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Clustering the data generate data groups, the groups considered classes.
Algorithm Attribute Reduction of Raw Data Suppose U is the entire data domain, Ui is the ith element in U, i∈ 1,2,3 ...
After removing certain "problem data", we obtained 94 groups of original data.
Some samples of input data C No.
DATA,2007,1-2:31-33

The data suggested that copper (II) was reduced and the resulting copper (I) complexed, with both reactions probably mediated by sulfur oxy-anions produced indirectly by the bacteria, in the anoxic sulfur column bioreactors.
Chemical reduction and complexation of copper.
Results and Discussion Performance of the iron reduction system.
Theory of reduction of copper (II) and complexation of copper (I).
Conclusions A two-stage bio-reductive process for recovering copper from PLS, devised and tested at the laboratory scale, generated interesting and unexpected data.

According to reduction-factors of shear strength indexes, cohesion C and angle of internal friction j, SRM is classified into two types, single reduction-factor method that reduction-factors of the two indexes are same and two reduction-factors method that reduction-factors are different.
The computed results of 9 different reduction conditions by FLAC SRM and SRSM are listed in table 1, where the 6th reduction condition is just single reduction-factor method, and errors mean the difference of two reduction-factors obtained by FLAC SRM and SRSM.
Table 1 Reduction conditions and reduction-factors computed by FLAC SRM and SRSM Number Reduction condition Two reductoin-factors Error [%] Single reduction-factor FLAC SRM SRSM 1 Only C is reduceed, i.e the 1st pattern.
As shown in table 1, these can be seen as follows: (1) under the different conditions, values of two reduction-factors of C and j are not completely equal obtained by either of FLAC SRM and SRSM, so safety margin of the two indexes should not be same; (2) values of two reduction-factors obtained by FLAC SRM and SRSM are rather close, small errors in which maximal data is only 2.04%; (3) two reduction-factors under the different conditions have regularity that with increase of n, SRF1 goes up, SRF2 goes down, and increase rate of SRF1 is more than decrease rate of SRF2; (4) all single reduction-factors F are more than the lowest safety factor Fmin=1.259 which is the value of the 6th reduction condition, and this illustrates that the every two reduction-factors condition is not the most dangerous in single reduction-factor case;(5) single reduction-factor method is only a special case among different reduction methods.
(4) Which reduction condition of two reduction-factors method is suitable for a specific slope?

Introduction The classification has been an important research topic in data mining, which aims at building a high-performance classifier to confirm the optimal class label of one or some specific data sets clearly [1].
This can improve the stability and accuracy of the algorithm and can be applied to more data sets.
The correct rate description is the percentage of the instance successfully predicted in the given test data sets and the given data sets. 10-fold cross-validation method is used in the test.
In this paper, attribute order is used to describe a set of data attributes and a weighted reduction based on attribute order Naive Bayes mining algorithms is proposed.
Data mining concepts and teachniques[M].Beijing：China Machine Press,2001:30-50

Introduction The theory of rough sets [1], proposed by Poland mathematician Pawlak in 1982, is a mathematical method to deal with insufficient and incomplete data.
It is a set-theory-based technique to handle data, that is, through the known information to approximately describe the uncertainty concept [2, 3].
Reduction of Multi-covering Information System and Consistent Decision System Reduction of multi-covering information system.
Then we study the reduction of this case.
Pawlak, Rough sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, boston,1991

The data indicate that both cultures are able to reduce soluble iron(III) by oxidation of sulfur compounds under anaerobic conditions.
A significant pH drop from 1.8 to ~1.2 indicated oxidation of sulfur compounds to sulfuric acid in all the tested assays (data not shown).
Table 1 summarizes the data for pressure effects on growth and iron(III) reduction by the enrichment culture TK65.
When the pressure increased from 1 bar to 100 bar, cell growth was inhibited by 27 up to 39% as indicated by direct cell counts and qPCR data.
Iron(II) ions (mM) Cell count (/mL) Gene copy number (/mL) S0, 1 bar 27 1×109 5×109 S0, 100 bar 20 8×108 3×109 Summary The data show that mesophilic and thermophilic acidophiles are able to reduce soluble iron(III) by oxidation of sulfur compounds under anaerobic conditions at 100 bar.

From the ring-disc data and other kinetic parameters it has been assumed that the oxygen reduction occurs by dissociative chemisorption at low overpotentials.
Id data used for these plots were corrected from mass transfer interference using the procedure described by Gojkovic et al
Plots of Id/Ir vs. ω-1/2 obtained from the experimental data of the present study for the LBM catalyst at various electrode potentials have been drawn (Fig. 4).
But in view of the present RRDE data in which one observes that the end product depends on the applied potential, it has been assumed that the HO2 ion maintains an adsorption-desorption equilibrium and this equilibrium constant may be dependent on the potential of the electrode.
Suggested model for O2 reduction in KOH solution.

For the mixture, the experimental TG-DSC curves of mixture are compared with the calculated weighted sum, which is the sum of the TGA-DSC data of pure iron ores and biomass according to their weighting percentages, shown in Fig. 2 (b).
It is clear that the experimental data of the mixture is almost consistent with the calculated weight sum before 450 oC, mainly relating to the remove of the water combined in the iron ores.
Thereby, we could conclude that the other components in the iron ores have somewhat effect on the pyrolysis of the biomass, which leads to the difference between the experimental data and the calculated results.
The reduction of goethite ores was conducted in a lab-scale reactor.
Valix, Reduction roasting of limonite ores: effect of dehydroxylation, Int.

Some attributes of data lose in the course of data collection due to the abnormal work of the terminals.
The incompleteness of data brings tremendous difficulties to data fusion and data mining, impeding the development of computer application, especially the Internet of Things.
After getting attribute reduction, the paper improves the method for filling incomplete data based on similarity to fill the important attribute of the incomplete data.
Conclusion With rapid development of the Internet of Things, a large number of collected data are incomplete, which brings difficult to data mining and data fusion and a serious impediment to the application of the Internet of Things data.
Study on data reduction algorithm based on rough set[J]. 2011,23(7):405-413

The structural effect value were 0.99% and -1.91% respectively, namely the breeding structure does not promote the COD discharge reduction but benefits NH4-N discharge reduction.
According to dynamically updated data from national census of pollution sources, the discharge of Chemical Oxygen Demand (COD) and ammonia nitrogen (NH4-N) of China’s livestock and poultry industry in 2010 were 11.48 million tons and 0.65 million tons respectively, which account for 45% and 25% of the total discharge of the country, and 95% and 79% of the total discharge of agricultural source.
Method and Data The pollutants discharge of large-scale livestock and poultry farms has been analyzed based on the hierarchical decomposition methods.
(8) (9) 1.2 Data source illustration and data processing The data used in the model for calculating breeding quantity and pollutant discharge is derived from 2010-2013 environmental statistics.
Structure effect presents an obvious affection on NH4-N discharge reduction of livestock and poultry breeding industry, but fails in COD reduction.