Universal lossless source coding with the Burrows Wheeler transform

The Burrows Wheeler transform (1994) is a reversible sequence transformation used in a variety of practical lossless source-coding algorithms. In each, the BWT is followed by a lossless source code that attempts to exploit the natural ordering of the BWT coefficients. BWT-based compression schemes are widely touted as low-complexity algorithms giving lossless coding rates better than those of the Ziv-Lempel codes (commonly known as LZ'77 and LZ'78) and almost as good as those achieved by prediction by partial matching (PPM) algorithms. To date, the coding performance claims have been made primarily on the basis of experimental results. This work gives a theoretical evaluation of BWT-based coding. The main results of this theoretical evaluation include: (1) statistical characterizations of the BWT output on both finite strings and sequences of length n → ∞, (2) a variety of very simple new techniques for BWT-based lossless source coding, and (3) proofs of the universality and bounds on the rates of convergence of both new and existing BWT-based codes for finite-memory and stationary ergodic sources. The end result is a theoretical justification and validation of the experimentally derived conclusions: BWT-based lossless source codes achieve universal lossless coding performance that converges to the optimal coding performance more quickly than the rate of convergence observed in Ziv-Lempel style codes and, for some BWT-based codes, within a constant factor of the optimal rate of convergence for finite-memory source

COMIC: Towards A Compact Image Captioning Model with Attention

Recent works in image captioning have shown very promising raw performance. However, we realize that most of these encoder-decoder style networks with attention do not scale naturally to large vocabulary size, making them difficult to be deployed on embedded system with limited hardware resources. This is because the size of word and output embedding matrices grow proportionally with the size of vocabulary, adversely affecting the compactness of these networks. To address this limitation, this paper introduces a brand new idea in the domain of image captioning. That is, we tackle the problem of compactness of image captioning models which is hitherto unexplored. We showed that, our proposed model, named COMIC for COMpact Image Captioning, achieves comparable results in five common evaluation metrics with state-of-the-art approaches on both MS-COCO and InstaPIC-1.1M datasets despite having an embedding vocabulary size that is 39x - 99x smaller. The source code and models are available at: https://github.com/jiahuei/COMIC-Compact-Image-Captioning-with-AttentionComment: Added source code link and new results in Table

The Google Similarity Distance

Words and phrases acquire meaning from the way they are used in society, from their relative semantics to other words and phrases. For computers the equivalent of `society' is `database,' and the equivalent of `use' is `way to search the database.' We present a new theory of similarity between words and phrases based on information distance and Kolmogorov complexity. To fix thoughts we use the world-wide-web as database, and Google as search engine. The method is also applicable to other search engines and databases. This theory is then applied to construct a method to automatically extract similarity, the Google similarity distance, of words and phrases from the world-wide-web using Google page counts. The world-wide-web is the largest database on earth, and the context information entered by millions of independent users averages out to provide automatic semantics of useful quality. We give applications in hierarchical clustering, classification, and language translation. We give examples to distinguish between colors and numbers, cluster names of paintings by 17th century Dutch masters and names of books by English novelists, the ability to understand emergencies, and primes, and we demonstrate the ability to do a simple automatic English-Spanish translation. Finally, we use the WordNet database as an objective baseline against which to judge the performance of our method. We conduct a massive randomized trial in binary classification using support vector machines to learn categories based on our Google distance, resulting in an a mean agreement of 87% with the expert crafted WordNet categories.Comment: 15 pages, 10 figures; changed some text/figures/notation/part of theorem. Incorporated referees comments. This is the final published version up to some minor changes in the galley proof

The optimality of word lengths. Theoretical foundations and an empirical study

Zipf's law of abbreviation, namely the tendency of more frequent words to be shorter, has been viewed as a manifestation of compression, i.e. the minimization of the length of forms -- a universal principle of natural communication. Although the claim that languages are optimized has become trendy, attempts to measure the degree of optimization of languages have been rather scarce. Here we present two optimality scores that are dualy normalized, namely, they are normalized with respect to both the minimum and the random baseline. We analyze the theoretical and statistical pros and cons of these and other scores. Harnessing the best score, we quantify for the first time the degree of optimality of word lengths in languages. This indicates that languages are optimized to 62 or 67 percent on average (depending on the source) when word lengths are measured in characters, and to 65 percent on average when word lengths are measured in time. In general, spoken word durations are more optimized than written word lengths in characters. Our work paves the way to measure the degree of optimality of the vocalizations or gestures of other species, and to compare them against written, spoken, or signed human languages.Comment: On the one hand, the article has been reduced: analyses of the law of abbreviation and some of the methods have been moved to another article; appendix B has been reduced. On the other hand, various parts have been rewritten for clarity; new figures have been added to ease the understanding of the scores; new citations added. Many typos have been correcte