Bayes factor based speaker clustering for speaker diarization

This paper proposes the use of the Bayes Factor to replace the Bayesian Information Criterion (BIC) as a criterion for speaker clustering within a speaker diarization system. The BIC is one of the most popular decision criteria used in speaker diarization systems today. However, it will be shown in this paper that the BIC is only an approximation to the Bayes factor of marginal likelihoods of the data given each hypothesis. This paper uses the Bayes factor directly as a decision criterion for speaker clustering, thus removing the error introduced by the BIC approximation. Results obtained on the 2002 Rich Transcription (RT-02) Evaluation dataset show an improved clustering performance, leading to a 14.7% relative improvement in the overall Diarization Error Rate (DER) compared to the baseline system.

Raman spectroscopy of gallium based hydrotalcites of formula Mg6Ga2(CO3)(OH)16•4H2O

Insight into the unique structure of hydrotalcites has been obtained using Raman spectroscopy. Gallium containing hydrotalcites of formula Mg4Ga2(CO3)(OH)12•4H2O (2:1 Ga-HT) to Mg8Ga2(CO3)(OH)20•4H2O (4:1 Ga-HT) have been successfully synthesised and characterized by X-ray diffraction and Raman spectroscopy. The d(003) spacing varied from 7.83 Å for the 2:1 hydrotalcite to 8.15 Å for the 3:1 gallium containing hydrotalcite. Raman spectroscopy complemented with selected infrared data has been used to characterise the synthesised gallium containing hydrotalcites of formula Mg6Ga2(CO3)(OH)16•4H2O. Raman bands observed at around 1046, 1048 and 1058 cm-1 were attributed to the symmetric stretching modes of the (CO32-) units. Multiple ν3 CO32- antisymmetric stretching modes are found at around 1346, 1378, 1446, 1464 and 1494 cm-1. The splitting of this mode indicates the carbonate anion is in a perturbed state. Raman bands observed at 710 and 717 cm-1 assigned to the ν4 (CO32-) modes support the concept of multiple carbonate species in the interlayer.

Synthesis and thermal analysis of Indium based hydrotalcites of formula Mg6In2(CO3)(OH)16•4H2O

Insight into the unique structure of layered double hydroxides has been obtained using a combination of X-ray diffraction and thermal analysis. Indium containing hydrotalcites of formula Mg4In2(CO3)(OH)12•4H2O (2:1 In-LDH) through to Mg8In2(CO3)(OH)18•4H2O (4:1 In-LDH) with variation in the Mg:In ratio have been successfully synthesised. The d(003) spacing varied from 7.83 Å for the 2:1 LDH to 8.15 Å for the 3:1 indium containing layered double hydroxide. Distinct mass loss steps attributed to dehydration, dehydroxylation and decarbonation are observed for the indium containing hydrotalcite. Dehydration occurs over the temperature range ambient to 205 °C. Dehydroxylation takes place in a series of steps over the 238 to 277 °C temperature range. Decarbonation occurs between 763 and 795 °C. The dehydroxylation and decarbonation steps depend upon the Mg:In ratio. The formation of indium containing hydrotalcites and their thermal activation provides a method for the synthesis of indium oxide based catalysts.

Infrared and infrared emission spectroscopy of nesquehonite Mg(OH)(HCO3)•2H2O : implications for the formula of nesquehonite

The mineral nesquehonite Mg(OH)(HCO3)•2H2O has been analysed by a combination of infrared (IR) and infrared emission spectroscopy (IES). Both techniques show OH vibrations, both stretching and deformation modes. IES proves the OH units are stable up to 450°C. The strong IR band at 934 cm-1 is evidence for MgOH deformation modes supporting the concept of HCO3- units in the molecular structure. Infrared bands at 1027, 1052 and 1098 cm-1 are attributed to the symmetric stretching modes of HCO3- and CO32- units. Infrared bands at 1419, 1439, 1511, and 1528 cm-1 are assigned to the antisymmetric stretching modes of CO32- and HCO3- units. IES supported by thermoanalytical results defines the thermal stability of nesquehonite IES defines the changes in the molecular structure of nesquehonite with temperature. The results of IR and IES supports the concept that the formula of nesquehonite is better defined as Mg(OH)(HCO3)•2H2O.

Empirical Bayes method in the study of traffic safety via heterogeneous negative multinomial model

In the study of traffic safety, expected crash frequencies across sites are generally estimated via the negative binomial model, assuming time invariant safety. Since the time invariant safety assumption may be invalid, Hauer (1997) proposed a modified empirical Bayes (EB) method. Despite the modification, no attempts have been made to examine the generalisable form of the marginal distribution resulting from the modified EB framework. Because the hyper-parameters needed to apply the modified EB method are not readily available, an assessment is lacking on how accurately the modified EB method estimates safety in the presence of the time variant safety and regression-to-the-mean (RTM) effects. This study derives the closed form marginal distribution, and reveals that the marginal distribution in the modified EB method is equivalent to the negative multinomial (NM) distribution, which is essentially the same as the likelihood function used in the random effects Poisson model. As a result, this study shows that the gamma posterior distribution from the multivariate Poisson-gamma mixture can be estimated using the NM model or the random effects Poisson model. This study also shows that the estimation errors from the modified EB method are systematically smaller than those from the comparison group method by simultaneously accounting for the RTM and time variant safety effects. Hence, the modified EB method via the NM model is a generalisable method for estimating safety in the presence of the time variant safety and the RTM effects.

Bayes Factor based speaker segmentation for speaker diarization

This paper proposes the use of the Bayes Factor as a distance metric for speaker segmentation within a speaker diarization system. The proposed approach uses a pair of constant sized, sliding windows to compute the value of the Bayes Factor between the adjacent windows over the entire audio. Results obtained on the 2002 Rich Transcription Evaluation dataset show an improved segmentation performance compared to previous approaches reported in literature using the Generalized Likelihood Ratio. When applied in a speaker diarization system, this approach results in a 5.1% relative improvement in the overall Diarization Error Rate compared to the baseline.

Synthesis and Raman spectroscopic characterisation of hydrotalcites based on the formula Ca6Al2(CO3)(OH)16· 4H2O

We have successfully synthesized hydrotalcites (HTs) contg. calcium, which are naturally occurring minerals. Insight into the unique structure of HTs has been obtained using a combination of X-ray diffraction (XRD) as well as IR and Raman spectroscopies. Calcium-contg. hydrotalcites (Ca-HTs) of the formula Ca4Al2(CO3)(OH)12·4H2O (2:1 Ca-HT) to Ca8Al2(CO3)(OH)20· 4H2O (4:1 Ca-HT) have been successfully synthesized and characterised by XRD and Raman spectroscopy. XRD has shown that 3:1 calcium HTs have the largest interlayer distance. Raman spectroscopy complemented with selected IR data has been used to characterize the synthesized Ca-HTs. The Raman bands obsd. at around 1086 and 1077 cm-1 were attributed to the ν1 sym. stretching modes of the (CO32-) units of calcite and carbonate intercalated into the HT interlayer. The corresponding ν3 CO32- antisym. stretching modes are found at around 1410 and 1475 cm-1.

Variational Bayes and the reduced dependence approximation for the autologistic model on an irregular grid with applications

Discrete Markov random field models provide a natural framework for representing images or spatial datasets. They model the spatial association present while providing a convenient Markovian dependency structure and strong edge-preservation properties. However, parameter estimation for discrete Markov random field models is difficult due to the complex form of the associated normalizing constant for the likelihood function. For large lattices, the reduced dependence approximation to the normalizing constant is based on the concept of performing computationally efficient and feasible forward recursions on smaller sublattices which are then suitably combined to estimate the constant for the whole lattice. We present an efficient computational extension of the forward recursion approach for the autologistic model to lattices that have an irregularly shaped boundary and which may contain regions with no data; these lattices are typical in applications. Consequently, we also extend the reduced dependence approximation to these scenarios enabling us to implement a practical and efficient non-simulation based approach for spatial data analysis within the variational Bayesian framework. The methodology is illustrated through application to simulated data and example images. The supplemental materials include our C++ source code for computing the approximate normalizing constant and simulation studies.