Mixtures of probabilistic principal component analysers

Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Previous attempts to formulate mixture models for PCA have therefore to some extent been ad hoc. In this paper, PCA is formulated within a maximum-likelihood framework, based on a specific form of Gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context of clustering, density modelling and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition.

The development of a modified dissolution method suitable for investigating powder mixtures

A novel dissolution method was developed, suitable for powder mixtures, based on the USP basket apparatus. The baskets were modified such that the powder mixtures were retained within the baskets and not dispersed, a potential difficulty that may arise when using conventional USP basket and paddle apparatus. The advantages of this method were that the components of the mixtures were maintained in close proximity, maximizing any drug:excipient interaction and leading to more linear dissolution profiles. Two weakly acidic model drugs, ibuprofen and acetaminophen, and a selection of pharmaceutical excipients, including potential dissolution-enhancing alkalizing agents, were chosen for investigation. Dissolution profiles were obtained for simple physical mixtures. The f1 fit factor values, calculated using pure drug as the reference material, demonstrated a trend in line with expectations, with several dissolution enhancers apparent for both drugs. Also, the dissolution rates were linear over substantial parts of the profiles. For both drugs, a rank order comparison between the f1 fit factor and calculated dissolution rate, obtained from the linear section of the dissolution profile, demonstrated a correlation using a significance level of P=0.05. The method was proven to be suitable for discriminating between the effects of excipients on the dissolution of the model drugs. The method design produced dissolution profiles where the dissolution rate was linear for a substantial time, allowing determination of the dissolution rate without mathematical transformation of the data. This method may be suitable as a preliminary excipient-screening tool in the drug formulation development process.