Adaptive Seeding for Gaussian Mixture Models

We present new initialization methods for the expectation-maximization algorithm for multivariate Gaussian mixture models. Our methods are adaptions of the well-known $K$-means++ initialization and the Gonzalez algorithm. Thereby we aim to close the gap between simple random, e.g. uniform, and complex methods, that crucially depend on the right choice of hyperparameters. Our extensive experiments indicate the usefulness of our methods compared to common techniques and methods, which e.g. apply the original $K$-means++ and Gonzalez directly, with respect to artificial as well as real-world data sets.Comment: This is a preprint of a paper that has been accepted for publication in the Proceedings of the 20th Pacific Asia Conference on Knowledge Discovery and Data Mining (PAKDD) 2016. The final publication is available at link.springer.com (http://link.springer.com/chapter/10.1007/978-3-319-31750-2 24

Development of an Acousto-Ultrasonic Scanning System for Nondestructive Evaluation of Wood and Wood Laminates

An acousto-ultrasonic (AU) scanning system was developed and optimized for wood products. It was found that AU probe alignment, coupling pressure, and stabilization time affect the repeatability of AU readings. After optimization of these factors, the error in AU reading (RMS) was negligible. AU transmission through solid wood also showed a relationship of acoustic attenuation to wood anisotropy. A calculated modulus of elasticity in the direction of wave propagation correlated with wave attenuation characteristics in the TR and LR planes. For wave propagation in the TR plane, the greatest attenuation was observed at a growth ring angle (GRA) of about 45°, corresponding to the lowest modulus of elasticity, which is in this plane. The effect of wood anisotropy (GRA) was found to be a major problem for evaluation of laminated wood, since the received signal was strongly affected by wood properties. Consequently, the effect of anisotropy and natural variability of wood will be the major limiting factor of any acoustic NDE technique applied to many wood products

Acoustic Monitoring of Cold-Setting Adhesive Curing in Wood Laminates: Effect of Clamping Pressure and Detection of Defective Bonds

Many variables affecting adhesive bonding of wood, including moisture content, temperature, surface roughness and contamination, and wood density, are difficult to control and/or measure in industrial conditions. However, the combined effect of these factors may be compensated by controlling process variables, such as clamping pressure and time, and adhesive viscosity, concentration, and spread. This research project investigated an ultrasonic method as a nondestructive means of monitoring bonding processes and assessing the quality of the cured bonds in wood laminates. Monitoring was performed simultaneously at normal and angular (5° nominal) incidence to the bond plane, using pairs of clear Douglas-fir laminates with a single bond line. It was previously reported that ultrasonic transmission is sensitive to curing phases, such as spreading, penetration, curing, and bond thickness. This paper reports the effect of bond defects (uncured, underspread, and uneven spread) and clamping pressure on ultrasonic transmission. The results showed that defective bonds can be detected using patterns of relative attenuation changes during curing and an "unloading effect," measured as the relative transmission reduction after the clamping load is released. Also, transmission through uncured bond lines was strongly affected by pressure, an observation that can be utilized to select optimum clamping pressure

Going further in cluster analysis and classification: Bi-clustering and co-clustering

International audienc

Acousto-Ultrasonic Assessment of Internal Decay in Glulam Beams

An acousto-ultrasonic (AU) through-transmission technique was evaluated for assessing brown-rot decay in Douglas-fir glulam beams that had been removed from service. The effect of decay on different AU signal features was compared to that from normal variations in wood, such as growth ring angle, knots, and moisture gradient. The analysis was based on measurement of velocity, attenuation, shape, and frequency content of the received signals. All of the studied signal features were correlated with the degree of decay; however, they were affected by natural characteristics of wood. Attenuation and signal shape were more affected by the growth ring angle variations and knots than were velocity and frequency features. The effect of knots depended upon size, type, orientation, and distance from the surface. A steep moisture gradient obscured the detection of small degrees of decay, with the greatest effect on signal shape and frequency parameters. This study suggests that multiple signal feature analysis can be used to distinguish decay from certain types of natural wood characteristics such as growth ring angle variations and knots

An efficient SEM algorithm for Gaussian Mixtures with missing data

International audienceThe missing data problem is well-known for statisticians but its frequency increases with the growing size of modern datasets. In Gaussian model-based clustering, the EM algorithm easily takes into account such data by dealing with two kinds of latent levels: the components and the variables. However, the quite familiar degeneracy problem in Gaussian mixtures is aggravated during the EM runs. Indeed, numerical experiments clearly reveal that degeneracy is quite slow and also more frequent than with complete data. In practice, such situations are difficult to detect efficiently. Consequently, degenerated solutions may be confused with valuable solutions and, in addition, computing time may be wasted through wrong runs. A theoretical and practical study of the degeneracy will be presented. Moreover a simple condition on the latent partition to avoid degeneracy will be exhibited. This condition is used in a constrained version of the Stochastic EM (SEM) algorithm. Numerical experiments on real and simulated data illustrate the good behaviour of the proposed algorithm

Fuzzy cluster validation using the partition negentropy criterion

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-04277-5_24Proceedings of the 19th International Conference, Limassol, Cyprus, September 14-17, 2009We introduce the Partition Negentropy Criterion (PNC) for cluster validation. It is a cluster validity index that rewards the average normality of the clusters, measured by means of the negentropy, and penalizes the overlap, measured by the partition entropy. The PNC is aimed at finding well separated clusters whose shape is approximately Gaussian. We use the new index to validate fuzzy partitions in a set of synthetic clustering problems, and compare the results to those obtained by the AIC, BIC and ICL criteria. The partitions are obtained by fitting a Gaussian Mixture Model to the data using the EM algorithm. We show that, when the real clusters are normally distributed, all the criteria are able to correctly assess the number of components, with AIC and BIC allowing a higher cluster overlap. However, when the real cluster distributions are not Gaussian (i.e. the distribution assumed by the mixture model) the PNC outperforms the other indices, being able to correctly evaluate the number of clusters while the other criteria (specially AIC and BIC) tend to overestimate it.This work has been partially supported with funds from MEC BFU2006-07902/BFI, CAM S-SEM-0255-2006 and CAM/UAM project CCG08-UAM/TIC-442

Model-based clustering via linear cluster-weighted models

A novel family of twelve mixture models with random covariates, nested in the linear $t$ cluster-weighted model (CWM), is introduced for model-based clustering. The linear $t$ CWM was recently presented as a robust alternative to the better known linear Gaussian CWM. The proposed family of models provides a unified framework that also includes the linear Gaussian CWM as a special case. Maximum likelihood parameter estimation is carried out within the EM framework, and both the BIC and the ICL are used for model selection. A simple and effective hierarchical random initialization is also proposed for the EM algorithm. The novel model-based clustering technique is illustrated in some applications to real data. Finally, a simulation study for evaluating the performance of the BIC and the ICL is presented