Adaptive Mixture Discriminant Analysis for Supervised Learning with Unobserved Classes

In supervised learning, an important issue usually not taken into account by classical methods is that a class represented in the test set may have not been encountered earlier in the learning phase. Classical supervised algorithms will automatically label such observations as belonging to one of the known classes in the training set and will not be able to detect new classes. This work introduces a model-based discriminant analysis method, called adaptive mixture discriminant analysis (AMDA), which can detect several unobserved groups of points and can adapt the learned classifier to the new situation. Two EM-based procedures are proposed for parameter estimation and model selection criteria are used for selecting the actual number of classes. Experiments on artificial and real data demonstrate the ability of the proposed method to deal with complex and real-world problems. The proposed approach is also applied to the detection of unobserved communities in social network analysis.     

Quantum Mechanics and Operational Probability Theory

We discuss a generalization of the standard notion of probability space and show that the emerging framework, to be called operational probability theory, can be considered as underlying quantal theories. The proposed framework makes special reference to the convex structure of states and to a family of observables which is wider than the familiar set of random variables: it appears as an alternative to the known algebraic approach to quantum probability.     

Ethics in Times of Posthumanism

This commentary is an attempt to rethink the ethics of taking care in posthumanist times. It is an effort to combine ethics, posthumanism and psychological theories. I examine how the psychological notion of long-term well-being can serve as an ethical yardstick and how it can be relevant to non-humans.     

Contemporary Epistemic Logic and the Lockean Thesis

This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much better. I briefly mention that it can successfully be extended from single-agent to multi-agent settings. More importantly, I show that accepting the Lockean thesis (and a more sophisticated version for conditional beliefs) leads to a significant and unexpected unification in the dynamic behavior of (conditional) belief and high (conditional) probability with respect to public announcements. This constitutes a methodological argument in favor of the Lockean thesis. Furthermore, if one accepts Baltag’s Erlangen program for epistemology, this technical observation has even stronger philosophical implications: because belief and high probability display the same dynamic behavior, it is plausible that they are indeed one and the same epistemic notion.     

Models as Points of View: The Case of System Dynamics

We propose an analysis of the notion of model as crucially related to the notion of point of view. A model in this sense would always suggest a certain way of looking at a real system, a certain way of thinking about it and a certain way of acting upon it. We focus on System Dynamics as a paradigmatic case with respect to many of the features and problems we can find in the field of modelling and simulation. We analyse in detail some of those features. All of them would be present in many other cases of construction and use of models. Furthermore, they would support the thesis that a model can be fruitfully understood as offering a point of view capable of improving our own points of view over a certain system. The point of view offered by the model could include both non-conceptual and conceptual contents, it would have a complex structure and behaviour, and it would have direct consequences on the decisions made by the subjects adopting that point of view.     

<Emphasis Type="Italic">k</Emphasis>-Adic Similarity Coefficients for Binary (Presence/Absence) Data

k-Adic formulations (for groups of objects of size k) of a variety of 2-adic similarity coefficients (for pairs of objects) for binary (presence/absence) data are presented. The formulations are not functions of 2-adic similarity coefficients. Instead, the main objective of the the paper is to present k-adic formulations that reflect certain basic characteristics of, and have a similar interpretation as, their 2-adic versions. Two major classes are distinguished. The first class is referred to as Bennani-Heiser similarity coefficients, which contains all coefficients that can be defined using just the matches, the number of attributes that are present and that are absent in k objects, and the total number of attributes. The coefficients in the second class can be formulated as functions of Dice’s association indices. The author thanks Willem Heiser and three anonymous reviewers for their helpful comments and valuable suggestions on earlier versions of this article.     

默认假定,枢轴承诺与闭合原则

本文聚焦于索萨关于默认假定的理论所存在的一个潜在问题,即索萨所声称的其理论与闭合原则的不相容性。基于索萨的"默认假定"概念与维特根斯坦所提出的"枢轴承诺"概念之间的相似性,本文试图从两种流行的枢轴知识论--怀特的资质论和普理查德的非信念论--中为索萨理论寻找可资借鉴的解决方案。本文主张默认假定属于"接受"这一非信念命题态度,因而索萨可采用非信念论对与闭合原则相容性问题的解决策略,同时又可规避非信念论所面临的理论问题。     

An Unsupervised and Nonparametric Classification Procedure Based on Mixtures with Known Weights

I consider a new problem of classification into n(n ≥ 2) disjoint classes based on features of unclassified data. It is assumed that the data are grouped into m(M ≥ n) disjoint sets and within each set the distribution of features is a mixture of distributions corresponding to particular classes. Moreover, the mixing proportions should be known and form a matrix of rank n. The idea of solution is, first, to estimate feature densities in all the groups, then to solve the linear system for component densities. The proposed classification method is asymptotically optimal, provided a consistent method of density estimation is used. For illustration, the method is applied to determining perfusion status in myocardial infarction patients, using creatine kinase measurements.     

The Academic Journal Ranking Problem: A Fuzzy-Clustering Approach

The Academic Journal Ranking Problem consists in formulating a formal assessment of scientific journals. An outcome variable must be constructed that allows valid journal comparison, either as a set of tiers (ordered classes) or as a numerical index. But part of the problem is also to devise a procedure to get this outcome, that is, how to get and use relevant data coming from expert opinions or from citations database. We propose a novel approach to the problem that applies fuzzy cluster analysis to peer reviews and opinion surveys. The procedure is composed of two steps: the first is to collect the most relevant qualitative assessments from international organizations (for example, the ones available in the Harzing database) and, as inductive analysis, to apply fuzzy clustering to determine homogeneous journal classes; the second deductive step is to determine the hidden logical rules that underlies the classification, using a classification tree to reproduce the same patterns of the first step.     

Clustering and isolation in the consensus problem for partitions

We examine the problem of aggregating several partitions of a finite set into a single consensus partition We note that the dual concepts of clustering and isolation are especially significant in this connection. The hypothesis that a consensus partition should respect unanimity with respect to either concept leads us to stress a consensus interval rather than a single partition. The extremes of this interval are characterized axiomatically. If a sufficient totality of traits has been measured, and if measurement errors are independent, then a true classifying partition can be expected to lie in the consensus interval. The structure of the partitions in the interval lends itself to partial solutions of the consensus problem Conditional entropy may be used to quantify the uncertainty inherent in the interval as a whole     

Partitions of Partitions

The paper presents methodology for analyzing a set of partitions of the same set of objects, by dividing them into classes of partitions that are similar to one another. Two different definitions are given for the consensus partition which summarizes each class of partitions. The classes are obtained using either constrained or unconstrained clustering algorithms. Two applications of the methodology are described.     

Unification of Mathematical Theories

In this article the problem of unification of mathematical theories is discussed. We argue, that specific problems arise here, which are quite different than the problems in the case of empirical sciences. In particular, the notion of unification depends on the philosophical standpoint. We give an analysis of the notion of unification from the point of view of formalism, Gödel's platonism and Quine's realism. In particular we show, that the concept of “having the same object of study” should be made precise in the case of mathematical theories. In the appendix we give a working proposal of a certain understanding of this notion.     

Cluster Differences Unfolding for Two-Way Two-Mode Preference Rating Data

Classification and spatial methods can be used in conjunction to represent the individual information of similar preferences by means of groups. In the context of latent class models and using Simulated Annealing, the cluster-unfolding model for two-way two-mode preference rating data has been shown to be superior to a two-step approach of first deriving the clusters and then unfolding the classes. However, the high computational cost makes the procedure only suitable for small or medium-sized data sets, and the hypothesis of independent and normally distributed preference data may also be too restrictive in many practical situations. Therefore, an alternating least squares procedure is proposed, in which the individuals and the objects are partitioned into clusters, while at the same time the cluster centers are represented by unfolding. An enhanced Simulated Annealing algorithm in the least squares framework is also proposed in order to address the local optimum problem. Real and artificial data sets are analyzed to illustrate the performance of the model.     

以实践为中心的两个科学抽象理论

本文分析最近卡特莱特和瑞德分别提出的两个科学抽象理论。论证两个理论的分歧来自于他们对抽象在认识论和方法论上的不同理解。这种分歧曾经十分清晰地表现在惠威尔和密尔的争论中。对这些问题的探求和解决不仅要求我们抛弃传统科学哲学中的关于抽象的观念,还要求将我们的出发点从理论转向实践。     

知识与默认

我们将为德性知识论引入一种独特的默认假设(default assumptions)概念,后者一般地构成了胜任力。一个默认假设就是一个特定背景条件获得的假设,即(a)是一种相应的SSS胜任力处于适当位置所必需的,但是(b)允许不安全地处于适当位置,而且不为行动者所知。因此,行动者可能要冒一个背景条件失败的风险,以及紧接着而来的胜任力的丧失,而且他们可能不知道自己冒了这种风险。一种实用论入侵解释了我们为什么在日常语境中能够诉诸默认假设。所以,我们的德性知识论包含默认假设之后,我们能够对哲学怀疑论进行一种全新的处理,从而为摩尔和笛卡尔施以援手。     

The Uses of Reason in Times of Technical Mediation

The art of living idiom suits well a practice-oriented approach in ethics of technology. But what remains or becomes of the functioning and use of reason in ethics? In reaction to the comments by Huijer this reply elaborates in more detail how Foucault’s art of living can be adapted for a critical contemporary ethics of technology. And the aesthetic-political rationality in Foucault’s ethics is compared with Wellner’s suggestions of holding on to the notion of code but with a new meaning. Foucault’s fourfold scheme of subjectivation and a distinction of “below and above reason” structure the argument.     

Using Wittgenstein’s Family Resemblance Principle to Learn Exemplars

The introduction of the notion of family resemblance represented a major shift in Wittgenstein’s thoughts on the meaning of words, moving away from a belief that words were well defined, to a view that words denoted less well defined categories of meaning. This paper presents the use of the notion of family resemblance in the area of machine learning as an example of the benefits that can accrue from adopting the kind of paradigm shift taken by Wittgenstein. The paper presents a model capable of learning exemplars using the principle of family resemblance and adopting Bayesian networks for a representation of exemplars. An empirical evaluation is presented on three data sets and shows promising results that suggest that previous assumptions about the way we categories need reopening.

The Remarkable Simplicity of Very High Dimensional Data: Application of Model-Based Clustering

An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or local. By quantifying extent or degree of ultrametricity in a data set, we show that ultrametricity becomes pervasive as dimensionality and/or spatial sparsity increases. This leads us to assert that very high dimensional data are of simple structure. We exemplify this finding through a range of simulated data cases. We discuss also application to very high frequency time series segmentation and modeling.     

Separating Latent Classes by Information Criteria

This study evaluates performance of information criteria used to separate latent classes. In the evaluations, various numbers of latent classes, sample sizes, parameter structures and latent-class complexities were designed to simulate datasets. The average accuracy rates of information criteria in selecting the designed numbers of latent classes were the core results in this experiment. The study revealed that widely used information criteria, e.g., AIC, BIC, CAIC, could perform poorly under some circumstances. By including a sample size adjustment (Rissanen, 1978), the unsatis-factory performances could be improved considerably. The sample size adjustment provides a plausible solution for separating latent classes. Guidelines are provided to help achieve optimum use of the model fit indices.     

OCLUS: An Analytic Method for Generating Clusters with Known Overlap

The primary method for validating cluster analysis techniques is throughMonte Carlo simulations that rely on generating data with known cluster structure (e.g., Milligan 1996). This paper defines two kinds of data generation mechanisms with cluster overlap, marginal and joint; current cluster generation methods are framed within these definitions. An algorithm generating overlapping clusters based on shared densities from several different multivariate distributions is proposed and shown to lead to an easily understandable notion of cluster overlap. Besides outlining the advantages of generating clusters within this framework, a discussion is given of how the proposed data generation technique can be used to augment research into current classification techniques such as finite mixture modeling, classification algorithm robustness, and latent profile analysis.