Joint EigenValue Decomposition Algorithms Based on First-Order Taylor Expansion
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Authors: Andre, Remi; Luciani, Xavier; Moreau, Eric
Abstract
In this paper, we propose a new approach to compute the Joint EigenValue Decomposition (JEVD) of real or complex matrix sets. JEVD aims to find a common basis of eigenvectors to a set of matrices. JEVD problem is encountered in many signal processing applications. In particular, recent and efficient algorithms for the Canonical Polyadic Decomposition (CPD) of multiway arrays resort to a JEVD step. The suggested method is based on multiplicative updates. It is distinguishable by the use of a first-order Taylor Expansion to compute the inverse of the updating matrix. We call this approach Joint eigenvalue Decomposition based on Taylor Expansion (JDTE). This approach is derived in two versions based on simultaneous and sequential optimization schemes respectively. Here, simultaneous optimization means that all entries of the updating matrix are simultaneously optimized at each iteration. To the best of our knowledge, such an optimization scheme had never been proposed to solve the JEVD problem in a multiplicative update procedure. Our numerical simulations show that, in many situations involving complex matrices, the proposed approach improves the eigenvectors estimation while keeping a limited computational cost. Finally, these features are highlighted in a practical context of source separation through the CPD of telecommunication signals.
A qualitative study exploring cues and other motivators among a racially diverse sample of light and intermittent smokers
JOURNAL OF SMOKING CESSATION
Authors: Fish, Laura J.; Oliver, Jason A.; Noonan, Devon; Davis, James M.; Pollak, Kathryn I.
Abstract
Introduction Light and intermittent smokers (LITS) represent almost 50% of all current smokers. Research is needed to understand smoking motives among adult light smokers. Aims To explore smoking cues and motivators among a racially diverse sample of adult LITS (<= 10 CPD). In addition, we explored differences between native (always smoked <= 10), and converted (former heavier) LITS. Methods We used purposive sampling to recruit participants who were native and converted LITS and to include equal numbers of African Americans, Whites and Latinos. We coded and analyzed transcripts using a stage approach to identify themes. Results Four main themes emerged that may be unique to light smokers and suggests potential strategies for intervention: (1) smoking in response to cues and control, (2) identifying as a smoker, (3) concern about health consequences, and (4) other priorities influencing smoking. There were some differences among smoking cues and motivators by race and ethnicity, and differences between native and converted LITS. Conclusions Overall, LITS reported drivers of smoking that were unrelated to symptoms of nicotine withdrawal. Even when experiencing salient cues, our LITS cohort expressed the ability to assert control over smoking by abstaining when situational contexts made smoking inconvenient.