Santos Tiago, Schrunner Stefan, Geiger Bernhard, Pfeiler Olivia, Zernig Anja, Kaestner Andre, Kern Roman
2019
Semiconductor manufacturing is a highly innovative branch of industry, where a high degree of automation has already been achieved. For example, devices tested to be outside of their specifications in electrical wafer test are automatically scrapped. In this paper, we go one step further and analyze test data of devices still within the limits of the specification, by exploiting the information contained in the analog wafermaps. To that end, we propose two feature extraction approaches with the aim to detect patterns in the wafer test dataset. Such patterns might indicate the onset of critical deviations in the production process. The studied approaches are: 1) classical image processing and restoration techniques in combination with sophisticated feature engineering and 2) a data-driven deep generative model. The two approaches are evaluated on both a synthetic and a real-world dataset. The synthetic dataset has been modeled based on real-world patterns and characteristics. We found both approaches to provide similar overall evaluation metrics. Our in-depth analysis helps to choose one approach over the other depending on data availability as a major aspect, as well as on available computing power and required interpretability of the results.
Geiger Bernhard, Koch Tobias
2019
In 1959, Rényi proposed the information dimension and the d-dimensional entropy to measure the information content of general random variables. This paper proposes a generalization of information dimension to stochastic processes by defining the information dimension rate as the entropy rate of the uniformly quantized stochastic process divided by minus the logarithm of the quantizer step size 1/m in the limit as m → ∞. It is demonstrated that the information dimension rate coincides with the rate-distortion dimension, defined as twice the rate-distortion function R(D) of the stochastic process divided by - log(D) in the limit as D ↓ 0. It is further shown that among all multivariate stationary processes with a given (matrixvalued) spectral distribution function (SDF), the Gaussian process has the largest information dimension rate and the information dimension rate of multivariate stationary Gaussian processes is given by the average rank of the derivative of the SDF. The presented results reveal that the fundamental limits of almost zero-distortion recovery via compressible signal pursuit and almost lossless analog compression are different in general.
Clemens Bloechl, Rana Ali Amjad, Geiger Bernhard
2019
We present an information-theoretic cost function for co-clustering, i.e., for simultaneous clustering of two sets based on similarities between their elements. By constructing a simple random walk on the corresponding bipartite graph, our cost function is derived from a recently proposed generalized framework for information-theoretic Markov chain aggregation. The goal of our cost function is to minimize relevant information loss, hence it connects to the information bottleneck formalism. Moreover, via the connection to Markov aggregation, our cost function is not ad hoc, but inherits its justification from the operational qualities associated with the corresponding Markov aggregation problem. We furthermore show that, for appropriate parameter settings, our cost function is identical to well-known approaches from the literature, such as “Information-Theoretic Co-Clustering” by Dhillon et al. Hence, understanding the influence of this parameter admits a deeper understanding of the relationship between previously proposed information-theoretic cost functions. We highlight some strengths and weaknesses of the cost function for different parameters. We also illustrate the performance of our cost function, optimized with a simple sequential heuristic, on several synthetic and real-world data sets, including the Newsgroup20 and the MovieLens100k data sets.