Time Series Motif Discovery (TSMD) is defined as searching for patterns that are previously unknown and appear with a given frequency in time series. Another problem strongly related with TSMD is Word Segmentation. This problem has received much attention from the community that studies early language acquisition in babies and toddlers. The development of biologically plausible models for word segmentation could greatly advance this field. Therefore, in this article, we propose the Variable Input Length Map (VILMAP) for Motif Discovery and Word Segmentation. The model is based on the Self-Organizing Maps and can identify Motifs with different lengths in time series. In our experiments, we show that VILMAP presents good results in finding Motifs in a standard Motif discovery dataset and can avoid catastrophic forgetting when trained with datasets with increasing values of input size. We also show that VILMAP achieves results similar or superior to other methods in the literature developed for the task of word segmentation.
The operation of the map takes place in three phases: the organization phase, the convergence phase, and the clustering phase @cite_20 . In the organization phase, nodes are dynamically inserted, removed and adjusted in the map in order to cover the regions of the input space in which the input patterns are found as well as possible. When an input pattern is presented for the network, a level of activation is computed for each node in the map, and the node with the highest activation is considered the winner of the competition. This activation level is an inverse function of the distance between the center of the node and the input pattern. An activation threshold, @math , is used for determining when if the winner node is close enough to be adjusted or if it is necessary to insert a new node in the map. The nodes that do not cluster a significant percentage of the input patterns are periodically removed.
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Large scale clusters running MapReduce, Spark etc. routinely process data that are on the orders of petabytes or more. The philosophy in these methods is to split the overall job into smaller tasks that are executed on different servers; this is called the map phase. This is followed by a data shuffling phase where appropriate data is exchanged between the servers. The final reduce phase, completes the computation. Prior work has explored a mechanism for reducing the overall execution time by operating on a computation vs. communication tradeoff. Specifically, the idea is to run redundant copies of map tasks that are placed on judiciously chosen servers. The shuffle phase exploits the location of the nodes and utilizes coded transmission. The main drawback of this approach is that it requires the original job to be split into a number of map tasks that grows exponentially in the system parameters. This is problematic, as we demonstrate that splitting jobs too finely can in fact adversely affect the overall execution time. In this work we show that one can simultaneously obtain low communication loads while ensuring that jobs do not need to be split too finely. Our approach uncovers a deep relationship between this problem and a class of combinatorial structures called resolvable designs. We present experimental results obtained on Amazon EC2 clusters for a widely known distributed algorithm, namely TeraSort. We obtain over 4.69x improvement in speedup over the baseline approach and more than 2.6x over current state of the art. A complex network is a powerful tool to research complex systems, traffic flow being one of the most complex systems. In this paper, we use complex network theory to study traffic time series, which provide a new insight into traffic flow analysis. Firstly, the phase space, which describes the evolution of the behavior of a nonlinear system, is reconstructed using the delay embedding theorem. Secondly, in order to convert the new time series into a complex network, the critical threshold is estimated by the characteristics of a complex network, which include degree distribution, cumulative degree distribution, and density and clustering coefficients. We find that the degree distribution of associated complex network can be fitted with a Gaussian function, and the cumulative degree distribution can be fitted with an exponential function. Density and clustering coefficients are then researched to reflect the change of connections between nodes in complex network, and the results are in accordance with the observation of the plot of an adjacent matrix. Consequently, based on complex network analysis, the proper range of the critical threshold is determined. Finally, to mine the nodes with the closest relations in a complex network, the modularity is calculated with the increase of critical threshold and the community structure is detected according to the optimal modularity. The work in our paper provides a new way to understand the dynamics of traffic time series. The success of fine-grained visual categorization (FGVC) extremely relies on the modeling of appearance and interactions of various semantic parts. This makes FGVC very challenging because: (i) part annotation and detection require expert guidance and are very expensive; (ii) parts are of different sizes; and (iii) the part interactions are complex and of higher-order. To address these issues, we propose an end-to-end framework based on higherorder integration of hierarchical convolutional activations for FGVC. By treating the convolutional activations as local descriptors, hierarchical convolutional activations can serve as a representation of local parts from different scales. A polynomial kernel based predictor is proposed to capture higher-order statistics of convolutional activations for modeling part interaction. To model inter-layer part interactions, we extend polynomial predictor to integrate hierarchical activations via kernel fusion. Our work also provides a new perspective for combining convolutional activations from multiple layers. While hypercolumns simply concatenate maps from different layers, and holistically-nested network uses weighted fusion to combine side-outputs, our approach exploits higher-order intra-layer and inter-layer relations for better integration of hierarchical convolutional features. The proposed framework yields more discriminative representation and achieves competitive results on the widely used FGVC datasets. In this paper we evaluate the quality of the activation layers of a convolutional neural network (CNN) for the gen- eration of object proposals. We generate hypotheses in a sliding-window fashion over different activation layers and show that the final convolutional layers can find the object of interest with high recall but poor localization due to the coarseness of the feature maps. Instead, the first layers of the network can better localize the object of interest but with a reduced recall. Based on this observation we design a method for proposing object locations that is based on CNN features and that combines the best of both worlds. We build an inverse cascade that, going from the final to the initial convolutional layers of the CNN, selects the most promising object locations and refines their boxes in a coarse-to-fine manner. The method is efficient, because i) it uses the same features extracted for detection, ii) it aggregates features using integral images, and iii) it avoids a dense evaluation of the proposals due to the inverse coarse-to-fine cascade. The method is also accurate; it outperforms most of the previously proposed object proposals approaches and when plugged into a CNN-based detector produces state-of-the- art detection performance.