By Hermann Moisl
The swiftly becoming quantity of electronic usual language textual content and the complexity of information abstracted from it have more and more rendered conventional corpus linguistic analytical technique out of date. This e-book describes a cluster analytic technique for producing linguistic hypotheses at the foundation of information abstracted from language corpora.
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A desktop computer can, for example, be described in terms of its role in an the administrative structure of an organization, its physical appearance, its hardware components, the functionality of the software installed on it, the programs which implement that functionality, the design of the chips on the circuit board, or the atomic and subatomic characteristics of the transistors on the chips, not to speak of its connectivity to the internet or its social and economic impact on the world at large.
This section first presents a few relevant mathematical and geometrical concepts and then shows how data can be represented and interpreted in terms of them. 1 Space In colloquial usage, the word ‘space’ denotes a fundamental aspect of how humans understand their world: that we live our lives in a three-dimensional space, that there are directions in that space, that distances along those directions can be measured, that relative distances between and among objects in the space can be compared, that objects in the space themselves have size and shape which can be measured and described.
2) where, in multiplication of a vector by a scalar, each component of the vector is multiplied by the scalar, and in vector addition corresponding components are added. For example, take V to be based on a twofold Cartesian product A = R × R of the set of real numbers ℝ. 8], adopting the convention that vectors are shown between square brackets and components are comma-separated. 5 then shows some linear combinations of v1 and v2, using randomly selected s-values. 9 . . 42] . . 5 that every different combination of scalars s1 and s2 results in a different vector generated from v1 and v2, and, because there is no constraint on the choice of scalars, there is correspondingly no constraint on the number of vectors than can be generated in this way.