[pt] Nos últimos anos, diversas fórmulas de diferença de cores foram desenvolvidas para o espaço CIELAB, tais como CMC, CIE94 e CIEDE2000. Embora essas fórmulas obtenham maior precisão na medida perceptual entre cores, muitas aplicações não podem usufruir desta maior precisão, pois as distâncias euclidianas no CIELAB não são isométricas de acordo com essas novas fórmulas. Com isso, aplicações como gamut mapping e interpolação de cores precisam de um espaço de cores que seja isométrico em relação as fórmulas mais recentes de medição de diferenças de cores. Esse trabalho estuda o mapeamento do espaço CIELAB, em particular do plano ab deste espaço, sob a métrica da fórmula CIEDE2000, por meio de técnicas de escalonamento multidimensional, ou Multidimensional Scaling (MDS), tais como o ISOMAP e uma otimizaçãobaseada em Sammon Mapping. / [en] In recent years, various color difference formulas were developed for the CIELAB space, such as CMC, CIE94 and CIEDE2000. Although these formulas have achieved greater accuracy in perceptual measurement between colors, many applications cannot take advantage of this greater precision, because the Euclidean distances in CIELAB are not isometric in accordance with these new formulas. Thus, applications such as gamut mapping and color interpolation need a color space that is isometric in relation to the latest color difference formulas. This paper studies the mapping of the CIELAB space, particularly the ab plane of this space according to the metrics of the CIEDE2000 formula, through multidimensional scaling (MDS) techniques, more specifically ISOMAP and an optimization based on Sammon Mapping.

Many geological deposits contain nonlinear anisotropic features such as veins, channels, folds or local changes in orientation; numerical property modeling must account for these features to be reliable and predictive. This work incorporates locally varying anisotropy into inverse distance estimation, kriging and sequential Gaussian simulation. The methodology is applicable to a range of fields including (1) mining-mineral grade modeling (2) petroleum-porosity, permeability, saturation and facies modeling (3) environmental-contaminate concentration modeling. An exhaustive vector field defines the direction and magnitude of anisotropy and must be specified prior to modeling. Techniques explored for obtaining this field include: manual; moment of inertia of local covariance maps; direct estimation and; automatic feature interpolation. The methodology for integrating locally varying anisotropy into numerical modeling is based on modifying the distance/covariance between locations in space. Normally, the straight line path determines distance but in the presence of nonlinear features the appropriate path between locations traces along the features. These paths are calculated with the Dijkstra algorithm and may be nonlinear in the presence of locally varying anisotropy. Nonlinear paths do not ensure positive definiteness of the required system of equations when used with kriging or sequential Gaussian simulation. Classical multidimensional scaling is applied to ensure positive definiteness but is found to be computationally infeasible for large models, thus, landmark points are used for efficiency with acceptable losses in precision. The methodology is demonstrated on two data sets (1) net thickness of the McMurray formation in northern Alberta and (2) gold grade in a porphyry copper deposit. Integrating LVA into numerical modeling increases local accuracy and improves leave-one-out cross validation analysis results in both case studies. / Mining Engineering

High-dimensional data take place from digital image processing, gene expression micro arrays, neuronal population activities to financial time series. Dimensionality Reduction - extracting low dimensional structure from high dimension - is a key problem in many areas like information processing, machine learning, data mining, information retrieval and pattern recognition, where we find some data reduction techniques. In this thesis we will give a survey about modern data reduction techniques, representing the state-of-the-art of theory, methods and application, by introducing the language of mathematics there. This needs a special care concerning the questions of, e.g., how to understand discrete structures as manifolds, to identify their structure, preparing the dimension reduction, and to face complexity in the algorithmically methods. A special emphasis will be paid to Principal Component Analysis, Locally Linear Embedding and Isomap Algorithms. These algorithms are studied by a research group from Vilnius, Lithuania and Zeev Volkovich, from Software Engineering Department, ORT Braude College of Engineering, Karmiel, and others. The main purpose of this study is to compare the results of the three of the algorithms. While the comparison is beeing made we will focus the results and duration.

No description available.

2011 IEEE Congress on Evolutionary Computation (CEC). June 5-8, 2011, Ritz-Carlton, New Orleans, LA, USA

High-dimensional data sets can be difficult to visualize and analyze, while data in low-dimensional space tend to be more accessible. In order to aid visualization of the underlying structure of a dataset, the dimension of the dataset is reduced. The simplest approach to accomplish this task of dimensionality reduction is by a random projection of the data. Even though this approach allows some degree of visualization of the underlying structure, it is possible to lose more interesting underlying structure within the data. In order to address this concern, various supervised and unsupervised linear dimensionality reduction algorithms have been designed, such as Principal Component Analysis and Linear Discriminant Analysis. These methods can be powerful, but often miss important non-linear structure in the data. In this thesis, manifold learning approaches to dimensionality reduction are developed. These approaches combine both linear and non-linear methods of dimension reduction.

No description available.

Šiame darbe nagrinėjami netiesiniai daugdarų atpažinimo metodai ir daugiamačių duomenų projekcijos metodai. Siūloma jais spręsti keliais laisvės laipsniais besisukančio objekto orientacijos radimo problemą. Aprašomi MDS, Trianguliacijos, Sammon, RPM, mRPM, CCA, PCA, LLE, LE, HLLE, LTSA, SMACOF ir Isomap metodai. Su kai kuriais iš jų atliekami web-kamera gautų galvos atvaizdų tyrimai. Isomap algoritmo pagrindu sukuriama programinė įranga ir su ja taipogi atliekami galvos orientacijos tyrimai. / This paper deals with Analysis of non-linear manifold learning methods and multidimensional data projection methods. It is proposed use them in solving problem of detection of orientation of object, moving in few degrees of freedom. Methods described: MDS, triangulation, Sammon, RPM, mRPM, CCA, PCA, LLE, LE, HLLE, LTSA, SMACOF and Isomap. Some of them are used to analyze head images acquired by webcam.. Application is created which is then used to analyze head orientation by implementing Isomap method.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Prehistoric cultures are often studied by intrasite artifact variation and quantity without much consideration of how prehistoric populations interacted locally and regionally. Archaeologists can identify and study patterns associated with activities within a specified radius in order to gain an understanding of cultural operations. Identifying a social framework for a prehistoric society allows the investigation of group organization such as status differentiation, shared rituals, and the construction and maintenance of earthworks and living areas. That facilities were constructed for specialized use within a community is evidenced by the presence of earthworks and mounds at many sites (Lewis et al. 1998:16-17). Less well understood is how community patterns reflect social organization. The purpose of this thesis is to better document the number and distribution of structures at Lyon’s Bluff, a Mississippian to Protohistoric-period mound site in Oktibbeha County, Mississippi. The focus will be on the last part of the occupation at the site, i.e., on materials recovered from the plowzone. A method employing molluscan remains and sedimentological evidence is used that allows for the delineation of structure locales using plowzone samples. Additional evidence is provided by artifact distributions and geophysical (magnetic gradiometer) data.