On Macroscopic Complexity and Perceptual Coding

The theoretical limits of 'lossy' data compression algorithms are considered. The complexity of an object as seen by a macroscopic observer is the size of the perceptual code which discards all information that can be lost without altering the perception of the specified observer. The complexity of this macroscopically observed state is the simplest description of any microstate comprising that macrostate. Inference and pattern recognition based on macrostate rather than microstate complexities will take advantage of the complexity of the macroscopic observer to ignore irrelevant noise

A Compression Technique Exploiting References for Data Synchronization Services

Department of Computer Science and EngineeringIn a variety of network applications, there exists significant amount of shared data between two end hosts. Examples include data synchronization services that replicate data from one node to another. Given that shared data may have high correlation with new data to transmit, we question how such shared data can be best utilized to improve the efficiency of data transmission. To answer this, we develop an encoding technique, SyncCoding, that effectively replaces bit sequences of the data to be transmitted with the pointers to their matching bit sequences in the shared data so called references. By doing so, SyncCoding can reduce data traffic, speed up data transmission, and save energy consumption for transmission. Our evaluations of SyncCoding implemented in Linux show that it outperforms existing popular encoding techniques, Brotli, LZMA, Deflate, and Deduplication. The gains of SyncCoding over those techniques in the perspective of data size after compression in a cloud storage scenario are about 12.4%, 20.1%, 29.9%, and 61.2%, and are about 78.3%, 79.6%, 86.1%, and 92.9% in a web browsing scenario, respectively.ope

Conditional Complexity of Compression for Authorship Attribution

We introduce new stylometry tools based on the sliced conditional compression complexity of literary texts which are inspired by the nearly optimal application of the incomputable Kolmogorov conditional complexity (and presumably approximates it). Whereas other stylometry tools can occasionally be very close for different authors, our statistic is apparently strictly minimal for the true author, if the query and training texts are sufficiently large, compressor is sufficiently good and sampling bias is avoided (as in the poll samplings). We tune it and test its performance on attributing the Federalist papers (Madison vs. Hamilton). Our results confirm the previous attribution of Federalist papers by Mosteller and Wallace (1964) to Madison using the Naive Bayes classifier and the same attribution based on alternative classifiers such as SVM, and the second order Markov model of language. Then we apply our method for studying the attribution of the early poems from the Shakespeare Canon and the continuation of Marlowe’s poem ‘Hero and Leander’ ascribed to G. Chapman.compression complexity, authorship attribution.

Data Discovery and Anomaly Detection Using Atypicality: Theory

A central question in the era of 'big data' is what to do with the enormous amount of information. One possibility is to characterize it through statistics, e.g., averages, or classify it using machine learning, in order to understand the general structure of the overall data. The perspective in this paper is the opposite, namely that most of the value in the information in some applications is in the parts that deviate from the average, that are unusual, atypical. We define what we mean by 'atypical' in an axiomatic way as data that can be encoded with fewer bits in itself rather than using the code for the typical data. We show that this definition has good theoretical properties. We then develop an implementation based on universal source coding, and apply this to a number of real world data sets.Comment: 40 page

Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts published in a same volume. Part II is dedicated to the relation between logic and information system, within the scope of Kolmogorov algorithmic information theory. We present a recent application of Kolmogorov complexity: classification using compression, an idea with provocative implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses how Kolmogorov complexity, besides being a foundation to randomness, is also related to classification. Another approach to classification is also considered: the so-called "Google classification". It uses another original and attractive idea which is connected to the classification using compression and to Kolmogorov complexity from a conceptual point of view. We present and unify these different approaches to classification in terms of Bottom-Up versus Top-Down operational modes, of which we point the fundamental principles and the underlying duality. We look at the way these two dual modes are used in different approaches to information system, particularly the relational model for database introduced by Codd in the 70's. This allows to point out diverse forms of a fundamental duality. These operational modes are also reinterpreted in the context of the comprehension schema of axiomatic set theory ZF. This leads us to develop how Kolmogorov's complexity is linked to intensionality, abstraction, classification and information system.Comment: 43 page