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Time series with missing values occur in almost any domain of applied sciences. Ignoring missing values can lead to a loss of efficiency and unreliable results, especially for large missing sub-sequence(s). This paper proposes an approach to fill in large gap(s) within time series data under the assumption of effective information. To obtain the imputation of missing values, we find the most similar sub-sequence to the sub-sequence before (resp. after) the missing values, then complete the gap by the next (resp. previous) sub-sequence of the most similar one. Dynamic Time Warping algorithm is applied to compare sub-sequences, and combined with the shape-feature extraction algorithm for reducing insignificant solutions. Eight well-known and real-world data sets are used for evaluating the performance of the proposed approach in comparison with five other methods on different indicators. The obtained results proved that the performance of our approach is the most robust one in case of time series data having high auto-correlation and cross-correlation, strong seasonality, large gap(s), and complex distribution.

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Abstract:Moving foreground detection is a very important step for many applications such as human behavior analysis for visual surveillance, model-based action recognition, road traffic monitoring, etc. Background subtraction is a very popular approach, but it is difficult to apply given that it must overcome many obstacles, such as dynamic background changes, lighting variations, occlusions, and so on. In the presented work, we focus on this problem (foreground/background segmentation), using a type-2 fuzzy modeling to manage the uncertainty of the video process and of the data. The proposed method models the state of each pixel using an imprecise and adjustable Gaussian mixture model, which is exploited by several fuzzy classifiers to ultimately estimate the pixel class for each frame. More precisely, this decision not only takes into account the history of its evolution, but also its spatial neighborhood and its possible displacements in the previous frames. Then we compare the proposed method with other close methods, including methods based on a Gaussian mixture model or on fuzzy sets. This comparison will allow us to assess our method's performance, and to propose some perspectives to this work.