259 research outputs found

    Fuzzy Interval-Valued Multi Criteria Based Decision Making for Ranking Features in Multi-Modal 3D Face Recognition

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    Soodamani Ramalingam, 'Fuzzy interval-valued multi criteria based decision making for ranking features in multi-modal 3D face recognition', Fuzzy Sets and Systems, In Press version available online 13 June 2017. This is an Open Access paper, made available under the Creative Commons license CC BY 4.0 https://creativecommons.org/licenses/by/4.0/This paper describes an application of multi-criteria decision making (MCDM) for multi-modal fusion of features in a 3D face recognition system. A decision making process is outlined that is based on the performance of multi-modal features in a face recognition task involving a set of 3D face databases. In particular, the fuzzy interval valued MCDM technique called TOPSIS is applied for ranking and deciding on the best choice of multi-modal features at the decision stage. It provides a formal mechanism of benchmarking their performances against a set of criteria. The technique demonstrates its ability in scaling up the multi-modal features.Peer reviewedProo

    A kernel-based framework for learning graded relations from data

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    Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are often expressed in a graded manner in real-world applications. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and graded relations are considered, and it unifies existing approaches because different types of graded relations can be modeled, including symmetric and reciprocal relations. This framework establishes important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated through various experiments on synthetic and real-world data.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

    Comparison Structure Analysis

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    This study presents an automatic, computer-aided analytical method called Comparison Structure Analysis (CSA), which can be applied to different dimensions of music. The aim of CSA is first and foremost practical: to produce dynamic and understandable representations of musical properties by evaluating the prevalence of a chosen musical data structure through a musical piece. Such a comparison structure may refer to a mathematical vector, a set, a matrix or another type of data structure and even a combination of data structures. CSA depends on an abstract systematic segmentation that allows for a statistical or mathematical survey of the data. To choose a comparison structure is to tune the apparatus to be sensitive to an exclusive set of musical properties. CSA settles somewhere between traditional music analysis and computer aided music information retrieval (MIR). Theoretically defined musical entities, such as pitch-class sets, set-classes and particular rhythm patterns are detected in compositions using pattern extraction and pattern comparison algorithms that are typical within the field of MIR. In principle, the idea of comparison structure analysis can be applied to any time-series type data and, in the music analytical context, to polyphonic as well as homophonic music. Tonal trends, set-class similarities, invertible counterpoints, voice-leading similarities, short-term modulations, rhythmic similarities and multiparametric changes in musical texture were studied. Since CSA allows for a highly accurate classification of compositions, its methods may be applicable to symbolic music information retrieval as well. The strength of CSA relies especially on the possibility to make comparisons between the observations concerning different musical parameters and to combine it with statistical and perhaps other music analytical methods. The results of CSA are dependent on the competence of the similarity measure. New similarity measures for tonal stability, rhythmic and set-class similarity measurements were proposed. The most advanced results were attained by employing the automated function generation – comparable with the so-called genetic programming – to search for an optimal model for set-class similarity measurements. However, the results of CSA seem to agree strongly, independent of the type of similarity function employed in the analysis.Tämä tutkimus esittelee uuden musiikkianalyyttisen metodin, vertailurakenneanalyysin (VRA, engl. Comparison Structure Analysis, CSA), jonka avulla voidaan analysoida musiikin eri ulottuvuuksia, kuten harmoniaa tai rytmiä. VRA:n ideana on mitata tietyn ennalta valitun musiikillisen rakenteen, vaikkapa jonkin sävelasteikon, vallitsevuutta musiikin kullakin ajanhetkellä. Tämä edellyttää kolmea asiaa. Ensiksi, intuitiivisesti tai muulla tavoin valittu musiikillinen piirre, jota tässä kutsutaan yleisesti vertailurakenteeksi, on esitettävä matemaattisessa muodossa, esimerkiksi matemaattisen avaruuden vektorina. Vertailurakenne voidaan muodostaa myös useiden eri tyyppisten, musiikin eri ulottuvuuksiin liittyvien tietorakenteiden yhdistelmänä. Toiseksi, analysoitava musiikillinen data, esimerkiksi musiikista muodostetut sävelluokat (C:stä H:hon), on pystyttävä ryhmittelemään vastaavantyyppisiksi objekteiksi. Lisäksi tarvitaan vielä matemaattinen funktio, joka kykenee mittaamaan valitun vertailurakenteen ja musiikista ryhmiteltyjen segmenttien välistä samankaltaisuutta tai vastaavasti, etäisyyttä. Toisin sanoen, VRA:ssa verrataan valittua vertailurakennetta, esimerkiksi diatonista asteikkoa, kaikkiin musiikista segmentoituihin vastaavantyyppisiin objekteihin. Mittaustulokset saadaan lukuarvoina yleensä välillä 0–1, jossa arvo 1 voi – mittausfunktion luonteesta riippuen – tarkoittaa joko täydellistä samankaltaisuutta tai suurinta mahdollista etäisyyttä. Havainnollisena analyysin kohteena voisimme kuvitella länsimaista taidemusiikkia edustavan sävellyksen, jossa siirrytään keskiaikaisesta diatonisesta musiikista historiallisesti ja tyylillisesti kohti 1900-luvun atonaalista musiikkia. Mikäli tässä tapauksessa vertailurakenteena käytettäisiin mainittua diatonista asteikkoa, VRA paljastaisi musiikissa korvinkin havaittavan ei-diatonisoitumisen. Tulosten esittämisellä esimerkiksi ajallisia muutoksia esittävin mittauskäyrin tai luokittelua havainnollistavin keskiarvopistein on merkittävä asema analyysissa. VRA sijoittuu perinteisen musiikkianalyysin ja tietokonetta hyödyntävien musiikin sisältöhakuun (music information retrieval, MIR) keskittyvien tekniikoiden välimaastoon. Sen avulla voidaan tunnistaa ja mitata perinteiselle musiikkianalyysille tyypillisia kohteita kuten karakteristisia rytmejä, sävelluokkajoukkoja, joukkoluokkia, tonaliteetteja ja käänteiskontrapunkteja soveltamalla MIR:lle tyypillisiä segmentointi- ja vertailualgoritmeja. Vertailurakenneanalyysin suurimmaksi haasteeksi on osoittautunut musiikillisten segmenttien muodostamiseen tarvittavan automaattisen algoritmin kehittäminen. Voidaan näet osoittaa, että sama musiikillinen data on useimmiten mahdollista segmentoida – musiikillisesti mielekkäästi – monella eri tavalla. Silloin, kun kyse on harmoniaan liittyvistä objekteista, tehtävä on erityisen haastava, sillä tällöin musiikin säveltapahtumia joudutaan tarkastelemaan niin ajallisessa kuin vertikaalisessakin suunnassa. Musiikin tonaalisuudessa ja sävelluokkasisällössä tapahtuvien muutosten analysoimista varten tässä tutkimuksessa kehitettiinkin kaksi erilaista segmentointialgoritmia, jotka muodostavat musiikillisesta datasta osin limittäisiä sävelluokkajoukkoja. Metodien erilaisuudesta huolimatta ‘herkkyysanalyysillä’ voitiin osoittaa, että molemmat menetelmät ovat hyvin vähän riippuvaisia syötetyn datan luonteesta; niiden avulla saadut tulokset olivat hyvin samankaltaisia. VRA:lla saatuja tuloksia voidaan edelleen tarkastella myös tilastollisen merkitsevyyden näkökulmasta. Koska VRA:lla pystytään havaitsemaan musiikin eri dimensioissa tapahtuvia muutoksia, tämän johdannaisena voidaan tutkia myös sitä, missä määrin jokin sävellys on tyylillisesti koherentti verrattuna johonkin toiseen sävellykseen eli kummassa muutokset ovat tarkasteltavan ominaisuuden suhteen keskimäärin pienemmät ja kummassa suuremmat. Lisäksi VRA tarjoaa mahdollisuuden musiikin luokitteluun saatujen mittausarvojen perusteella: mitä enemmän musiikillisia parametrejä ja useampia vertailurakenteita analyysissa hyödynnetään, sitä tarkemmin sävellyksiä voidaan luokitella. Niinpä VRA:n keinoja voidaan tulevaisuudessa kuvitella käytettävän myös musiikin sisältöhakuun (MIR). Tällaisessa tapauksessa vertailurakenne tai -rakenteet voitaisiin ‘laskea’ musiikillisesta datasta suoraan jollakin matemaattisella menetelmällä – kuten pääkomponenttianalyysilla – etukäteen suoritettavan intuitiivisen valinnan sijaan. Tutkimuksen tuloksiin lukeutuvat myös useat VRA:n tarpeisiin kehitetyt samankaltaisuusmittarit. Näistä mielenkiintoisin lienee sävelluokkajoukkojen välisen samankaltaisuuden mittaamiseen kehitetty funktio expcos, joka löytyi ns. geneettisen ohjelmoinnin avulla. Mainitussa kokeessa tietokoneella generoitiin arviolta n. 800 000 samankaltaisuusmittaria, joiden tuottamia tuloksia verrattiin ihmisten tekemiin samankaltaisuusarvioihin. Niistä n. 450 osoittautui käyttökelpoiseksi. Sensitiivisyysanalyysi osoitti, että em. funktio paitsi korreloi voimakkaammin empiiristen samankaltaisuusarvioiden kanssa, on VRA:ssa myös robustimpi kuin kenties tunnetuin samaan tarkoitukseen kehitetty funktio, REL (David Lewin, 1980). Käytännössä tällä ei ole kuitenkaan merkitystä: REL toimii VRA:ssa aivan yhtä hyvin kuin expcos. VRA:n avulla musiikkia tarkastellaan ikään kuin jonkinlaisena tilastollisena sävelmassana, eikä se niin muodoin kykene kertomaan siitä, miten analysoitava musiikki on yksityiskohtien tasolla sävelletty; perinteiset musiikkianalyysimenetelmät pureutuvat tehtävään paremmin. Toisaalta, tämä ei ole VRA:n tarkoituskaan vaan päinvastoin, sen avulla sävellysten muodosta pystytään muodostamaan laajoja yleiskuvia, jotka ovat useimmiten havaintokykymme ulottumattomissa. Vertailurakenneanalyysi on hyvin joustava menetelmä. Mikään ei nimittäin estä tarkastelemasta musiikin eri dimensioista saatuja mittaustuloksia keskenään ja näin etsimästä niiden välisiä yhteyksiä. Lisäksi menetelmän periaatteita voitaisiin kuvitella käytettävän yleisemminkin, esimerkiksi linnunlaulun muodon tarkasteluun tai vaikkapa jokipuron solinasta löytyvien toistuvien jaksojen havainnointiin. VRA:n periaatteita voidaankin soveltaa mihin tahansa numeerisesti diskreettiin muotoon saatettuun aikasarjaan.Siirretty Doriast

    An effective similarity measurement under epistemic uncertainty

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    The epistemic uncertainty stems from the lack of knowledge and it can be reduced when the knowledge increases. Such inter-pretation works well with data represented as a set of possible states and therefore, multivalued similarity measures. Unfortunately, set-valued extensions of similarity measures are not computationally feasible even when the data is finite. Measures with properties that allow efficient calculation of their extensions, need to be found. Analysis of various similarity measures indicated logic-based (additive) measures as an excellent candidate. Their unique properties are discussed and efficient algorithms for computing set-valued extensions are given. The work presents results related to various classes of fuzzy set families: general ones, intervals of fuzzy sets, and their finite sums. The first case is related to the concept of the Fuzzy Membership Function Family, the second corresponds to the Interval-Valued Fuzzy Sets, while the third class is equivalent to the concept of Typical Interval-Valued Hesitant Fuzzy Sets

    Efficient computation of rank probabilities in posets

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    As the title of this work indicates, the central theme in this work is the computation of rank probabilities of posets. Since the probability space consists of the set of all linear extensions of a given poset equipped with the uniform probability measure, in first instance we develop algorithms to explore this probability space efficiently. We consider in particular the problem of counting the number of linear extensions and the ability to generate extensions uniformly at random. Algorithms based on the lattice of ideals representation of a poset are developed. Since a weak order extension of a poset can be regarded as an order on the equivalence classes of a partition of the given poset not contradicting the underlying order, and thus as a generalization of the concept of a linear extension, algorithms are developed to count and generate weak order extensions uniformly at random as well. However, in order to reduce the inherent complexity of the problem, the cardinalities of the equivalence classes is fixed a priori. Due to the exponential nature of these algorithms this approach is still not always feasible, forcing one to resort to approximative algorithms if this is the case. It is well known that Markov chain Monte Carlo methods can be used to generate linear extensions uniformly at random, but no such approaches have been used to generate weak order extensions. Therefore, an algorithm that can be used to sample weak order extensions uniformly at random is introduced. A monotone assignment of labels to objects from a poset corresponds to the choice of a weak order extension of the poset. Since the random monotone assignment of such labels is a step in the generation process of random monotone data sets, the ability to generate random weak order extensions clearly is of great importance. The contributions from this part therefore prove useful in e.g. the field of supervised classification, where a need for synthetic random monotone data sets is present. The second part focuses on the ranking of the elements of a partially ordered set. Algorithms for the computation of the (mutual) rank probabilities that avoid having to enumerate all linear extensions are suggested and applied to a real-world data set containing pollution data of several regions in Baden-Württemberg (Germany). With the emergence of several initiatives aimed at protecting the environment like the REACH (Registration, Evaluation, Authorisation and Restriction of Chemicals) project of the European Union, the need for objective methods to rank chemicals, regions, etc. on the basis of several criteria still increases. Additionally, an interesting relation between the mutual rank probabilities and the average rank probabilities is proven. The third and last part studies the transitivity properties of the mutual rank probabilities and the closely related linear extension majority cycles or LEM cycles for short. The type of transitivity is translated into the cycle-transitivity framework, which has been tailor-made for characterizing transitivity of reciprocal relations, and is proven to be situated between strong stochastic transitivity and a new type of transitivity called delta*-transitivity. It is shown that the latter type is situated between strong stochastic transitivity and a kind of product transitivity. Furthermore, theoretical upper bounds for the minimum cutting level to avoid LEM cycles are found. Cutting levels for posets on up to 13 elements are obtained experimentally and a theoretic lower bound for the cutting level to avoid LEM cycles of length 4 is computed. The research presented in this work has been published in international peer-reviewed journals and has been presented on international conferences. A Java implementation of several of the algorithms presented in this work, as well as binary files containing all posets on up to 13 elements with LEM cycles, can be downloaded from the website http://www.kermit.ugent.be

    Fuzzy Family Ties: Familial Similarity Between Melodic Contours of Different Cardinalities

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    All melodies have shape: a pattern of ascents, descents, and plateaus that occur as music moves through time. This shape—or contour—is one of a melody’s defining characteristics. Music theorists such as Michael Friedmann (1985), Robert Morris (1987), Elizabeth Marvin (1987), and Ian Quinn (1997) have developed models for analyzing contour, but only a few compare contours with different numbers of notes (cardinalities), and fewer still compare entire families of contours. Since these models do not account for familial relations between different-sized contours, they apply only to a limited musical repertoire, and therefore it seems unlikely that they reflect how listeners perceive melodic shape. This dissertation introduces a new method for evaluating familial similarities between related contours, even if the contours have different cardinalities. My Familial Contour Membership model extends theories of contour transformation by using fuzzy set theory and probability. I measure a contour’s degree of familial membership by examining the contour’s transformational pathway and calculating the probability that each move in the pathway is shared by other family members. Through the potential of differing alignments along these pathways, I allow for the possibility that pathways may be omitted or inserted within a contour that exhibits familial resemblance, despite its different cardinality. Integrating variable cardinality into contour similarity relations more adequately accounts for familial relationships between contours, opening up new possibilities for analytical application to a wide variety of repertoires. I examine familial relationships between variants of medieval plainchant, and demonstrate how the sensitivity to familial variation illuminated by fuzzy theoretical models can contribute to our understanding of musical ontology. I explain how melodic shape contributes to motivic development and narrative creation in Brahms’s “Regenlied” Op. 59, No. 3, and the related Violin Sonata No. 1, Op. 78. Finally, I explore how melodic shape is perceived within the repetitive context of melodic phasing in Steve Reich’s The Desert Music. Throughout each study, I show that a more flexible attitude toward cardinality can open contour theory to more nuanced judgments of similarity and familial membership, and can provide new and valuable insights into one of music’s most fundamental elements

    Heuristic-based feature selection for rough set approach

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    The paper presents the proposed research methodology, dedicated to the application of greedy heuristics as a way of gathering information about available features. Discovered knowledge, represented in the form of generated decision rules, was employed to support feature selection and reduction process for induction of decision rules with classical rough set approach. Observations were executed over input data sets discretised by several methods. Experimental results show that elimination of less relevant attributes through the proposed methodology led to inferring rule sets with reduced cardinalities, while maintaining rule quality necessary for satisfactory classification

    From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data

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    One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time and space semidistance that comes from the "best" approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, hence they occur as extremal regions on a spanning structure of the state space under this semidistance---in fact, under any distance measure arising from the physical notion of transport. Based on this notion we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.Comment: J Nonlinear Sci, 201
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