Degenerating Families of Dendrograms

Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist p-adic representations of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the Bruhat-Tits tree associated to the p-adic projective line. The implications are that certain moduli spaces known in algebraic geometry are in fact p-adic parameter spaces of dendrograms, and stochastic classification can also be handled within this framework. At the end, we calculate the topology of the hidden part of a dendrogram.     

On the Properties of <Emphasis Type="Italic">α</Emphasis>-Unchaining Single Linkage Hierarchical Clustering

In the election of a hierarchical clustering method, theoretic properties may give some insight to determine which method is the most suitable to treat a clustering problem. Herein, we study some basic properties of two hierarchical clustering methods: α-unchaining single linkage or SL(α) and a modified version of this one, SL?(α). We compare the results with the properties satisfied by the classical linkage-based hierarchical clustering methods.     

Perceiving the Infinite and the Infinitesimal World: Unveiling and Optical Diagrams in Mathematics

Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point (as in the standard limit theory) but “in” the point. We are interested in our research in the diagrams which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role (to externalize rough mental models), and an unveiling role (to help create new and interesting mathematical concepts, theories, and structures). In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations.     

The Documentary Real and the Shoah

Without the support of imagination, one would not have the slightest idea of the cruel ‘real’ that has occurred in the Nazi extermination camps. Yet, in documentaries imaging the events of the Shoah, one runs the risk of missing their most basic property, namely their unimaginability. The mere idea that one is able to imagine the unimaginable comes down to a denial of the Shoah’s status as an event that defies our understanding. The unimaginable ‘real’ of the Shoah, however, is not simply located in its object, in the cruelty of what happened in the camp. The Shoah makes us at the same time facing the unimaginable ‘real’ of the modern subject—the blind spot in our own identity. If we need imagination to deal with the Shoah, it is also because of an ungraspable ‘real’ in ourselves. This is why adequate Shoah representations, acknowledging their object as being beyond representation, include the same ‘beyond’ concerning the subject of the Holocaust memory. The essay makes this clear in an elaborated comparison of Claude Lanzmann’s 1985 film, Shoah, with some conceptual works of art from the late nineties—all of this ‘fine-tuned’ in a reflection upon Ingmar Bergman’s Persona.     

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.     

The Death and the Resurrection of (Psy)critique: The Case of Neuroeducation

A rapidly emerging hegemonic neuro-culture and a booming neural subjectivity signal the entry point for an inquiry into the status of the signifier neuro as a universal passe-partout. The wager of this paper is that the various (mis)appropriations of the neurosciences in the media and in academia itself point to something essential, if not structural, in connection with both the discipline of the neurosciences and the current socio-cultural and ideological climate. Starting from the case of neuroeducation (the application of neuroscience within education), the genealogy of the neurological turn is linked to the history of psychology and its inextricable bond with processes of psychologisation. If the neurological turn risks not merely neglecting the dimension of critique, but also obviating its possibility, then revivifying a psy-critique (understanding the academified modern subject as grounded in the scientific point of view from nowhere) might be necessary in order to understand today’s neural subjectivity and its place within current biopolitics.     

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.     

Whose Agency Now?

I agree with my readers on the necessary alliance of personal agency and collective agency. My point is to prioritize the former. The reasons to prioritize the latter were excellent, and it was undoubtedly a sound decision to start with this scenario: political and institutional improvement of the collectives, enlightened by progressive social sciences. My argument for suggesting a different priority—toward personal microactions and their emergent effects—relies on the opinion that we are stuck in a sustainability crisis due to our current approach. In the question “whose agency now?”, my stress is on “now”.     

Classification of Asymmetric Proximity Data

When clustering asymmetric proximity data, only the average amounts are often considered by assuming that the asymmetry is due to noise. But when the asymmetry is structural, as typically may happen for exchange flows, migration data or confusion data, this may strongly affect the search for the groups because the directions of the exchanges are ignored and not integrated in the clustering process. The clustering model proposed here relies on the decomposition of the asymmetric dissimilarity matrix into symmetric and skew-symmetric effects both decomposed in within and between cluster effects. The classification structures used here are generally based on two different partitions of the objects fitted to the symmetric and the skew-symmetric part of the data, respectively; the restricted case is also presented where the partition fits jointly both of them allowing for clusters of objects similar with respect to the average amounts and directions of the data. Parsimonious models are presented which allow for effective and simple graphical representations of the results.     

The Unseen Déjà-Vu: From Erkki Huhtamo’s <Emphasis Type="Italic">Topoi</Emphasis> to Ken Jacobs’ Remakes

This commentary on Edwin Carels’ essay “Revisiting Tom Tom: Performative anamnesis and autonomous vision in Ken Jacobs’ appropriations of Tom Tom the Piper’s Son” broadens up the media-archaeological framework in which Carels places his text. Notions such as Huhtamo’s topos and Zielinski’s “deep time” are brought into the discussion in order to point out the difficulty to see what there is to see and to question the position of the viewer in front of experimental films like Tom Tom the Piper’s Son and its remakes.     

Fidelity-Commensurability Tradeoff in Joint Embedding of Disparate Dissimilarities

In various data settings, it is necessary to compare observations from disparate data sources. We assume the data is in the dissimilarity representation (P?kalska and Duin, 2005) and investigate a joint embedding method (Priebe et al., 2013) that results in a commensurate representation of disparate dissimilarities. We further assume that there are “matched” observations from different conditions which can be considered to be highly similar, for the sake of inference. The joint embedding results in the joint optimization of fidelity (preservation of within-condition dissimilarities) and commensurability (preservation of between-condition dissimilarities between matched observations). We show that the tradeoff between these two criteria can be made explicit using weighted raw stress as the objective function for multidimensional scaling. In our investigations, we use a weight parameter, w, to control the tradeoff, and choose match detection as the inference task. Our results show weights that are optimal (with respect to the inference task) are different than equal weights for commensurability and fidelity and the proposed weighted embedding scheme provides significant improvements in statistical power.     

The representation of three-way proximity data by single and multiple tree structure models

Models for the representation of proximity data (similarities/dissimilarities) can be categorized into one of three groups of models: continuous spatial models, discrete nonspatial models, and hybrid models (which combine aspects of both spatial and discrete models). Multidimensional scaling models and associated methods, used for thespatial representation of such proximity data, have been devised to accommodate two, three, and higher-way arrays. At least one model/method for overlapping (but generally non-hierarchical) clustering called INDCLUS (Carroll and Arabie 1983) has been devised for the case of three-way arrays of proximity data. Tree-fitting methods, used for thediscrete network representation of such proximity data, have only thus far been devised to handle two-way arrays. This paper develops a new methodology called INDTREES (for INdividual Differences in TREE Structures) for fitting various(discrete) tree structures to three-way proximity data. This individual differences generalization is one in which different individuals, for example, are assumed to base their judgments on the same family of trees, but are allowed to have different node heights and/or branch lengths.We initially present an introductory overview focussing on existing two-way models. The INDTREES model and algorithm are then described in detail. Monte Carlo results for the INDTREES fitting of four different three-way data sets are presented. In the application, a single ultrametric tree is fitted to three-way proximity data derived from intention-to-buy-data for various brands of over-the-counter pain relievers for relieving three common types of maladies. Finally, we briefly describe how the INDTREES procedure can be extended to accommodate hybrid modelling, as well as to handle other types of applications.     

Weighted Graphs with Distances in Given Ranges

Let \( \mathcal{G} \) = (G,w) be a weighted simple finite connected graph, that is, let G be a simple finite connected graph endowed with a function w from the set of the edges of G to the set of real numbers. For any subgraph G′ of G, we define w(G′) to be the sum of the weights of the edges of G′. For any i, j vertices of G, we define D _{i,j}(\( \mathcal{G} \)) to be the minimum of the weights of the simple paths of G joining i and j. The D _{i,j}(\( \mathcal{G} \)) are called 2-weights of \( \mathcal{G} \). Weighted graphs and their reconstruction from 2-weights have applications in several disciplines, such as biology and psychology.Let \( {\left\{{m}_I\right\}}_{I\in \left(\frac{\left\{1,\dots, n\right\}}{2}\right)} \) and \( {\left\{{M}_I\right\}}_{I\in \left(\frac{\left\{1,\dots, n\right\}}{2}\right)} \) be two families of positive real numbers parametrized by the 2-subsets of {1, …, n} with m _I ≤ M _I for any I; we study when there exist a positive-weighted graph G and an n-subset {1, …, n} of the set of its vertices such that D _I (\( \mathcal{G} \)) ∈ [m _I ,M _I ] for any \( I\in \left(\frac{\left\{1,\dots, n\right\}}{2}\right) \). Then we study the analogous problem for trees, both in the case of positive weights and in the case of general weights.     

Approximation,Mad Men and the Death of JFK

In this article I take the US television series Mad Men (2007—present) as an exemplary ‘approximation’, a term I adopt to signal the way in which certain texts construct a changeable, fluid ‘truth’ resulting from collisions, exchange and dialectical argument. Approximations are layered, their formal layerings mirroring a layered, multifaceted argument. Mad Men integrates and represents real historical events within a fictional setting, and act that suggests that an event or action can never be finished, fixed and not open to reassessment. Specifically, this article examines ‘The Grown Ups’, Episode 12 of Season 3, which charts the events of 22 November 1963, the day Kennedy was assassinated. Although we might be able to bring to mind the images and conspiracy theories that have been made available since (such Abraham Zapruder’s 8 mm home movie footage of the assassination), these images were not available at the time. Mad Men as a series always strives to represent its historical milieu as authentically as possible, so the characters re-enact 22 November 1963 as authentically as possible by watching only what was on television that day (the news bulletin, Walter Kronkite’s announcement that Kennedy is dead). The contemporary backdrop to these events, including the resonances of ‘9/11’ through Mad Men, inform and collide with the authenticity on the screen.     

A Criterion Based on the Mahalanobis Distance for Cluster Analysis with Subsampling

A two-level data set consists of entities of a higher level (say populations), each one being composed of several units of the lower level (say individuals). Observations are made at the individual level, whereas population characteristics are aggregated from individual data. Cluster analysis with subsampling of populations is a cluster analysis based on individual data that aims at clustering populations rather than individuals. In this article, we extend existing optimality criteria for cluster analysis with subsampling of populations to deal with situations where population characteristics are not the mean of individual data. A new criterion that depends on the Mahalanobis distance is also defined. The criteria are compared using simulated examples and an ecological data set of tree species in a tropical rain forest.     

Social Autonomy and Heteronomy in the Age of ICT: The Digital <Emphasis Type="Italic">Pharmakon</Emphasis> and the (Dis)Empowerment of the General Intellect

‘The art of living with ICTs (information and communication technologies)’ today not only means finding new ways to cope, interact and create new lifestyles on the basis of the new digital (network) technologies individually, as ‘consumer-citizens’. It also means inventing new modes of living, producing and, not in the least place, struggling collectively, as workers and producers. As the so-called digital revolution unfolds in the context of a neoliberal cognitive and consumerist capitalism, its ‘innovations’ are predominantly employed to modulate and control both production processes and consumer behavior in view of the overall goal of extracting surplus value. Today, the digital networks overwhelmingly destroy social autonomy, instead engendering increasing social heteronomy and proletarianization. Yet it is these very networks themselves, as technical pharmaka in the sense of French ‘technophilosopher’ Bernard Stiegler, that can be employed as no other to struggle against this tendency. This paper briefly explores this possibility by reflecting upon current diagnoses of our ‘technological situation’ by some exemplary post-operaist Marxists from a Stieglerian, pharmacological perspective.     

Belief Systems and Partial Spaces

One important role of belief systems is to allow us to represent information about a certain domain of inquiry. This paper presents a formal framework to accommodate such information representation. Three cognitive models to represent information are discussed: conceptual spaces (Gärdenfors in Conceptual spaces: the geometry of thought. MIT Press, Cambridge, 2000), state-spaces (van Fraassen in Quantum mechanics: an empiricist view. Clarendon Press, Oxford, 1991), and the problem spaces familiar from artificial intelligence. After indicating their weakness to deal with partial information, it is argued that an alternative, formulated in terms of partial structures (da Costa and French in Science and partial truth. Oxford University Press, New York, 2003), can be provided which not only captures the positive features of these models, but also accommodates the partiality of information ubiquitous in science and mathematics.     

The Emergence of Symbolic Algebra as a Shift in Predominant Models

Historians of science find it difficult to pinpoint to an exact period in which symbolic algebra came into existence. This can be explained partly because the historical process leading to this breakthrough in mathematics has been a complex and diffuse one. On the other hand, it might also be the case that in the early twentieth century, historians of mathematics over emphasized the achievements in algebraic procedures and underestimated the conceptual changes leading to symbolic algebra. This paper attempts to provide a more precise setting for the historical context in which this decisive step to symbolic reasoning took place. For that purpose we will consider algebraic problem solving as model-based reasoning and symbolic representation as a model. This allows us to characterize the emergence of symbolic algebra as a shift from a geometrical to a symbolic mode of representation. The use of the symbolic as a model will be situated in the context of mercantilism where merchant activity of exchange has led to reciprocal relations between money and wealth.

Revisiting <Emphasis Type="Italic">Tom Tom:</Emphasis> Performative Anamnesis and Autonomous Vision in Ken Jacobs’ Appropriations of <Emphasis Type="Italic">Tom Tom the Piper’s Son</Emphasis>

In 1969 the American avant-garde filmmaker Ken Jacobs gained wide recognition with a two-hour long interpretation of a 1905 silent short film. Ever since, the artist has kept on revisiting the same material, each time with a different technological approach. Originally hailed as a prime example of structural filmmaking, Jacobs’ more recent variations on the theme of Tom Tom the Piper’s Son beg for a broader understanding of his methods and the meanings implied. To gain a deeper insight in this on-going mise-en-abyme (and an obsession dominating a large part of his career), this essay expands comments by the artist himself with concepts taken from animation, media-archaeology and Warburg’s Mnemosyne atlas. Rereading a filmic text with minute attention, remediating it from an analogue to an electronic format, and reanimating the original action by adding a variety of intervals: all Jacobs’ strategies are aimed at demonstrating the afterlife of Tom Tom in a contemporary cultural context.