Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation

This paper introduces a novel mixture model-based approach to the simultaneous clustering and optimal segmentation of functional data, which are curves presenting regime changes. The proposed model consists of a finite mixture of piecewise polynomial regression models. Each piecewise polynomial regression model is associated with a cluster, and within each cluster, each piecewise polynomial component is associated with a regime (i.e., a segment). We derive two approaches to learning the model parameters: the first is an estimation approach which maximizes the observed-data likelihood via a dedicated expectation-maximization (EM) algorithm, then yielding a fuzzy partition of the curves into K clusters obtained at convergence by maximizing the posterior cluster probabilities. The second is a classification approach and optimizes a specific classification likelihood criterion through a dedicated classification expectation-maximization (CEM) algorithm. The optimal curve segmentation is performed by using dynamic programming. In the classification approach, both the curve clustering and the optimal segmentation are performed simultaneously as the CEM learning proceeds. We show that the classification approach is a probabilistic version generalizing the deterministic K-means-like algorithm proposed in Hébrail, Hugueney, Lechevallier, and Rossi (2010). The proposed approach is evaluated using simulated curves and real-world curves. Comparisons with alternatives including regression mixture models and the K-means-like algorithm for piecewise regression demonstrate the effectiveness of the proposed approach.     

Estimation of Generalized DINA Model with Order Restrictions

Cognitive diagnostic models provide valuable information on whether a student has mastered each of the attributes a test intends to evaluate. Despite its generality, the generalized DINA model allows for the possibility of lower correct rates for students who master more attributes than those who know less. This paper considers the use of order-constrained parameter space of the G-DINA model to avoid such a counter-intuitive phenomenon and proposes two algorithms, the upward and downward methods, for parameter estimation. Through simulation studies, we compare the accuracy in parameter estimation and in classification of attribute patterns obtained from the proposed two algorithms and the current approach when the restricted parameter space is true. Our results show that the upward method performs the best among the three, and therefore it is recommended for estimation, regardless of the distribution of respondents’ attribute patterns, types of test items, and the sample size of the data.     

Divisive Latent Class Modeling as a Density Estimation Method for Categorical Data

Traditionally latent class (LC) analysis is used by applied researchers as a tool for identifying substantively meaningful clusters. More recently, LC models have also been used as a density estimation tool for categorical variables. We introduce a divisive LC (DLC) model as a density estimation tool that may offer several advantages in comparison to a standard LC model. When using an LC model for density estimation, a considerable number of increasingly large LC models may have to be estimated before sufficient model-fit is achieved. A DLC model consists of a sequence of small LC models. Therefore, a DLC model can be estimated much faster and can easily utilize multiple processor cores, meaning that this model is more widely applicable and practical. In this study we describe the algorithm of fitting a DLC model, and discuss the various settings that indirectly influence the precision of a DLC model as a density estimation tool. These settings are illustrated using a synthetic data example, and the best performing algorithm is applied to a real-data example. The generated data example showed that, using specific decision rules, a DLC model is able to correctly model complex associations amongst categorical variables.     

Improved Classification for Compositional Data Using the <Emphasis Type="Italic">α</Emphasis>-transformation

In compositional data analysis, an observation is a vector containing nonnegative values, only the relative sizes of which are considered to be of interest. Without loss of generality, a compositional vector can be taken to be a vector of proportions that sum to one. Data of this type arise in many areas including geology, archaeology, biology, economics and political science. In this paper we investigate methods for classification of compositional data. Our approach centers on the idea of using the α-transformation to transform the data and then to classify the transformed data via regularized discriminant analysis and the k-nearest neighbors algorithm. Using the α-transformation generalizes two rival approaches in compositional data analysis, one (when α=1) that treats the data as though they were Euclidean, ignoring the compositional constraint, and another (when α = 0) that employs Aitchison’s centered log-ratio transformation. A numerical study with several real datasets shows that whether using α = 1 or α = 0 gives better classification performance depends on the dataset, and moreover that using an intermediate value of α can sometimes give better performance than using either 1 or 0.     

Civic Meaningfulness ‘Revisited’: A Final Reply to Honohan and Dekker

This final reply responds to Honohan’s invitation to articulate the Arendtian tone of the key-note paper. It spells out the philosophical intuition that the political life of citizens, at least potentially, is capable of making visible what makes human life worthwhile and fully meaningful, and the philosophical curiosity to see whether traces of this deep political awareness can be retrieved in dialogues with volunteers. In response to Dekker’s critical doubts, this final reply clarifies the central stakes of Claes’s paper. The core argument was not to show that the biographical model of meaningfulness is the prevailing approach of meaning in/of volunteering, but to assess the potentials and limits of the model’s interpretive power. Moreover, the paper argues for an alternative, existential model of meaningfulness. This approach refers to deep experiences of meaning that emerge from the practice of volunteering and that shift into powerful political experiences of hope, and a lived sense of equality.     

Reasons of Love: Response to Wolf

According to Wolf’s fitting fulfillment view, meaningfulness depends on the person’s subjective attraction to an activity being grounded in ‘reasons of love’ that concern the objective value of those activities. In this short comment, I argue that ‘reasons of love’—and thus reasons for regarding as meaningful—are not limited to those having to do with the objective value of activities and relationships, but include also what I call ‘reasons for the initiated’ and ‘reasons for me’.     

Electro-deoxidation of V<Subscript>2</Subscript>O<Subscript>3</Subscript> in molten CaCl<Subscript>2</Subscript>-NaCl-CaO

The electro-deoxidation of V₂O₃ precursors was studied. Experiments were carried out with a two-terminal electrochemical cell, which was comprised of a molten electrolyte of CaCl₂ and NaCl with additions of CaO, a cathode of compact V₂O₃, and a graphite anode under the potential of 3.0 V at 1173 K. The phase constitution and composition as well as the morphology of the samples were studied by X-ray diffraction (XRD) and scanning electron microscopy (SEM). 3 g of V₂O₃ could be converted to vanadium metal powder within the processing time of 8 h. The kinetic pathway was investigated by analyzing the product phase in samples prepared at different reduction stages. CaO added in the reduction path of V₂O₃ formed the intermediate product CaV₂O₄.     

Electrochemical properties of LiNi<Subscript>0.5</Subscript>Mn<Subscript>1.3</Subscript>Ti<Subscript>0.2</Subscript>O<Subscript>4</Subscript>/Li<Subscript>4</Subscript>Ti<Subscript>5</Subscript>O<Subscript>12</Subscript> cells

Spinel compounds LiNi_0.5Mn_1.3Ti_0.2O₄ (LNMTO) and Li₄Ti₅O₁₂ (LTO) were synthesized by different methods. The particle sizes of LNMTO and LTO are 0.5–2 and 0.5–0.8 μm, respectively. The LNMTO/LTO cell exhibits better electrochemical properties at both a low current rate of 0.2C and a high current rate of 1C. When the specific capacity was determined based on the mass of the LNMTO cathode, the LNMTO/LTO cell delivered 137 mA·h·g⁻¹ at 0.2C and 118.2 mA·h·g⁻¹ at 1C, and the corresponding capacity retentions after 30 cycles are 88.5% and 92.4%, respectively.     

Microwave sintering of Ca<Subscript>0.6</Subscript>La<Subscript>0.2667</Subscript>TiO<Subscript>3</Subscript> microwave dielectric ceramics

Ca_0.6La_0.2667TiO₃ ceramics were prepared by conventional and microwave sintering techniques and their sinterability, microstructure, and microwave dielectric properties were investigated in detail for comparison. Densified Ca_0.6La_0.2667TiO₃ ceramics were obtained by microwave sintering at 1350°C for 30 min and by conventional sintering at 1450°C for 4 h. An unusual phenomenon was found that some larger grains (grain size range: 8–10 μm) inclined to assemble in one area but some smaller ones (grain size range: 2–4 μm) inclined to gather in another area in the microwave sintered ceramics. The microwave dielectric properties of Ca_0.6La_0.2667TiO₃ ceramics prepared by microwave sintering at 1350°C were as follows: dielectric constant (ɛ _r) = 119.6, quality factor (Qf) = 17858.5 GHz, and temperature coefficient of resonant frequency (τ _f) = 155.5 ppm/°C. In contrast, the microwave dielectric properties of the ceramics prepared by conventional sintering at 1450°C were ɛ _r = 117.4, Qf = 13375 GHz, and τ _f = 217.2 ppm/°C.     

Hydrogen-induced cracking behaviors of Incoloy alloy 825

The effect of hydrogen on the fracture behaviors of Incoloy alloy 825 was investigated by means of slow strain rate testing (SSRT). Hydrogen was introduced into the sample by electrochemical charging. The results show that surface microcracks form gradually during aging at room temperature when desorption of hydrogen takes place after hydrogen charging at a current density of 5 mA/cm2 for 24 h. SSRT shows that the increase of ductility loss is significantly obvious as the hydrogen charging current density increases. Scanning electron microscopy (SEM) images reveal ductile fracture in the pre-charged sample with low current densities, while the fracture includes small quasi-cleavage regions and tends to be brittle fracture as the hydrogen charging current density increases to 5 mA/cm2.