Flexible constrained sampling with guarantees for pattern mining

Pattern sampling has been proposed as a potential solution to the infamous pattern explosion. Instead of enumerating all patterns that satisfy the constraints, individual patterns are sampled proportional to a given quality measure. Several sampling algorithms have been proposed, but each of them has its limitations when it comes to 1) flexibility in terms of quality measures and constraints that can be used, and/or 2) guarantees with respect to sampling accuracy. We therefore present Flexics, the first flexible pattern sampler that supports a broad class of quality measures and constraints, while providing strong guarantees regarding sampling accuracy. To achieve this, we leverage the perspective on pattern mining as a constraint satisfaction problem and build upon the latest advances in sampling solutions in SAT as well as existing pattern mining algorithms. Furthermore, the proposed algorithm is applicable to a variety of pattern languages, which allows us to introduce and tackle the novel task of sampling sets of patterns. We introduce and empirically evaluate two variants of Flexics: 1) a generic variant that addresses the well-known itemset sampling task and the novel pattern set sampling task as well as a wide range of expressive constraints within these tasks, and 2) a specialized variant that exploits existing frequent itemset techniques to achieve substantial speed-ups. Experiments show that Flexics is both accurate and efficient, making it a useful tool for pattern-based data exploration.Comment: Accepted for publication in Data Mining & Knowledge Discovery journal (ECML/PKDD 2017 journal track

Mercury concentrations in plaice, flounder and dab from Belgian continental shelf waters (1971-1990)

Results obtained during a survey of 20 years on plaice (Pleuronectes platessa) and 15 years on flounder (Platichthys flesus) and dab (Limanda limanda) are reported. With flounder, two periods could be distinguished. In 1975-1981, higher mercury concentrations (0.38 mg/kg on average) with rather large variations were noted. From 1982 on, concentrations fluctuated around the same mean value (0.23 mg/kg). A gradual decrease of mercury levels in plaice was observed during the twenty years' monitoring period. The mean concentration in 1990 (0.06 mg/kg) was only one third of that of 1971 (0.18 mg/kg). In contrast with flounder and plaice, mercury concentrations in dab remained practically at the same level (0.09-0.13 mg/kg)

Trace metals in the Belgian dumping area for acid wastes from the titanium dioxide industry (1985-89)

During the period of investigation, two stations in the dumping site and six reference stations were monitored. In water and sediments only the iron content, a key parameter, was determined. In benthos, Fe, Cr, Ni, Zn, Pb, Cu and Cd were assessed. The iron content was very similar in both the dumping area and in five reference stations (0.06-0.08 mg/1). In the station nearest to the coast however, the concentrations were 2 to 3 times higher, showing the influence of river inputs. There was no temporal trend. A lack of dissolved oxygen was never observed and no marked differences between the eight areas were noted indicating that the oxidation of Fe++, the main component of the waste stream, had no measurable consequences in the water column. Abnormally low pH-values were not observed. In the sediments, no temporal trend in iron concentrations could be detected. No higher amounts were noted in the dumping area. The concentration of iron did not appear to be linked directly to the disposal of titanium dioxide waste but to input sources in general. The distance to the coast seems to play an important role. The iron content in the total mud fraction (<63 µm) decreased seawards (from ca 4.2 to 0.12 g/kg) up to about 20 nautical miles. In sea star (Asterias rubens), hermit crab (Pagurus bernhardus), swimming crab (Macropipus holsatus) brittle star (Ophiura texturata) and cut trough shell (Spisula subtruncata), there was neither a clear temporal trend nor evidence of accumulation of metals due to the dumping of titanium dioxide waste. Nevertheless, large amounts of heavy metals associated with particulate matter can be carried over long distances before being deposited. For this reason, all dumpings were banned since 1990