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Natural Language Processing (NLP) Methods for Cognitive IoT Systems
Published in Pethuru Raj, Anupama C. Raman, Harihara Subramanian, Cognitive Internet of Things, 2022
Pethuru Raj, Anupama C. Raman, Harihara Subramanian
To process and pre-process the text, words, and documents, use text or word normalization methods in the NLP. Such procedures are usually used for the correct text (words or speech) interpretation to acquire more accurate NLP models.Context-independent normalization: removing non-alphanumeric text symbols.Canonicalization: convert data to “standard”, “normal”, or canonical form.Stemming: extracts the word’s root.Lemmatization: transforms word to its lemma.
Canonical Forms
Published in Leslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias, Handbook of Linear Algebra, 2006
A canonical form of a matrix is a special form with the properties that every matrix is associated to a matrix in that form (the canonical form of the matrix), it is unique or essentially unique (typically up to some type of permutation), and it has a particularly simple form (or a form well suited to a specific purpose). A canonical form partitions the set matrices in Fm×n into sets of matrices each having the same canonical form, and that canonical form matrix serves as the representative. The canonical form of a given matrix can provide important information about the matrix. For example, reduced row echelon form (RREF) is a canonical form that is useful in solving systems of linear equations; RREF partitions Fm×n into sets of row equivalent matrices.
Unimodular equivalence and similarity for linear systems
Published in International Journal of Control, 2019
Dimitris Vafiadis, Nicos Karcanias
In the theory of canonical forms under similarity, the canonical representation is related to the denominator matrix of the echelon canonical form of the composite matrix of the MFD of the i.s.t.f. (Forney, 1975; Kailath, 1980; Popov, 1969) . The strict properness of a state-space system (A, B) ensures that when T(s) is in echelon form, D(s) is also in echelon form and vice versa. Then, the so-called Popov parameters (Kailath, 1980; Popov, 1972), of the canonical representation, are directly related to the echelon form of D(s). Actually they are the coefficients of the polynomial entries of the latter polynomial matrix. This is the controllable canonical form (Kailath, 1980) and it can be obtained by any of the i.s.t.f. corresponding to the orbit of the systems related by similarity. Each one member of the equivalence class of the system (A, B) has its uniquely defined corresponding minimal composite matrix T(s) in echelon form, since the composite matrix is a basis matrix of the right null space of the controllability pencil (recall that [sI − A, −B]T(s) = 0, T(s) is a minimal basis and [sI − A, −B] has full row rank). All the echelon composite matrices share the same denominator and differ on the numerators as shown in the following:
Petri net models for Physarum machines built to realise Boolean functions
Published in International Journal of Parallel, Emergent and Distributed Systems, 2018
Boolean functions are a powerful mathematical tool used in different areas of electronics and computer science, e.g. for designing digital circuits, computer systems, control systems, reasoning systems, etc. In general, they describe relationships between entities with binary states. The theory of Boolean functions is well established. Each Boolean function can be written in one of its two canonical forms, a disjunctive canonical form or a conjunctive canonical form. Both of canonical forms are equivalent. Moreover, each canonical form can be minimised to simplify a device realising a Boolean function. Basics of Boolean functions are briefly recalled in Section 2.1.