna cada instancia a cada cluster con una probabilidad de pertenencia (soft clustering) y se basa en integrar las etiquetas conocidas y la búsqueda en subespacios dentro de clustering basado en modelos. Las propuestas son probadas utilizando diferentes bases de datos reales y sintéticas, incluyendo comparaciones con otros métodos cuando resulten apropiadas. Finalmente, a modo de ejemplo de una aplicación real y actual, se aplican diferentes técnicas de aprendizaje automático, incluyendo una de las propuestas de este trabajo (la más sofisticada) a una tarea de uno de los problemas biológicos más desafiantes hoy en día, el modelado del cerebro humano. Específicamente, expertos neurocientíficos no se ponen de acuerdo en una clasificación de neuronas para la corteza cerebral, lo que imposibilita no sólo cualquier intento de modelado sino también el trabajo del día a día al no tener una forma estándar de llamar a las neuronas. Por lo tanto, las técnicas de aprendizaje automático pueden ayudar a conseguir una solución aceptada para este problema, lo cual puede ser un importante hito para investigaciones futuras en neurociencia.

The WOMAC knee and hip osteoarthritis indices: Development, validation, globafization and influence on the development of the AUSCAN hand osteoarthritis indices

Clinical measurement in both clinical research and clinical practice requires tools and techniques that are valid, reliable and responsive. Patient-centred self-reported measures provide opportunity to evaluate consequences of osteoarthritis, that are important and relevant to patients with the condition. The WOMAC and AUSCAN Indices are health status measurement questionnaires that are valid, reliable and responsive, easy to complete, simple to score and available in multiple language forms and scaling formats. They provide opportunities to capture patient relevant information, relating to the impact of interventions, in clinical research and clinical practice environments. WOMAC data have also contributed to the development of proposed definitions for responder criteria and state-attainment criteria in osteoarthritis.

Comparing Near-infrared Conventional Diffuse Reflectance Spectroscopy And Hyperspectral Imaging For Determination Of The Bulk Properties Of Solid Samples By Multivariate Regression: Determination Of Mooney Viscosity And Plasticity Indices Of Natural Rubber.

Conventional reflectance spectroscopy (NIRS) and hyperspectral imaging (HI) in the near-infrared region (1000-2500 nm) are evaluated and compared, using, as the case study, the determination of relevant properties related to the quality of natural rubber. Mooney viscosity (MV) and plasticity indices (PI) (PI0 - original plasticity, PI30 - plasticity after accelerated aging, and PRI - the plasticity retention index after accelerated aging) of rubber were determined using multivariate regression models. Two hundred and eighty six samples of rubber were measured using conventional and hyperspectral near-infrared imaging reflectance instruments in the range of 1000-2500 nm. The sample set was split into regression (n = 191) and external validation (n = 95) sub-sets. Three instruments were employed for data acquisition: a line scanning hyperspectral camera and two conventional FT-NIR spectrometers. Sample heterogeneity was evaluated using hyperspectral images obtained with a resolution of 150 × 150 μm and principal component analysis. The probed sample area (5 cm(2); 24,000 pixels) to achieve representativeness was found to be equivalent to the average of 6 spectra for a 1 cm diameter probing circular window of one FT-NIR instrument. The other spectrophotometer can probe the whole sample in only one measurement. The results show that the rubber properties can be determined with very similar accuracy and precision by Partial Least Square (PLS) regression models regardless of whether HI-NIR or conventional FT-NIR produce the spectral datasets. The best Root Mean Square Errors of Prediction (RMSEPs) of external validation for MV, PI0, PI30, and PRI were 4.3, 1.8, 3.4, and 5.3%, respectively. Though the quantitative results provided by the three instruments can be considered equivalent, the hyperspectral imaging instrument presents a number of advantages, being about 6 times faster than conventional bulk spectrometers, producing robust spectral data by ensuring sample representativeness, and minimizing the effect of the presence of contaminants.

Fluorescence spectroscopy for the detection of tongue carcinoma - validation in an animal model

The efficacy of fluorescence spectroscopy to detect squamous cell carcinoma is evaluated in an animal model following laser excitation at 442 and 532 nm. Lesions are chemically induced with a topical DMBA application at the left lateral tongue of Golden Syrian hamsters. The animals are investigated every 2 weeks after the 4th week of induction until a total of 26 weeks. The right lateral tongue of each animal is considered as a control site (normal contralateral tissue) and the induced lesions are analyzed as a set of points covering the entire clinically detectable area. Based on fluorescence spectral differences, four indices are determined to discriminate normal and carcinoma tissues, based on intraspectral analysis. The spectral data are also analyzed using a multivariate data analysis and the results are compared with histology as the diagnostic gold standard. The best result achieved is for blue excitation using the KNN (K-nearest neighbor, a interspectral analysis) algorithm with a sensitivity of 95.7% and a specificity of 91.6%. These high indices indicate that fluorescence spectroscopy may constitute a fast noninvasive auxiliary tool for diagnostic of cancer within the oral cavity. (C) 2008 Society of Photo-Optical Instrumentation Engineers.

Prognostic modelling of breast cancer patients: a benchmark of predictive models with external validation

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Electrotécnica e de Computadores – Sistemas Digitais e Percepcionais pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Comparing clustering solutions: the use of adjusted paired indices

In the present paper we compare clustering solutions using indices of paired agreement. We propose a new method - IADJUST - to correct indices of paired agreement, excluding agreement by chance. This new method overcomes previous limitations known in the literature as it permits the correction of any index. We illustrate its use in external clustering validation, to measure the accordance between clusters and an a priori known structure. The adjusted indices are intended to provide a realistic measure of clustering performance that excludes agreement by chance with ground truth. We use simulated data sets, under a range of scenarios - considering diverse numbers of clusters, clusters overlaps and balances - to discuss the pertinence and the precision of our proposal. Precision is established based on comparisons with the analytical approach for correction specific indices that can be corrected in this way are used for this purpose. The pertinence of the proposed correction is discussed when making a detailed comparison between the performance of two classical clustering approaches, namely Expectation-Maximization (EM) and K-Means (KM) algorithms. Eight indices of paired agreement are studied and new corrected indices are obtained.

Validation de la version française du questionnaire I7 d'impulsivité. Influence de la personnalité, du sexe et de la religion = Validation of the french version of the eysenck's impulsiveness questionnaire (I7). Influence of personality, gender, and religion

L'objectif de cette étude est de vérifier la validité interne de la version française du questionnaire d'impulsivité d'Eysenck (I7), traduite par Dupont et al., sur un échantillon d'étudiants suisses (n = 220). Dans leur questionnaire, Eysenck et Eysenck proposent trois échelles : les deux premières évaluant deux composantes distinctes de l'impulsivité (l'Impulsivité caractérisant les individus qui agissent sans penser, sans être conscients des risques associés à leurs actions, et la Recherche d'aventure caractérisant les individus qui agissent en étant conscients, et en tenant compte des risques associés à leurs actions), et la troisième servant de « distracteur » (l'Empathie caractérisant les individus qui ont la faculté de s'identifier à l'autre). La structure à trois facteurs de l'instrument a été confirmée par notre analyse factorielle en composantes principales. La solution factorielle retenue n'explique toutefois qu'une faible proportion de la variance (21.9 %). L'homogénéité interne des échelles, mesurée à l'aide d'alphas de Cronbach, est acceptable pour l'échelle d'Impulsivité (.78) et de Recherche d'aventure (.71), mais elle est, en revanche, faible pour l'échelle d'Empathie (.62). Les échelles de l'I7 d'Eysenck entretiennent des corrélations cohérentes avec les cinq grandes dimensions de la personnalité mesurées par le NEO PI-R. L'Impulsivité est associée négativement à la dimension Conscience (r = - .32), alors que la Recherche d'aventures est associée positivement à la dimension Extraversion (r = .33). Le sexe a un impact sur les échelles Recherche d'aventure et Empathie. Les qualités métrologiques de la version française du questionnaire d'impulsivité d'Eysenck (I7) sont satisfaisantes, mais l'estimation d'autres indices de validité, comme la fidélité test-retest et la validité convergente, devrait être réalisée.

Validation of the post-delivery perceived stress inventory

This article presents the post-delivery perceived stress inventory (PDPSI) and its psychometric properties. This inventory is unique in that it links the measurement of perceived stress to events experienced during and after delivery. A total of 235 French-speaking, primiparous mothers completed the PDPSI two days after their delivery. To evaluate the predictive validity of the PDPSI on anxiety and depression, participants also completed the EPDS and the STAI two days and six weeks postpartum. The exploratory analysis revealed a 16-item structure divided into five factors: F1: relationship with the child; F2: delivery; F3: fatigue after delivery; F4: breastfeeding; and F5: relationship with the caregivers. The PDPSI demonstrated good internal consistency. Moreover, confirmatory factor analysis produced excellent indices, indicating that the complexity of the PDPSI was taken into account and its fit to the sample. The discriminant analysis showed that the PDPSI was not sensitive to specific changes in the sample making the inventory generalizable to other populations. Predictive validity showed that the scale significantly predicted depression and anxiety in the early postpartum period as well as anxiety six weeks postpartum. Overall, the PDPSI showed excellent psychometric qualities, making it a useful tool for future research-evaluating interventions related to perceived stress during the postpartum period.

Mesurer la stigmatisaion perçue chez les personnes souffrant de troubles psychiques : traduction française, validation et adaptation de la Stigma Scale

L'objectif de l'étude présentée est d'adapter et de valider une version française de la Stigma Scale (King, 2007) auprès d'une population de personnes souffrant de troubles psychiques. Dans une première phase, la stabilité temporelle (fidélité test-retest), la cohérence interne et la validité convergente de l'instrument original à 28 items traduit en français ont été évaluées auprès d'un échantillon de 183 patients. Les résultats d'analyses factorielles confirmatoires ne nous ont pas permis de confirmer la structure originale de l'instrument. Nous avons donc proposé, sur la base des résultats d'une analyse factorielle exploratoire, une version courte de l'échelle de stigmatisation (9 items) qui conserve la structure en trois facteurs du modèle original. Dans une deuxième phase, nous avons examiné les qualités psychométriques et validé cette version abrégée de l'échelle de stigmatisation auprès d'un second échantillon de 234 patients. Les indices d'ajustements de notre analyse factorielle confirmatoire confirme la structure en trois facteurs de la version abrégée de la Stigma Scale. Les résultats suggèrent que la version française abrégée de l'échelle de stigmatisation constitue un instrument utile, fiable et valide dans l'autoévaluation de la stigmatisation perçue par des personnes souffrant de troubles psychiques. - Aim People suffering from mental illness are exposed to stigma. However, only few tools are available to assess stigmatization as perceived from the patient's perspective. The aim of this study is to adapt and validate a French version of the Stigma Scale (King, 2007). This self-report questionnaire has a three-factor structure: discrimination, disclosure and positive aspects of mental illness. Discrimination subscale refers to perceived negative reactions by others. Disclosure subscale refers mainly to managing disclosure to avoid discrimination and finally positive aspects subscale taps into how patients are becoming more accepting, more understanding toward their illness. Method In the first step, internal consistency, convergent validity and test-retest reliability of the French adaptation of the 28-item scale have been assessed on a sample of 183 patients. Results of confirmatory factor analyses (CFA) did not confirm the hypothesized structure. In light of the failed attempts to validate the original version, an alternative 9-item short-form version of the Stigma Scale, maintaining the integrity of the original model, was developed based on results of exploratory factor analyses in the first sample and cross- validated in a new sample of 234 patients. Results Results of CFA did not confirm that the data fitted well to the three-factor model of the 28-item Stigma Scale (χ2/άί=2.02, GFI=0.77, AGFI=0.73, RMSEA=0.07, CFI=0.77 et NNFI=0.75). Cronbach's α are excellent for discrimination (0.84) and disclosure (0.83) subscales but poor for potential positive aspects (0.46). External validity is satisfactory. Overall Stigma Scale total score is negatively correlated with score on Rosenberg's Self-Esteem Scale (r = -0.49), and each sub-scale is significantly correlated with a visual analogue scale that refers to the specific aspect of stigma (0.43 < |r| < 0.60). Intraclass correlation coefficients between 0.68 and 0.89 indicate good test- retest reliability. Results of CFA demonstrate that the items chosen for the short version of the Stigma Scale have the expected fit properties fa2/df=1.02, GFI=0.98, AGFI=0.98, RMSEA=0.01, CFI=1.0 et NNFI=1.0). Considering the small number (3 items) of items in each subscales of the short version of the Stigma Scale, a coefficients for the discrimination (0.57), disclosure (0.80) and potential positive aspects subscales (0.62) are considered as good. Conclusion Our results suggest that the 9-item French short-version of the Stigma Scale is a useful, reliable and valid self-report questionnaire to assess perceived stigmatization in people suffering from mental illness. The time of completion is really short and questions are well understood and accepted by the patients.

Seasonal fluctuations of bacterial community diversity in agricultural soil and experimental validation by laboratory disturbance experiments.

Natural fluctuations in soil microbial communities are poorly documented because of the inherent difficulty to perform a simultaneous analysis of the relative abundances of multiple populations over a long time period. Yet, it is important to understand the magnitudes of community composition variability as a function of natural influences (e.g., temperature, plant growth, or rainfall) because this forms the reference or baseline against which external disturbances (e.g., anthropogenic emissions) can be judged. Second, definition of baseline fluctuations in complex microbial communities may help to understand at which point the systems become unbalanced and cannot return to their original composition. In this paper, we examined the seasonal fluctuations in the bacterial community of an agricultural soil used for regular plant crop production by using terminal restriction fragment length polymorphism profiling (T-RFLP) of the amplified 16S ribosomal ribonucleic acid (rRNA) gene diversity. Cluster and statistical analysis of T-RFLP data showed that soil bacterial communities fluctuated very little during the seasons (similarity indices between 0.835 and 0.997) with insignificant variations in 16S rRNA gene richness and diversity indices. Despite overall insignificant fluctuations, between 8 and 30% of all terminal restriction fragments changed their relative intensity in a significant manner among consecutive time samples. To determine the magnitude of community variations induced by external factors, soil samples were subjected to either inoculation with a pure bacterial culture, addition of the herbicide mecoprop, or addition of nutrients. All treatments resulted in statistically measurable changes of T-RFLP profiles of the communities. Addition of nutrients or bacteria plus mecoprop resulted in bacteria composition, which did not return to the original profile within 14 days. We propose that at less than 70% similarity in T-RFLP, the bacterial communities risk to drift apart to inherently different states.

Mise au point et validation d'un fantôme spécifique pour asssurer le suivi des mesures quantitatives en tomographie par émission de positons.

L'index de consommation du glucose, SUV pour standardized uptake value, est largement utilisé en tomographie par émission de positons (TEP) pour quantifier la concentration relative de [18F]2-fluoro-2-désoxy-D-glucose (18F-FDG) dans les tissus. Cependant, cet indice dépend de nombreux facteurs méthodologiques et biologiques et son utilisation fait débat. Il est donc primordial d'instaurer un contrôle qualité régulier permettant d'assurer la stabilité de la mesure des indices quantitatifs. Dans cette optique, un fantôme spécifique avec inserts cylindriques de différentes tailles a été développé. L'objectif de cette étude est de montrer la sensibilité et l'intérêt de ce fantôme. Méthodes. - La sensibilité du fantôme a été étudiée à travers la mesure des SUV et des coefficients de recouvrement (RC). Plusieurs méthodes de mesure ont été utilisées. Les données ont été reconstruites en utilisant les algorithmes de routine clinique. Nous avons étudié la variation des RC en fonction de la taille des cylindres et le changement relatif de fixation, en utilisant des activités différentes. Le fantôme a ensuite été testé sur l'appareil d'un autre centre. Résultats. - Pour toutes les méthodes de mesure, une forte variation des RC avec la taille des cylindres, de l'ordre de 50 %, a été obtenue. Ce fantôme a également permis de mesurer un changement relatif de fixation qui s'est révélé être indépendant de la méthode de mesure. Malgré un étalonnage des deux systèmes TEP/TDM, des différences de quantification d'environ 20 % ont subsisté. Conclusion. - Les résultats obtenus montrent l'intérêt de ce fantôme dans le cadre du suivi des mesures quantitatives.

DRIS norms validation for sugarcane crop

The objectives of this study were to evaluate the relationship between the diagnosis and recommendation integrated system (DRIS) indices and foliar nutrient concentrations, to establish optimum foliar nutrient concentrations with DRIS and to validate the DRIS norms for sugarcane crop. Foliar nutrient concentrations from 126 sugarcane commercial fields were analyzed during the 1996/97 season, to calculate DRIS indices. Regression analysis was used to fit a model relating DRIS indices to nutrient concentrations. Experiments were carried out during the 1997/98 season, whose treatments consisted of the addition of the most limiting nutrients according to DRIS. A new diagnosis was performed. At the end of 1997/98 season, the yields of each plot were collected. Analysis of variance and Duncan test (5%) were used for the evaluation of the collected data. There was a positive and significant relationship between sugarcane foliar nutrient concentrations and DRIS indices. The optimum foliar nutrient concentrations for sugarcane are: 13.4 g ha-1 for N, 1.91 g ha-1 for P, 12.2 g ha-1 for K, 2.99 g ha-1 for Ca, 2.15 g ha-1 for Mg, 1.61 g ha-1 for S, 4.48 mg ha-1 for Cu, 67.8 mg ha-1 for Mnand 11.7 mg ha-1 for Zn. DRIS norms evaluated are useful to correct nutritional imbalances and to increase sugarcane yield.