Relaxed Functional Dependencies - A Survey of Approaches

Recently, there has been a renovated interest in functional dependencies due to the possibility of employing them in several advanced database operations, such as data cleaning, query relaxation, record matching, and so forth. In particular, the constraints defined for canonical functional dependencies have been relaxed to capture inconsistencies in real data, patterns of semantically related data, or semantic relationships in complex data types. In this paper, we have surveyed 35 of such functional dependencies, providing a classification criteria, motivating examples, and a systematic analysis of them

Characterization of order-like dependencies with formal concept analysis

Functional Dependencies (FDs) play a key role in many fields of the relational database model, one of the most widely used database systems. FDs have also been applied in data analysis, data quality, knowl- edge discovery and the like, but in a very limited scope, because of their fixed semantics. To overcome this limitation, many generalizations have been defined to relax the crisp definition of FDs. FDs and a few of their generalizations have been characterized with Formal Concept Analysis which reveals itself to be an interesting unified framework for charac- terizing dependencies, that is, understanding and computing them in a formal way. In this paper, we extend this work by taking into account order-like dependencies. Such dependencies, well defined in the database field, consider an ordering on the domain of each attribute, and not sim- ply an equality relation as with standard FDs.Peer ReviewedPostprint (published version

Survey on Combinatorial Register Allocation and Instruction Scheduling

Register allocation (mapping variables to processor registers or memory) and instruction scheduling (reordering instructions to increase instruction-level parallelism) are essential tasks for generating efficient assembly code in a compiler. In the last three decades, combinatorial optimization has emerged as an alternative to traditional, heuristic algorithms for these two tasks. Combinatorial optimization approaches can deliver optimal solutions according to a model, can precisely capture trade-offs between conflicting decisions, and are more flexible at the expense of increased compilation time. This paper provides an exhaustive literature review and a classification of combinatorial optimization approaches to register allocation and instruction scheduling, with a focus on the techniques that are most applied in this context: integer programming, constraint programming, partitioned Boolean quadratic programming, and enumeration. Researchers in compilers and combinatorial optimization can benefit from identifying developments, trends, and challenges in the area; compiler practitioners may discern opportunities and grasp the potential benefit of applying combinatorial optimization

Cosmological Systematics Beyond Nuisance Parameters : Form Filling Functions

In the absence of any compelling physical model, cosmological systematics are often misrepresented as statistical effects and the approach of marginalising over extra nuisance systematic parameters is used to gauge the effect of the systematic. In this article we argue that such an approach is risky at best since the key choice of function can have a large effect on the resultant cosmological errors. As an alternative we present a functional form filling technique in which an unknown, residual, systematic is treated as such. Since the underlying function is unknown we evaluate the effect of every functional form allowed by the information available (either a hard boundary or some data). Using a simple toy model we introduce the formalism of functional form filling. We show that parameter errors can be dramatically affected by the choice of function in the case of marginalising over a systematic, but that in contrast the functional form filling approach is independent of the choice of basis set. We then apply the technique to cosmic shear shape measurement systematics and show that a shear calibration bias of |m(z)|< 0.001(1+z)^0.7 is required for a future all-sky photometric survey to yield unbiased cosmological parameter constraints to percent accuracy. A module associated with the work in this paper is available through the open source iCosmo code available at http://www.icosmo.org .Comment: 24 pages, 18 figures, accepted to MNRA

Characterizing approximate-matching dependencies in formal concept analysis with pattern structures

Functional dependencies (FDs) provide valuable knowledge on the relations between attributes of a data table. A functional dependency holds when the values of an attribute can be determined by another. It has been shown that FDs can be expressed in terms of partitions of tuples that are in agreement w.r.t. the values taken by some subsets of attributes. To extend the use of FDs, several generalizations have been proposed. In this work, we study approximatematching dependencies that generalize FDs by relaxing the constraints on the attributes, i.e. agreement is based on a similarity relation rather than on equality. Such dependencies are attracting attention in the database field since they allow uncrisping the basic notion of FDs extending its application to many different fields, such as data quality, data mining, behavior analysis, data cleaning or data partition, among others. We show that these dependencies can be formalized in the framework of Formal Concept Analysis (FCA) using a previous formalization introduced for standard FDs. Our new results state that, starting from the conceptual structure of a pattern structure, and generalizing the notion of relation between tuples, approximate-matching dependencies can be characterized as implications in a pattern concept lattice. We finally show how to use basic FCA algorithms to construct a pattern concept lattice that entails these dependencies after a slight and tractable binarization of the original data.Postprint (author's final draft

Geometric Multi-Model Fitting with a Convex Relaxation Algorithm

We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by minimising the energy of the overall classification. Our approach is similar to state-of-the-art energy minimisation techniques which use a global energy. However, we deal with the scaling factor (as the number of models increases) of the original combinatorial problem by relaxing the solution. This relaxation brings two advantages: first, by operating in the continuous domain we can parallelize the calculations. Second, it allows for the use of different metrics which results in a more general formulation. We demonstrate the versatility of our technique on two different problems of estimating structure from images: plane extraction from RGB-D data and homography estimation from pairs of images. In both cases, we report accurate results on publicly available datasets, in most of the cases outperforming the state-of-the-art

On the Effect of Semantically Enriched Context Models on Software Modularization

Many of the existing approaches for program comprehension rely on the linguistic information found in source code, such as identifier names and comments. Semantic clustering is one such technique for modularization of the system that relies on the informal semantics of the program, encoded in the vocabulary used in the source code. Treating the source code as a collection of tokens loses the semantic information embedded within the identifiers. We try to overcome this problem by introducing context models for source code identifiers to obtain a semantic kernel, which can be used for both deriving the topics that run through the system as well as their clustering. In the first model, we abstract an identifier to its type representation and build on this notion of context to construct contextual vector representation of the source code. The second notion of context is defined based on the flow of data between identifiers to represent a module as a dependency graph where the nodes correspond to identifiers and the edges represent the data dependencies between pairs of identifiers. We have applied our approach to 10 medium-sized open source Java projects, and show that by introducing contexts for identifiers, the quality of the modularization of the software systems is improved. Both of the context models give results that are superior to the plain vector representation of documents. In some cases, the authoritativeness of decompositions is improved by 67%. Furthermore, a more detailed evaluation of our approach on JEdit, an open source editor, demonstrates that inferred topics through performing topic analysis on the contextual representations are more meaningful compared to the plain representation of the documents. The proposed approach in introducing a context model for source code identifiers paves the way for building tools that support developers in program comprehension tasks such as application and domain concept location, software modularization and topic analysis