A survey on pre-processing techniques: Relevant issues in the context of environmental data mining <s> Structure of original data matrix <s> Compositional data consisting of vectors of positive components subject to a unit-sum constraint arise in many disciplines, for example in geology as majoroxide compositions of rocks, in economics as budget share patterns of household expenditures, in medicine as compositions of renal calculi, in psychology as activity patterns of subjects. 'Standard' multivariate techniques, designed for unconstrained data, are wholly inappropriate and uninterpretable for such data and yet are still being commonly misapplied. Recognition that the study of compositions must satisfy simple principles has led recently to the advocacy of new forms of analysis of compositional data. The nature of the absurdities arising from applying traditional multivariate techniques to compositions is briefly highlighted and a description of the essential aspects and the advantages of the new methodology is provided. <s> BIB001 </s> A survey on pre-processing techniques: Relevant issues in the context of environmental data mining <s> Structure of original data matrix <s> The Millennium Development Goals set the target to “halve by 2015 the proportion of people without sustainable access to safe drinking water and basic sanitation”. The current international definition of indicators of access is insufficient for measuring this target. Furthermore, the lack of an internationally agreed definition and measurement methodology is causing confusion and uncertainty regarding the figures that are disseminated worldwide. Moreover, the current context, in which almost 70% of funds for the sector are channelled through national governments, emphasises the importance of a monitoring system for national water sectors in developing countries. From this, an improvement in investment efficiency is expected. The water point mapping methodology, promoted and widely developed by the international organization WaterAid, is presented as an alternative way of defining water access indicators. The present paper describes its potential for defining new indicators and making improvements. Our research is based on the results of a pilot study carried out by Ingenieria Sin Fronteras (Engineering without Borders, Spain) in the Same district, Tanzania. The paper concludes with a discussion of the challenges posed by the implementation of this methodology and proposes further steps for improvement. <s> BIB002
In the classical data mining applications, the original data matrix is a two-dimensional table containing n rows representing the set I of n observations (also named individuals or instances) and K columns, which are the variables used to describe the observations. In cell (i, k), i = 1 : n, k = 1 : K, the value of variable X_k observed for object i is registered, x ik . Usually, these data matrices can be represented in plain text files or CSV formats. Variables are in columns, and can be numerical (like pressures, concentrations of pollutants, depths, etc.), ordinal (level of risk of fire in a forest), binary (presence of certain microorganism in water, dangerous levels of a certain pollutant in air, etc.) or qualitative with more than two modalities (color of algae, type or eruption in a volcano, etc.). Along this paper, the terminology used to refer to both the variables and observations of the usual twodimensional data matrix changes according to the most usual term used in the concrete field of study providing the different pre-processing techniques (i.e., statistics, machine learning, etc.). Therefore, in the text, we refer to a variable with the following words: feature, attribute, property or data column. Likewise, we refer to an observation with the following words: instance, example, object or data row. Eventually, when observations are taken along the time, one of the variables is the timestamp, which can be expressed in any date format, and requires attention to ensure it is properly interpreted by the software. Also, when observations are linked to a specific location, some variables giving geographical information may appear, like Cs radioactivity measures in points of a surrounding area of a nuclear plant. They could refer to 2D or 3D spatial information. In 2D situations, each geographical position is determined by a pair of values, like latitude and longitude values, a pair of UTM coordinates, etc. [31] . In the case of 3D, in addition to the pair of coordinates, an additional elevation or deep value is provided. This data is relevant for territorial graphical models where geographical areas are identified with the same coordinates. Then, data can be visualized over digital maps, by using this information as Gibert pointers to particular map areas, to visualize or induce some spatial predictive model. In this paper two special cases of subsets of related variables that require special pre-processing are also considered: multivalued qualitative variables and compositional data, both common in ESs. Multivalued qualitative variables are qualitative variables that can have several values simultaneously. This is the case, for example, of the water access technologies available in cities. Imagine a data matrix containing one city per row. The qualitative variable water access technology can take a set of possible values (for example, gravity water service, pump water services, well water services and call water services) BIB002  . As the same city can have different districts with different access technologies, this variable is taking a list of values (technologies) in each city. Formally, it corresponds to the case where the corresponding cell of the data matrix is a vector of modalities. As this would not be manageable in a classical data mining software, it is usual to represent each of the modalities as a binary variable and report a Boolean for each city, by indicating whereas the city has households with gravity water services or not, pump water services or not and so on. Thus, for a multivalued variable with s modalities, a set of s binary variables will be used, which is different from dummy variables, as here, more than one can be true simultaneously. Finally, compositional data are sets of s strictly positive real variables with constant sum Z > 0  . Z is generally 100 (percentage) or 1 (proportion). This implies the existence of a linear relationship among the s variables, with implications in the results of the data mining process, particularly when methods assuming independence of variables are used. This is the case, for example, of geochemical composition of rocks, composition of sediments in rivers, sources of pollution in a lake, land use composition, waste/wastewater composition, among others BIB001 .