By Suykens J.

• dangers of classical neural nets• SVM homes and conventional SVM classifier• comparable kernelbased studying tools• Use of the "kernel trick" (Mercer Theorem)• LS-SVMs: extending the SVM framework• in the direction of a subsequent iteration of universally acceptable models?• the matter of studying and generalization

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An epistemological crisis and a plausible solution 21 psychic operations. As noted, the operation of inversion, in combination with the operation of bounding, yields the affectual content of the fourth, and determines the particulars of its usage, and the same operation of inversion in combination with some unspecified operation we might provisionally term "thirdness" yields the very different affectual content of the sixth and the particulars of its usage. Again, one might (justifiably) object that Schenker never develops an ars combinatoria ofpsychic operations sufficiently for it to stand truly as a theory of musical perception.

Schenker, rereading Chopin's passage, does not deny the affect of the sequence of fifths. The same psychological friction he attempts to explain in Counterpoint I through the immediate repetition of the psychic operation prompted by the fifth clearly prompts his reading of immediate condensations in Free Composition. In fact, the latter work even preserves the distinction drawn in the former between the psychological content respectively of the fifth and the octave: Schenker encloses the concluding section of the mazurka within parallel dt—cf motions, indicating with the figure"8- -8"that there is no question of these octaves being displaced into any sort of dissonance-consonance formation.

This rethinking of the agenda and methodologies of music theory would promise potentially more than a clear appeal to scientific prestige. Most immediately, it would loosen theory from its pedagogical or prescriptive antecedents (a sort of theory destined not to make its appearance until mid-century), and could thus make strong claims to disciplinary priority, could situate itself anterior to both composition and the history of music. )32 In other words, ourfictionalSchenker could assert his theory as the same sort of master-discourse for music as does the historical Schenker (or at least the Schenker of Free Composition).

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A short Introduction to Support Vector Machines and Kernelbased Learning by Suykens J.

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