Efficient estimation of AUC in a sliding window

In many applications, monitoring area under the ROC curve (AUC) in a sliding window over a data stream is a natural way of detecting changes in the system. The drawback is that computing AUC in a sliding window is expensive, especially if the window size is large and the data flow is significant. In this paper we propose a scheme for maintaining an approximate AUC in a sliding window of length $k$. More specifically, we propose an algorithm that, given $\epsilon$, estimates AUC within $\epsilon / 2$, and can maintain this estimate in $O((\log k) / \epsilon)$ time, per update, as the window slides. This provides a speed-up over the exact computation of AUC, which requires $O(k)$ time, per update. The speed-up becomes more significant as the size of the window increases. Our estimate is based on grouping the data points together, and using these groups to calculate AUC. The grouping is designed carefully such that ($i$) the groups are small enough, so that the error stays small, ($ii$) the number of groups is small, so that enumerating them is not expensive, and ($iii$) the definition is flexible enough so that we can maintain the groups efficiently. Our experimental evaluation demonstrates that the average approximation error in practice is much smaller than the approximation guarantee $\epsilon / 2$, and that we can achieve significant speed-ups with only a modest sacrifice in accuracy

Environmental Implications of Peri-urban Sprawl and the Urbanization of Secondary Cities in Latin America

This paper examines the environmental and social implications of peri-urban growth in small to medium sized cities in Latin America and the Caribbean and proposes approaches to address this challenge. Key recommendations include cities should stimulate strategies for compact growth and efforts to regularize existing irregular settlements should be strongly supported, among other recommendations.Environment & Natural Resources, Urban Development, IDB-TN-237

Gesture Recognition Aplication based on Dynamic Time Warping (DTW) FOR Omni-Wheel Mobile Robot

This project presents of the movement of omni-wheel robot moves in the trajectory obtained from the gesture recognition system based on Dynamic Time Warping. Single camera is used as the input of the system, which is also a reference to the movement of the omni-wheel robot. Some systems for gesture recognition have been developed using various methods and different approaches. The movement of the omni-wheel robot using the method of Dynamic Time Wrapping (DTW) which has the advantage able to calculate the distance of two data vectors with different lengths. By using this method we can measure the similarity between two sequences at different times and speeds. Dynamic Time Warping to compare the two parameters at varying times and speeds. Application of DTW widely applied in video, audio, graphics, etc. Due to data that can be changed in a linear manner so that it can be analyzed with DTW. In short can find the most suitable value by minimizing the difference between two multidimensional signals that have been compressed. DTW method is expected to gesture recognition system to work optimally, have a high enough value of accuracy and processing time is realtime

Evaluation of recommender systems in streaming environments

Evaluation of recommender systems is typically done with finite datasets. This means that conventional evaluation methodologies are only applicable in offline experiments, where data and models are stationary. However, in real world systems, user feedback is continuously generated, at unpredictable rates. Given this setting, one important issue is how to evaluate algorithms in such a streaming data environment. In this paper we propose a prequential evaluation protocol for recommender systems, suitable for streaming data environments, but also applicable in stationary settings. Using this protocol we are able to monitor the evolution of algorithms' accuracy over time. Furthermore, we are able to perform reliable comparative assessments of algorithms by computing significance tests over a sliding window. We argue that besides being suitable for streaming data, prequential evaluation allows the detection of phenomena that would otherwise remain unnoticed in the evaluation of both offline and online recommender systems.Comment: Workshop on 'Recommender Systems Evaluation: Dimensions and Design' (REDD 2014), held in conjunction with RecSys 2014. October 10, 2014, Silicon Valley, United State