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Data integration involves combining data residing in different sources and providing users with a unified view of them. This process becomes significant in a variety of situations, which include both commercial (such as when two similar companies need to merge their databases) and scientific (combining research results from different bioinformatics repositories, for example) domains. Data integration appears with increasing frequency as the volume (that is, big data) and the need to share existing data explodes. It has become the focus of extensive theoretical work, and numerous open problems remain unsolved. Data integration encourages collaboration between internal as well as external users. The data being integrated must be received from a heterogeneous database system and transformed to a single coherent data store that provides synchronous data across a network of files for clients. A common use of data integration is in data mining when analyzing and extracting information from existing databases that can be useful for Business information. Issues with combining heterogeneous data sources are often referred to as information silos, under a single query interface have existed for some time. In the early 1980s, computer scientists began designing systems for interoperability of heterogeneous databases. The first data integration system driven by structured metadata was designed at the University of Minnesota in 1991, for the Integrated Public Use Microdata Series (IPUMS). IPUMS used a data warehousing approach, which extracts, transforms, and loads data from heterogeneous sources into a unique view schema so data from different sources become compatible. By making thousands of population databases interoperable, IPUMS demonstrated the feasibility of large-scale data integration. The data warehouse approach offers a tightly coupled architecture because the data are already physically reconciled in a single queryable repository, so it usually takes little time to resolve queries.
[2]Paolo Prandoni, [3]LCAV, EPFL
The concept of "basis" for a vector space is one of the most profound
and fruitful ideas in linear algebra. Basis vectors are the "building
blocks" that all other vectors are built from; by "disassembling" a
vector into a linear combination of basis elements we are able to "look
inside" the vector and highlight many of its relevant features.
A vector space has an infinite number o