Matrix Product Representation of Locality Preserving Unitaries

The matrix product representation provides a useful formalism to study not only entangled states, but also entangled operators in one dimension. In this paper, we focus on unitary transformations and show that matrix product operators that are unitary provides a necessary and sufficient representation of 1D unitaries that preserve locality. That is, we show that matrix product operators that are unitary are guaranteed to preserve locality by mapping local operators to local operators while at the same time all locality preserving unitaries can be represented in a matrix product way. Moreover, we show that the matrix product representation gives a straight-forward way to extract the GNVW index defined in Ref.\cite{Gross2012} for classifying 1D locality preserving unitaries. The key to our discussion is a set of `fixed point' conditions which characterize the form of the matrix product unitary operators after blocking sites. Finally, we show that if the unitary condition is relaxed and only required for certain system sizes, the matrix product operator formalism allows more possibilities than locality preserving unitaries. In particular, we give an example of a simple matrix product operator which is unitary only for odd system sizes, does not preserve locality and carries a `fractional' index as compared to their locality preserving counterparts.Comment: 14 page

Two-Stage Bagging Pruning for Reducing the Ensemble Size and Improving the Classification Performance

Ensemble methods, such as the traditional bagging algorithm, can usually improve the performance of a single classifier. However, they usually require large storage space as well as relatively time-consuming predictions. Many approaches were developed to reduce the ensemble size and improve the classification performance by pruning the traditional bagging algorithms. In this article, we proposed a two-stage strategy to prune the traditional bagging algorithm by combining two simple approaches: accuracy-based pruning (AP) and distance-based pruning (DP). These two methods, as well as their two combinations, “AP+DP” and “DP+AP” as the two-stage pruning strategy, were all examined. Comparing with the single pruning methods, we found that the two-stage pruning methods can furthermore reduce the ensemble size and improve the classification. “AP+DP” method generally performs better than the “DP+AP” method when using four base classifiers: decision tree, Gaussian naive Bayes, K-nearest neighbor, and logistic regression. Moreover, as compared to the traditional bagging, the two-stage method “AP+DP” improved the classification accuracy by 0.88%, 4.06%, 1.26%, and 0.96%, respectively, averaged over 28 datasets under the four base classifiers. It was also observed that “AP+DP” outperformed other three existing algorithms Brag, Nice, and TB assessed on 8 common datasets. In summary, the proposed two-stage pruning methods are simple and promising approaches, which can both reduce the ensemble size and improve the classification accuracy

Exploring Regional Development of Digital Humanities Research: A Case Study for Taiwan

This study analyzed references and source papers of the Proceedings of 2009-2012 International Conference of Digital Archives and Digital Humanities (DADH), which was held annually in Taiwan. A total of 59 sources and 1,104 references were investigated, based on descriptive analysis and subject analysis of library practices on cataloguing. Preliminary results showed historical materials, events, bureaucracies, and people of Taiwan and China in the Qing Dynasty were the major subjects in the tempo-spatial dimensions. The subject-date figure depicted a long-low head and short-high tail curve, which demonstrated both characteristics of research of humanities and application of technology in digital humanities. The dates of publication of the references spanned over 360 years, which shows a long time span in research materials. A majority of the papers (61.41%) were single-authored, which is in line with the common research practice in the humanities. Books published by general publishers were the major type of references, and this was the same as that of established humanities research. The next step of this study will focus on the comparison of characteristics of both sources and references of international journals with those reported in this article.Comment: 25 pages, 10 tables, 5 figure

A Novel Apex-Time Network for Cross-Dataset Micro-Expression Recognition

The automatic recognition of micro-expression has been boosted ever since the successful introduction of deep learning approaches. As researchers working on such topics are moving to learn from the nature of micro-expression, the practice of using deep learning techniques has evolved from processing the entire video clip of micro-expression to the recognition on apex frame. Using the apex frame is able to get rid of redundant video frames, but the relevant temporal evidence of micro-expression would be thereby left out. This paper proposes a novel Apex-Time Network (ATNet) to recognize micro-expression based on spatial information from the apex frame as well as on temporal information from the respective-adjacent frames. Through extensive experiments on three benchmarks, we demonstrate the improvement achieved by learning such temporal information. Specially, the model with such temporal information is more robust in cross-dataset validations.Comment: 6 pages, 3 figures, 3 tables, code available, accepted in ACII 201