Sentence summarization aims at compressing a long sentence into a short one that conveys the main idea of the input.

Sentence summarization aims at compressing a long sentence into a short one that conveys the main idea of the input.

In real-world time series recognition applications, it is possible to have data with varying length patterns. However, when using artificial neural networks (ANN), it is standard practice to use fixed-sized mini-batches. To do this, time series data with varying lengths are typically normalized so that all the patterns are the same length. Normally, this is done using zero padding or truncation without much consideration. We propose a novel method of normalizing the lengths of the time series in a dataset by exploiting the dynamic matching ability of Dynamic Time Warping (DTW). In this way, the time series lengths in a dataset can be set to a fixed size while maintaining features typical to the dataset. In the experiments, all 11 datasets with varying length time series from the 2018 UCR Time Series Archive are used. We evaluate the proposed method by comparing it with 18 other length normalization methods on a Convolutional Neural Network (CNN), a Long-Short Term Memory network (LSTM), and a Bidirectional LSTM (BLSTM).

Sentence summarization aims at compressing a long sentence into a short one that keeps the main gist, and has extensive real-world applications such as headline generation. In previous work, researchers have developed various approaches to improve the ROUGE score, which is the main evaluation metric for summarization, whereas controlling the summary length has not drawn much attention. In our work, we address a new problem of explicit character-level length control for summarization, and propose a dynamic programming algorithm based on the Connectionist Temporal Classification (CTC) model. Results show that our approach not only achieves higher ROUGE scores but also yields more complete sentences.

We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family of high dimensional latent variable models, including high dimensional Gaussian mixture and mixtures of sparse regressions. A thorough theoretical investigation is further conducted. In particular, we show that the final decomposition estimator is guaranteed to achieve a local statistical rate, and further strengthen it to the global statistical rate by introducing a proper initialization procedure. In high dimensional regimes, the obtained statistical rate significantly improves those shown in the existing non-sparse decomposition methods. The empirical advantages of TTP are confirmed in extensive simulated results and two real applications of click-through rate prediction and high-dimensional gene clustering.