Recent convergence results for the fuzzy c-means clustering algorithms

One of the main techniques embodied in many pattern recognition systems is cluster analysis — the identification of substructure in unlabeled data sets. The fuzzy c-means algorithms (FCM) have often been used to solve certain types of clustering problems. During the last two years several new local results concerning both numerical and stochastic convergence of FCM have been found. Numerical results describe how the algorithms behave when evaluated as optimization algorithms for finding minima of the corresponding family of fuzzy c-means functionals. Stochastic properties refer to the accuracy of minima of FCM functionals as approximations to parameters of statistical populations which are sometimes assumed to be associated with the data. The purpose of this paper is to collect the main global and local, numerical and stochastic, convergence results for FCM in a brief and unified way.     

华蘅芳《积较术》数学方法分析

在《积较术》中,基于独特的差分定义,华蘅芳构造了一个与Ｎｅｗｔｏｎ有限差分公式完全不同的差分体系,针对各种数表的使用,华蘅芳设计了一种”乘表相加“的计算方法。算理分析表明,这一算法与近代矩阵乘法一致。对《积较术》 中的数学思想与数学方法的分析,揭示了清末传统数学研究所的生长点及其在向近代数学转变过程的积极意义。     

Additive Biclustering: A Comparison of One New and Two Existing ALS Algorithms

The additive biclustering model for two-way two-mode object by variable data implies overlapping clusterings of both the objects and the variables together with a weight for each bicluster (i.e., a pair of an object and a variable cluster). In the data analysis, an additive biclustering model is fitted to given data by means of minimizing a least squares loss function. To this end, two alternating least squares algorithms (ALS) may be used: (1) PENCLUS, and (2) Baier’s ALS approach. However, both algorithms suffer from some inherent limitations, which may hamper their performance. As a way out, based on theoretical results regarding optimally designing ALS algorithms, in this paper a new ALS algorithm will be presented. In a simulation study this algorithm will be shown to outperform the existing ALS approaches.     

Variable Selection for Clustering and Classification

As data sets continue to grow in size and complexity, effective and efficient techniques are needed to target important features in the variable space. Many of the variable selection techniques that are commonly used alongside clustering algorithms are based upon determining the best variable subspace according to model fitting in a stepwise manner. These techniques are often computationally intensive and can require extended periods of time to run; in fact, some are prohibitively computationally expensive for high-dimensional data. In this paper, a novel variable selection technique is introduced for use in clustering and classification analyses that is both intuitive and computationally efficient. We focus largely on applications in mixture model-based learning, but the technique could be adapted for use with various other clustering/classification methods. Our approach is illustrated on both simulated and real data, highlighted by contrasting its performance with that of other comparable variable selection techniques on the real data sets.     

The God Concept: Aristotle and the Philosophical Tradition

Before beginning a paper on metaphysics, it is wise to acknowledge the paper’s own “metaphysical” assumptions. In what follows, we must bear in mind that the history of philosophy is as interpretively diverse as it is long. We will begin with the premise that Metaphysics is indeed a foundational science. We will posit that Aristotle’s corpus is unified; that is, that Aristotle can be read as a “systematic” philosopher. Moreover, we will assume that the history of philosophy is itself a unity. If we posit such, “philosophy” can be read as a comprehensible continuity: a certainly contestable position. We must bear in mind that similitude is decidedly not identity; however, similitude does imply a certain conceptual correlation, one which, when pressed, may yield interesting, if not unexpected, results. Thus, we will travel at lightning speed through what took a snail’s pace to develop, “mapping,” so to speak, the structure of the unmoved mover of Aristotle’s Metaphysics (1941) onto the traditional historical divisions of the history of philosophy. We will begin with Aristotle himself in the Ancient period, move to Averroes (the Ibn-Rushd of this paper) in the Medieval period, focus on Descartes and Spinoza as Modern thinkers and, finally, end in Heidegger and Sartre in Contemporary philosophy. This is philosophy with a capital “P,” which may or may not be the reader’s preferred position, let alone the writer’s. But, for our purposes here, it is, nonetheless, inevitable.     

“懿王元年天再旦于郑”考证

“懿王元年天再旦于郑”,是《竹书纪年》中的记载“日食说”提出后,它成为西周年代学研究的一条重要线索,文章考察了这条记录在古书中的各种来源;讨论了它作为天象记录的可靠性,评述了近人对这一问题的提出和研究,并提出进一步研究的方案,对于“郑”的地望,文章在简述前人的工作后提出它与“日食说”有关的种种线索。     

Agnostic Science. Towards a Philosophy of Data Analysis

In this paper we will offer a few examples to illustrate the orientation of contemporary research in data analysis and we will investigate the corresponding role of mathematics. We argue that the modus operandi of data analysis is implicitly based on the belief that if we have collected enough and sufficiently diverse data, we will be able to answer most relevant questions concerning the phenomenon itself. This is a methodological paradigm strongly related, but not limited to, biology, and we label it the microarray paradigm. In this new framework, mathematics provides powerful techniques and general ideas which generate new computational tools. But it is missing any explicit isomorphism between a mathematical structure and the phenomenon under consideration. This methodology used in data analysis suggests the possibility of forecasting and analyzing without a structured and general understanding. This is the perspective we propose to call agnostic science, and we argue that, rather than diminishing or flattening the role of mathematics in science, the lack of isomorphisms with phenomena liberates mathematics, paradoxically making more likely the practical use of some of its most sophisticated ideas.     

How Research on Microbiomes is Changing Biology: A Discussion on the Concept of the Organism

Multicellular organisms contain numerous symbiotic microorganisms, collectively called microbiomes. Recently, microbiomic research has shown that these microorganisms are responsible for the proper functioning of many of the systems (digestive, immune, nervous, etc.) of multicellular organisms. This has inclined some scholars to argue that it is about time to reconceptualise the organism and to develop a concept that would place the greatest emphasis on the vital role of microorganisms in the life of plants and animals. We believe that, unfortunately, there is a problem with this suggestion, since there is no such thing as a universal concept of the organism which could constitute a basis for all biological sciences. Rather, the opposite is true: numerous alternative definitions exist. Therefore, comprehending how microbiomics is changing our understanding of organisms may be a very complex matter. In this paper we will demonstrate that this pluralism proves that claims about a change in our understanding of organisms can be treated as both true and untrue. Mainly, we assert that the existing concepts differ substantially, and that only some of them have to be reconsidered in order to incorporate the discoveries of microbiomics, while others are already flexible enough to do so. Taking into account the plurality of conceptualisations within different branches of modern biology, we will conduct our discussion using the developmental and the cooperation–conflict concepts of the organism. Then we will explain our results by referring to the recent philosophical debate on the nature of the concept of the organism within biology.     

论知识定义的困境与转向

关于知识定义的传统分析自从葛梯尔问题出现之后就陷入了困境.反思"知道"与"知识"的区别,指出传统分析所体现的"主体-客体"二元认识模式的缺陷,从"知识的功能"角度反思"知识的条件是什么",从讨论和解决"知识是否具有客观有效性"、"客观有效性是否就是公共性"、"公共性是否是确证知识的合理条件"等问题,可为知识的准确定义提供新途径.     

How Not to Attack Intelligent Design Creationism: Philosophical Misconceptions About Methodological Naturalism

In recent controversies about Intelligent Design Creationism (IDC), the principle of methodological naturalism (MN) has played an important role. In this paper, an often neglected distinction is made between two different conceptions of MN, each with its respective rationale and with a different view on the proper role of MN in science. According to one popular conception, MN is a self-imposed or intrinsic limitation of science, which means that science is simply not equipped to deal with claims of the supernatural (Intrinsic MN or IMN). Alternatively, we will defend MN as a provisory and empirically grounded attitude of scientists, which is justified in virtue of the consistent success of naturalistic explanations and the lack of success of supernatural explanations in the history of science (Provisory MN or PMN). Science does have a bearing on supernatural hypotheses, and its verdict is uniformly negative. We will discuss five arguments that have been proposed in support of IMN: the argument from the definition of science, the argument from lawful regularity, the science stopper argument, the argument from procedural necessity, and the testability argument. We conclude that IMN, because of its philosophical flaws, proves to be an ill-advised strategy to counter the claims of IDC. Evolutionary scientists are on firmer ground if they discard supernatural explanations on purely evidential grounds, instead of ruling them out by philosophical fiat.     

A modification of the SINDCLUS algorithm for fitting the ADCLUS and INDCLUS models

The SINDCLUS algorithm for fitting the ADCLUS and INDCLUS models deals with a parameter matrix that occurs twice in the model by considering the two occurrences as independent parameter matrices. This procedure has been justified empirically by the observation that upon convergence of the algorithm to the global optimum, the two independently treated parameter matrices turn out to be equal. In the present paper, results are presented that contradict this finding, and a modification of SINDCLUS is presented which obviates the need for independently treating two occurrences of the same parameter matrix.     

2008年日全食观测到的太阳闪耀线偏振光谱

在2008年8月1日发生在中国的日全食食既时,我们测量到了从502.8—528.5nm波段范围内的闪耀光谱的线偏振信号。我们发现了一大组光谱线(特别是那些由中性铁、中性铜还有碳分子产生的谱线)相对于连续谱拥有非常高的偏振度,而线偏振光谱比闪耀光谱本身呈现出更强的结构特征。根据观测结果,我们认为相干散射、散射几何还有其它的机制在产生如此高的偏振度中共同发挥了作用。这一观测将深化我们对太阳高层大气物理状态和物理过程的认识。     

Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches

In this paper two techniques for units clustering and factorial dimensionality reduction of variables and occasions of a three-mode data set are discussed. These techniques can be seen as the simultaneous version of two procedures based on the sequential application of k-means and Tucker2 algorithms and vice versa. The two techniques, T3Clus and 3Fk-means, have been compared theoretically and empirically by a simulation study. In the latter, it has been noted that neither T3Clus nor 3Fk-means outperforms the other in every case. From these results rises the idea to combine the two techniques in a unique general model, named CT3Clus, having T3Clus and 3Fk-means as special cases. A simulation study follows to show the effectiveness of the proposal.     

生物合成可降解材料PHA的研究进展和产业化趋势

聚羟基脂肪酸酯（PHA）是一种天然的可降解高分子生物材料,可应用于生物医用和生物可降解包装材料方面。目前,生物合成PHA的研究进展和产业化趋势集中在两个方面：一是进一步降低生产成本,实现生物可降解塑料的大规模生产;另一个就是改善生物可降解塑料的性质,提高生物可降解塑料的应用范围。本文主要针对性质改造方面的研究进展和趋势进行讨论。     

The Deluge of Spurious Correlations in Big Data

Very large databases are a major opportunity for science and data analytics is a remarkable new field of investigation in computer science. The effectiveness of these tools is used to support a “philosophy” against the scientific method as developed throughout history. According to this view, computer-discovered correlations should replace understanding and guide prediction and action. Consequently, there will be no need to give scientific meaning to phenomena, by proposing, say, causal relations, since regularities in very large databases are enough: “with enough data, the numbers speak for themselves”. The “end of science” is proclaimed. Using classical results from ergodic theory, Ramsey theory and algorithmic information theory, we show that this “philosophy” is wrong. For example, we prove that very large databases have to contain arbitrary correlations. These correlations appear only due to the size, not the nature, of data. They can be found in “randomly” generated, large enough databases, which—as we will prove—implies that most correlations are spurious. Too much information tends to behave like very little information. The scientific method can be enriched by computer mining in immense databases, but not replaced by it.     

科学研究中的项目管理思想--大科学时代科研项目的管理方法论

我们已经步入了大科学研究的时代,与传统的科学研究不同,它面对着更复杂的研究对象或研究领域,涉及到更复杂的环境与过程.为此迫切需要提供一套与之相协调的科学研究方法,特别是大科学时代的科研项目管理方法.20世纪中期发展起来的项目管理方法,在处理复杂问题方面具有很大的优势,它所提供的时间管理、质量管理和人力资源管理等模块,完全能被借鉴到大科学时代的科研项目管理中.     

Identifiability of Finite Mixtures of Multinomial Logit Models with Varying and Fixed Effects

Unique parametrizations of models are very important for parameter interpretation and consistency of estimators. In this paper we analyze the identifiability of a general class of finite mixtures of multinomial logits with varying and fixed effects, which includes the popular multinomial logit and conditional logit models. The application of the general identifiability conditions is demonstrated on several important special cases and relations to previously established results are discussed. The main results are illustrated with a simulation study using artificial data and a marketing dataset of brand choices.     

Matter in Z3

In this paper, I will discuss a certain conception of matter that Aristotle introduces in Metaphysics Z3. It is often assumed that Aristotle came to distinguish between matter and form only in his physical writings, and that this lead to a conflict with the doctrine of primary substances in the Categories that he tries to resolve in Z3. I will argue that there is no such conflict. In Z3, Aristotle seems to suggest that matter is what is left over when we strip a thing of all its properties. I take it that he does not want us to strip away these properties by physical means or in our imagination. Rather, we are asked to strip a referring noun phrase of all its predicative parts. We are thus not supposed to be able to refer to something that has no qualities whatsoever, but to construct a phrase that refers to something that has properties without referring to its having them, and without implying which properties it has. The idea that there might be a way of referring to something definite without mentioning any of its qualities is platonic and it still underlies modern predicate logic. In Z3, Aristotle argues against this conception and thus against the basic idea of predicate logic. According to him, matter is at best an inseparable aspect of a primary substance, which substance is best referred to as a compound τóδε τι (“this such”). Matter is what the τóδε refers to as part of this phrase. But it cannot exist in separation from form, and we cannot refer to it by a separated term, without also referring to the substantial form of the substance of which it is an aspect.     

Design of Blurring Mean-Shift Algorithms for Data Classification

The mean-shift algorithm is an iterative method of mode seeking and data clustering based on the kernel density estimator. The blurring mean-shift is an accelerated version which uses the original data only in the first step, then re-smoothes previous estimates. It converges to local centroids, but may suffer from problems of asymptotic bias, which fundamentally depend on the design of its smoothing components. This paper develops nearest-neighbor implementations and data-driven techniques of bandwidth selection, which enhance the clustering performance of the blurring method. These solutions can be applied to the whole class of mean-shift algorithms, including the iterative local mean method. Extended simulation experiments and applications to well known data-sets show the goodness of the blurring estimator with respect to other algorithms.