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Determining the number of clusters is one of the research questions attracting considerable interests in recent years. Majority of the existing methods require parametric assumptions and substantiated computations. In this paper we propose a simple yet powerful method for determining the number of clusters based on curvature. Our technique is computationally efficient and straightforward to implement. We compare our method with 6 other approaches on a wide range of simulated and real-world datasets. Theoretical motivation underlying the proposed method is also presented. [ABSTRACT FROM AUTHOR]

k nearest neighbors ( k NN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially when a very limited amount of labeled samples are available. In this paper, we propose a new graph-based k NN algorithm which can effectively handle both Gaussian distributed data and nonlinear manifold distributed data. To achieve this goal, we first propose a constrained Tired Random Walk (TRW) by constructing an R -level nearest-neighbor strengthened tree over the graph, and then compute a TRW matrix for similarity measurement purposes. After this, the nearest neighbors are identified according to the TRW matrix and the class label of a query point is determined by the sum of all the TRW weights of its nearest neighbors. To deal with online situations, we also propose a new algorithm to handle sequential samples based a local neighborhood reconstruction. Comparison experiments are conducted on both synthetic data sets and real-world data sets to demonstrate the validity of the proposed new k NN algorithm and its improvements to other version of k NN algorithms. Given the widespread appearance of manifold structures in real-world problems and the popularity of the traditional k NN algorithm, the proposed manifold version k NN shows promising potential for classifying manifold-distributed data. [ABSTRACT FROM AUTHOR]

This paper presented integrated electromigration (EM) studies through experiment, theory, and simulation. First, extensive EM tests were performed using Blech and standard wafer-level electromigration acceleration test (SWEAT)-like structures, which were fabricated on four-inch wafers. Second, a molecular dynamics (MD) simulation-based diffusion-induced strain was incorporated into the existing coupled theory. Third, one-dimensional (1D) governing equations in terms of atomic concentration for un-passivated and passivated configurations were derived for void formation and growth, using a modified Eshelby's solution to consider the effect of passivation. Fourth, a systematic approach was established, including theoretical formulations and experimental methods, to obtain key material properties, i.e., critical atomic concentration and diffusivity. We then determined the material's properties from a specific set of experimental data, using aluminium (Al) as a carrier for demonstration. These properties were then used to predict the time to failure and void growth under various conditions. The theoretical results agreed well with the experimental data. Moreover, we theoretically determined the critical threshold products of current density and conductor length for the un-passivated and passivated configurations, respectively. Both experiment and theory showed that, in the absence of mechanical stress in un-passivated configurations, the atomic self-diffusion, which was opposite to electron wind, was significant in resisting EM development. However, when mechanical stress was present, such as in passivated configurations, stress migration played a dominant role in resisting EM development. Our numerical results showed that the current density exponent n in Black's law remained as 2 in the range of the current density greater than 0.2 MA/cm2 and rapidly approached infinity at a low level of current density. [ABSTRACT FROM AUTHOR]

This paper presented a comprehensive experimental and simulation study for thermomigration (TM) accompanying electromigration (EM) at elevated current densities. Both Blech and standard wafer-level electromigration acceleration test (SWEAT)-like test structures, with aluminum (Al) as a carrier, were used for testing and analysis. In Part I of our study (Cui et al., 2023a), the experimental and numerical results with the current density of 1 MA/cm2 were presented. We observed that Al stripes with a SWEAT structure did not show damage in the entire length, while Blech structures showed void and hillock formations only at the cathode and anode, respectively. The temperature gradient owing to Joule heating was neglected in our previous simulations, and the predicted results agreed well with the experimental observations. However, we have not theoretically verified the effect of the temperature gradient. In this paper, we first reported the new experimental data under the elevated current densities of 3 and 5 MA/cm2. In both Blech and SWEAT structures, the spreading of voids in the middle region of conductors was observed. Moreover, in Blech structures, voiding in the middle region occurred after a period of time when voids/hillocks were formed at the cathode and anode, while the SWEAT structures did not show damage at the two ends. Next, based on the coupled 3D theory (Cui et al., 2023a), new analytical one-dimensional (1D) solutions were derived for the Blech and SWEAT structures in the un-passivated configuration considering TM. We found that TM played a significant role in the EM development in the middle of conductors under the elevated current density. The numerical results were in excellent agreement with the experimental data with the consideration of TM. We further established new EM failure's threshold criteria for the SWEAT structures in the form of the product of current density and square of conductor length. This is a major departure from the original Blech's theory in which only mechanical stress gradient was considered. We also studied the acceleration factor of the current density exponent and presented an insight into failure mechanisms associated with TM. [ABSTRACT FROM AUTHOR]