Likelihood adjusted semidefinite programs for clustering heterogeneous data

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed $K$-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the \emph{exact} observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including $K$-means, SDP and EM algorithms

Metal-insulator transition in transition metal dichalcogenide heterobilayer: accurate treatment of interaction

Transition metal dichalcogenide superlattices provide an exciting new platform for exploring and understanding a variety of phases of matter. The moir\'e continuum Hamiltonian, of two-dimensional jellium in a modulating potential, provides a fundamental model for such systems. Accurate computations with this model are essential for interpreting experimental observations and making predictions for future explorations. In this work, we combine two complementary quantum Monte Carlo (QMC) methods, phaseless auxiliary field quantum Monte Carlo and fixed-phase diffusion Monte Carlo, to study the ground state of this Hamiltonian. We observe a metal-insulator transition between a paramagnetic and a $120^\circ$ N\'eel ordered state as the moir\'e potential depth and the interaction strength are varied. We find significant differences from existing results by Hartree-Fock and exact diagonalization studies. In addition, we benchmark density-functional theory, and suggest an optimal hybrid functional which best approximates our QMC results.Comment: 7 pages, 4 figure

O impacto dos atributos de smartphone na lealdade dos consumidores

Mestrado Bolonha em MarketingCom o desenvolvimento da tecnologia dos smartphones, surgiram muitos tipos diferentes de smartphones e o mercado dos smartphones torna-se cada vez mais competitivo. Ao mesmo tempo, de simples tecnologia de comunicação a uma ferramenta importante, pode-se dizer que a função de smartphone de hoje, tal como as funções da água ou da comida, é um aspeto tão importante da vida quotidiana das pessoas. Por conseguinte, compreender a tendência dos smartphones é a chave para o sucesso das empresas de smartphones. Este artigo partiu dos atributos emocionais e funcionais dos smartphones e combinou os resultados da investigação de diferentes académicos sobre a lealdade dos clientes para explorar como os atributos emocionais e funcionais dos smartphones afetam a lealdade dos clientes. As etapas principais da dissertação foram os seguintes: 1. Com base na revisão da literatura, analisou-se a relação entre atributos emocionais e funcionais e satisfação, e os fatores que afetam a lealdade; 2. Combinou-se os resultados da literatura para estabelecer um modelo de pesquisa e apresentar hipóteses; 3. Projetou-se e divulgou-se um questionário, recolheram-se dados e usou-se o software SPSS para analisar, testaram-se as hipóteses, tiraram-se conclusões de pesquisa e, finalmente, apresentaram-se sugestões de marketing para o mercado de smartphones. Através do trabalho acima, esta dissertação tira as seguintes conclusões: as pessoas de diferentes características culturais são influenciadas por diferentes atributos de smartphone; o sistema operativo de smartphones tem o impacto positivo na satisfação; a autonomia da bateria de smartphones tem o impacto positivo na satisfação; o armazenamento de smartphones tem o impacto positivo na satisfação; a câmara de smartphones não tem o impacto positivo na satisfação; o design de smartphones tem o impacto positivo na satisfação; o assistente virtual de smartphones tem o impacto positivo na satisfação; o logotipo de smartphones tem o impacto positivo na satisfação; os custos de mudança e satisfação têm o impacto positivo na lealdadeWith the development of smartphone technology, many different types of smartphones have emerged, and the smartphone market is becoming more and more competitive. At the same time, from simple communication technology to an important tool, you can say that today's smartphone function, like the functions of water or food, becomes as important an aspect of people's daily lives. Therefore, grasping the development trend of smartphones is the key to the success of mobile phone companies. This paper starts with the emotional and functional attributes of smartphones, combined with the research results of different scholars on customer loyalty, to discuss how the emotional and functional attributes of smartphones affect customer loyalty. The main research work of this dissertation is as follows: 1. On the basis of literature review, the relationship between emotional and functional attributes and satisfaction, and several factors that affect loyalty; 2. Were analyzed the research results of previous literature were combined to establish a research Model, and hypotheses were put forward; 3. a questionnaire was designed and shared, data were collected, and SPSS software was used to analyze and test the hypotheses. Through the above work, this dissertation draws the following conclusions: people of different cultural background are influenced by different smartphone attributes; smartphone operating system has a positive impact on satisfaction; smartphone battery life has a positive impact on satisfaction; smartphone storage has a positive impact on satisfaction; smartphone camera doesn’t have a positive impact on satisfaction; smartphone design has a positive impact on satisfaction; smartphone virtual assistant a positive impact on satisfaction; smartphone logo has a positive impact on satisfaction; switching costs and satisfaction have a positive impact on loyalty.info:eu-repo/semantics/publishedVersio