En la última década, los métodos kernel (métodos núcleo) han demostrado ser técnicas muy eficaces en la resolución de problemas no lineales. Parte de su éxito puede atribuirse a su sólida base matemática dentro de los espacios de Hilbert generados por funciones kernel ("reproducing kernel Hilbert spaces", RKHS); y al hecho de que resultan en problemas convexos de optimización. Además, son aproximadores universales y la complejidad computacional que requieren es moderada. Gracias a estas características, los métodos kernel constituyen una alternativa atractiva a las técnicas tradicionales no lineales, como las series de Volterra, los polinómios y las redes neuronales. Los métodos kernel también presentan ciertos inconvenientes que deben ser abordados adecuadamente en las distintas aplicaciones, por ejemplo, las dificultades asociadas al manejo de grandes conjuntos de datos y los problemas de sobreajuste ocasionados al trabajar en espacios de dimensionalidad infinita.En este trabajo se desarrolla un conjunto de algoritmos basados en métodos kernel para resolver una serie de problemas no lineales, dentro del ámbito del procesado de señal y las comunicaciones. En particular, se tratan problemas de identificación e igualación de sistemas no lineales, y problemas de separación ciega de fuentes no lineal ("blind source separation", BSS). Esta tesis se divide en tres partes. La primera parte consiste en un estudio de la literatura sobre los métodos kernel. En la segunda parte, se proponen una serie de técnicas nuevas basadas en regresión con kernels para resolver problemas de identificación e igualación de sistemas de Wiener y de Hammerstein, en casos supervisados y ciegos. Como contribución adicional se estudia el campo del filtrado adaptativo mediante kernels y se proponen dos algoritmos recursivos de mínimos cuadrados mediante kernels ("kernel recursive least-squares", KRLS). En la tercera parte se tratan problemas de decodificación ciega en que las fuentes son dispersas, como es el caso en comunicaciones digitales. La dispersidad de las fuentes se refleja en que las muestras observadas se agrupan, lo cual ha permitido diseñar técnicas de decodificación basadas en agrupamiento espectral. Las técnicas propuestas se han aplicado al problema de la decodificación ciega de canales MIMO rápidamente variantes en el tiempo, y a la separación ciega de fuentes post no lineal. / In the last decade, kernel methods have become established techniques to perform nonlinear signal processing. Thanks to their foundation in the solid mathematical framework of reproducing kernel Hilbert spaces (RKHS), kernel methods yield convex optimization problems. In addition, they are universal nonlinear approximators and require only moderate computational complexity. These properties make them an attractive alternative to traditional nonlinear techniques such as Volterra series, polynomial filters and neural networks.This work aims to study the application of kernel methods to resolve nonlinear problems in signal processing and communications. Specifically, the problems treated in this thesis consist of the identification and equalization of nonlinear systems, both in supervised and blind scenarios, kernel adaptive filtering and nonlinear blind source separation.In a first contribution, a framework for identification and equalization of nonlinear Wiener and Hammerstein systems is designed, based on kernel canonical correlation analysis (KCCA). As a result of this study, various other related techniques are proposed, including two kernel recursive least squares (KRLS) algorithms with fixed memory size, and a KCCA-based blind equalization technique for Wiener systems that uses oversampling. The second part of this thesis treats two nonlinear blind decoding problems of sparse data, posed under conditions that do not permit the application of traditional clustering techniques. For these problems, which include the blind decoding of fast time-varying MIMO channels, a set of algorithms based on spectral clustering is designed. The effectiveness of the proposed techniques is demonstrated through various simulations.

Summaries in English, Afrikaans and Zulu / Orientation: Security personnel work in a high risk and consequently high stress environment. This may negatively affect their wellbeing. Owing to the high crime rate in South Africa, one of the continuous stressors security personnel experience might be fearing for their lives. If security personnel fail to use effective coping strategies they will remain stressed, and this may have a negative impact on them, and their organisation or community. Challenges such as work stress in the South African security industry have not been comprehensively researched or documented (Sibanyoni, 2014). Consequently, no South African questionnaire measuring coping with stress or a stress management model for dealing with stress in a security environment, could be found. Research purpose: The general aim of the research was to develop a valid and reliable coping questionnaire and stress management model for high stress security occupations. Research methodology: A questionnaire development process, as suggested by scientific literature, was followed. The process entailed (1) determining coping strategies by means of a literature review, (2) developing the coping questionnaire, (3) administering the questionnaire to the target population, and (4) statistical analysis. The stress management model was developed by combining the results of the confirmatory factor analysis (CFA) and canonical correlation analysis (CCA). The development of the questionnaire was based on a sample of 381 active duty security personnel working in a high stress security environment in South Africa. Main findings: The study resulted in the development of a psychometrically sound 39-item questionnaire. The following 12 empirically validated healthy and unhealthy coping strategies were identified: (1) social support, (2) group cohesion, (3) physical exercise, (4) relaxation, (5) social media addiction, (6) healthy sleeping habits, (7) healthy diet, (8) training, (9) humour, (10) religion, (11) avoidance, and (12) denial. CFA confirmed both the construct and content validity, and composite reliability. The questionnaire was found to be invariant, and could thus be applied to different groups in high stress security occupations. A stress management model indicating the interrelationship between personality and coping was also developed. Contribution/value-add: The main contribution of this study was the development of a valid coping questionnaire and stress management model. By identifying the specific coping strategies, targeted stress management interventions could be developed. This could contribute to the overall wellness of security personnel working in high stress occupations, resulting in a healthy organisation and sound relationships with the community. Security organisations could also use the model during assessments to identify candidates with personality traits that would lead to healthier coping strategies, thereby selecting personnel that could better adapt to a security environment. / Oriëntasie: Sekuriteitspersoneel werk in ’n hoë risiko en gevolglik ’n stresvolle omgewing. Dit kan hulle welstand negatief beïnvloed. As gevolg van die hoë misdaadsyfer in Suid-Afrika kan een van die deurlopende stressors wat sekuriteitspersoneel ervaar ’n vrees vir hulle lewens wees. Indien sekuriteitspersoneel nie effektiewe streshantering strategieë gebruik nie, kan hulle voortdurend stres ervaar en dit kan ’n negatiewe impak op hulleself, hulle organisasie of gemeenskap hê. Uitdagings soos beroepstres in die Suid-Afrikaanse sekuriteitsindustrie is nog nie deeglik nagevors of gedokumenteer nie (Sibanyoni, 2014). Gevolglik kon daar vir die sekuriteitsomgewing geen Suid-Afrikaanse vraelys wat streshantering meet of ’n stresbestuursmodel gevind word nie. Doel van die navorsing: Die algemene doel van die navorsing was om vir stresvolle sekuriteitsberoepe ’n geldige en betroubare streshanteringsvraelys en stresbestuursmodel te ontwikkel. Navorsingsmetodologie: ’n Vraelys ontwikkelingsproses, soos deur wetenskaplike literatuur voorgestel, is gevolg. Die proses het die volgende behels: (1) die vasstel van die streshantering strategieë deur middel van ’n literatuuroorsig, (2) die ontwikkeling van die streshanteringsvraelys, (3) administrasie van die vraelys aan die teiken populasie en (4) statistiese analise. Die stresbestuursmodel is ontwikkel deur die resultate van die bevestigende faktoranalise (BFA) en die kanoniese korrelasie analise te kombineer. Die ontwikkeling van die vraelys is gebaseer op ’n steekproef van 381 aktiewe diens sekuriteitspersoneel wat in Suid-Afrika in ’n stresvolle sekuriteitsomgewing werk. Hoofbevindinge: Die studie het tot ’n psigometries betroubare 39-item vraelys gelei. Twaalf empiries gestaafde gesonde en ongesonde streshantering strategieë is geïdentifiseer naamlik: (1) sosiale ondersteuning, (2) groep kohesie, (3) fisiese oefening, (4) ontspanning, (5) sosiale media verslawing, (6) gesonde slaapgewoontes, (7) gesonde dieet, (8) opleiding, (9) humor, (10) godsdiens, (11) vermyding en (12) ontkenning. BFA het die konstruk- en inhoudsgeldigheid so wel as die saamgestelde betroubaarheid bevestig. Die vraelys is invariant en kan dus op verskillende groepe in hoë stres sekuriteitsberoepe toegepas word. ’n Stresbestuursmodel wat die verwantskap tussen persoonlikheid en streshantering aandui is ook ontwikkel. Bydrae/waardetoevoeging: Die belangrikste bydrae van hierdie studie was die ontwikkeling van ’n geldige streshanteringsvraelys en stresbestuursmodel. Deur die spesifieke streshantering strategieë te identifiseer kan gefokusde streshantering intervensies ontwikkel word. Dit kan tot die algehele welstand van sekuriteitspersoneel wat in stresvolle beroepe werk bydra en derhalwe ’n gesonde organisasie en goeie verhoudings met die gemeenskap. Sekuriteitsorganisasies kan ook tydens keurings die model gebruik om kandidate met persoonlikheidstrekke, wat tot gesonder streshantering strategieë sal lei, te identifiseer en dus personeel kies wat beter by ’n sekuriteitsomgewing sal aanpas. / Isimo somqondo: Abasebenzi bezokuphepha basebenza ezindaweni ezinobungozi obuphakeme nengcindezi ephakeme. Lokhu kungaba nomthelela omubi esimeni sabo sempilo. Ngenxa yezinga lobugebengu eliphezulu eNingizimu Afrika, okukodwa okudala ingcindezi ngokuqhubekayo kubasebenzi bezokuphepha ukwesabela izimpilo zabo. Uma abasebenzi bezokuphepha bengasebenzisi amasu aphumelelayo okubhekana nalezi zimo, bazohlala benengcindezi futhi lokhu kungaba nomphumela omubi kubona, enhlanganweni yabo noma emphakathini wabo. Ucwaningo ngezinselelo ezinjengokucindezeleka emsebenzini ezimbonini zokuphepha lapha eNingizimu Afrika alwenziwanga futhi akubhaliwe kabanzi ngakho (Sibanyoni, 2014). Kanjalo, alutholakalanga uhlu lwemibuzo lwaseNingizimu Afrika olungalinganisa ukuthi abasebenzi bezokuphepha babhekana kanjani nengcindezi kanye nomlinganiso olawula ingcindezi ukubhekana nengcindezi ezindaweni zezokuphepha. Inhloso yocwaningo: Inhloso enkulu yocwaningo kwakuwukuqamba uhlu lwemibuzo oluqinisekile noluthembekile ukubhekana nengcindezi nomlinganiso wokulawula ingcindezi emisebenzini yezokuphepha enengcindezi ephakeme. Indlela yokwenza ucwaningo: Isenzo sokuqamba uhlu lwemibuzo njengoba kuhlongozwa yimibhalo yezesayensi silandelwe kulolu cwaningo. Lesi senzo sibe (1) nokuthola amasu okubhekana nengcindezi ngokubhekisa emibhalweni ehloliwe, (2) nokuqamba uhlu lwemibuzo ephathelene nokubhekana nengcindezi, (3) nokunikeza uhlu lwemibuzo kubantu abathintekayo, kanye (4) nokwenza uhlaziyo lwezibalo. Umlinganiso wokulawula ingcindezi wenziwe ngokuhlanganisa imiphumela yeConfirmatory Factor Analysis (CFA) neyeCanonical Correlation Analysis (CCA). Ukuqanjwa kohlu lwemibuzo kweyeme esampuleni labasebenzi bezokuphepha abangama-381 abamatasa emsebenzini abasebenza ezindaweni ezinengcindezi ephakeme eNingizimu Afrika. Okukhulu okutholakele ocwaningweni: Ucwaningo lube nomphumela ekuqanjweni kohlu lwemibuzo oluqinisekile ngokwesayikhomethri olunemibuzo angama-39. Kukhonjwe amasu okubhekana nengcindezi ayishumi nambili aqinisekiswe ngokubukisiswa asesimeni esiphilile nesingaphilile sempilo, okubalwa kuwo, (1) uxhaso lomphakathi, (2) ukuba ndawonye kweqembu, (3) ukuzivocavoca umzimba, (4) ukuziphumuza, (5) ukuba yisigqili semithombo yomphakathi, (6) imikhuba emihle yokulala, (7) uqeqesho, (8) amahlaya, (10) inkolo, (11) ukuxwaya, kanye (12) nokwala. ICFA iqinisekise ukuba neqiniso kombono nokuqukethwe, kanye nokwethembeka okuxubile. Kutholakele ukuthi uhlu lwemibuzo aluguquki futhi lungasetshenziswa emaqenjini ehlukene emisebenzini yezokuphepha anengcindezi ephakeme. Kuthuthukiswe nomlinganiso olawula ingcindezi okhombisa ubudlelwano phakathi komuntu isibili nokubhekana nengcindezi. Umnikelo: Umnikelo omkhulu walolu cwaningo kube ukuqamba uhlu lwemibuzo oluqinisekile ukubhekana nengcindezi kanye nomlinganiso wokulawula ingcindezi. Ngokukhomba amasu aqondene nokubhekana nengcindezi, kungathuthukiswa izindlela ezihlosiwe zokulawula ingcindezi. Lokhu kunganikela esimeni esihle sempilo yabasebenzi bezokuphepha abasebenza imisebenzi enengcindezi ephakeme, okuzoholela enhlanganweni esesimeni esihle nasebudlelwaneni obuhle nomphakathi. Izinhlangano zezokuphepha nazo zingawusebenzisa lomlinganiso ngesikhathi sokuhlola ukubona abafundi abanezici ezinomthelela omuhle, kumasu abhekana nengcindezi asesimeni esihle, ezizobenza bakhethe abasebenzi abazongena kahle ezindaweni zokuphepha. / Industrial and Organisational Psychology / D. Phil. (Industrial and Organisational Psychology)