Aluno: João Henrique Ferreira Flores
Orientador: Prof. Dr. Paulo Martins Engel
Título: Improving online incremental one-shot learning applying parametric statistical methods
Linha de Pesquisa: Inteligência Artificial
Data: 17/10/2013
Horário: 13h30min
Local: Auditório José Mauro Volkmer de Castilho, Prédio 43424 – Instituto de Informática
Banca Examinadora:
Prof. Dr. Dante Augusto Couto Barone (UFRGS)
Profa. Dra. Liane Werner (PPGEP/UFRGS)
Prof. Dr. Luís da Cunha Lamb (UFRGS)
Presidente da Banca: Prof. Dr. Paulo Martins Engel
Resumo:
Filtering is arguably the single most important operation in image and video processing. In particular, high-dimensional filters are a fundamental building block for several applications (FATTAL, 2009; FARBMAN; FATTAL; LISCHINSKI, 2010), having received considerable attention from the research community over the last two decades. Unfortunately, naive implementations of such an important class of filters are too slow for many practical uses, specially in light of the ever increasing resolution of digitally captured images (80-megapixel digital cameras are already available on the market, as of 2013). This dissertation describes two novel approaches to efficiently perform high-dimensional filtering: the domain transform, and the adaptive manifolds.
The domain transform defines an isometry between curves on the 2D image manifold in 5D and the real line. It preserves the geodesic distance between points on these curves, adaptively warping the input signal so that high-dimensional geodesic filtering can be efficiently performed in linear time. This approach has several desirable features: the use of simple operations leads to considerable speedups over existing techniques and potential memory savings; its computational cost is not affected by the choice of the filter parameters; and it is the first filter of its kind to work on color images at arbitrary scales in real time, without resorting to subsampling or quantization.
The adaptive manifolds compute the filter’s response at a reduced set of sampling points, and uses these for interpolation at all input pixels, so that high-dimensional Euclidean filtering can be efficiently performed in linear time. We show that for a proper choice of sampling points, the total cost of the filtering operation is linear both in the number of pixels and in the dimension of the space in which the filter operates. As such, ours is the first high-dimensional filter with such a complexity. We present formal derivations for the equations that define our filter, as well as for an algorithm to compute the sampling points. This provides a sound theoretical justification for our method and for its properties. The resulting filter is quite flexible, being capable of producing responses that approximate either standard Gaussian, bilateral, or non-local-means filters. Such flexibility also allows us to demonstrate the first hybrid Euclidean-geodesic filter that runs in a single pass.
The high-dimensional filters we propose provide the fastest performance (on both CPU and GPU) for a variety of real-world applications. Thus, our filters provide a valuable tool for the image and video processing, computer graphics, computer vision, and computational photography communities.
This work shows that the use of some statistical tools can improve the modelling and use of incremental models for time series using, basically, the IGMN algorithm (incremental gaussian mixture network) for verification of the results. The statistical tools presented here are reasonably well known and widely used for the (S)ARIMA models (seasonal autoregressive integrated moving average), considered classical or parametric statistical models. These models consist of three basic parts: the autoregressive part (AR), the moving average part (MA) and an integration (I) or difference variable. Based on these three parts, with each one being adjustable and modelled using parameters, the classical models can work with a wide range of time series. The use of these tools in classical models helps the user to choose the model parameters, which also occurs for incremental models. The results presented here show that there is an improvement, in some cases significant, using only the graphs of autocorrelation function (acf) and the partial autocorrelation function (pacf) to assist in choosing an optimal window. However, while the autoregressive (AR) part of the classical models can be easily adapted, the moving average (MA) part still fails. Despite the generated models using the IGMN have achieved superior performance to other time series models, it is still possible to improve this performance, based on a better adaptation for the moving average part.
Palavras chave: neural networks, time series, forecasting, ARIMA, IGMN.
