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Individual subjects’ ratings neither are metric nor have homogeneous meanings, so digital- labeled collections of subjects’ ratings are intrinsically ordinal and categorical. However, in these situations the literature privileges the use of measures conceived for numerical data. In this paper, we discuss the exploratory theme of employing conditional entropy to measure degrees of uncertainty in responding to self-rating questions, and that of displaying the computed entropies along the ordinal axis for visible pattern recognition. We apply this theme to the study of an online data set which contains responses to the Rosenberg Self-Esteem Scale. We report three major findings. First, at the fine scale level, the resultant multiple ordinal-display of response-vs-covariate entropy measures reveals that the subjects on both extreme labels (high self-esteem and low self-esteem), show distinct degrees of uncertainty. Secondly, at the global scale level, in responding to positively posed questions, the degree of uncertainty decreases for increasing levels of self-esteem, while, in responding to negative questions, the degree of uncertainty increases. Thirdly, such entropy-based computed patterns are preserved across age groups. We provide a set of tools developed in R that are ready to implement for the analysis of rating data and for exploring pattern-based knowledge in related research.

Although prior studies have compared sensory event-related potential (ERP) responses between groups of autistic and typically-developing participants, it is unclear how heterogeneity contributes to the results of these studies. The present study used examined individual differences in these responses. 130 autistic children and 81 typically-developing children, aged between 2 and 5 years, listened to tones at four identity levels while 61-channel electroencephalography was recorded. Hierarchical clustering was used to group participants based on rescaled ERP topographies between 51 and 350 ms. The hierarchical clustering analysis revealed substantial heterogeneity. Some of the seven clusters defined in this analysis were characterized by prolonged fronto-central positivities and/or weak or absent N2 negativities. However, many other participants fell into clusters in which N2 responses were present at varying latencies. Atypical response morphologies such as absent N2 responses and/or prolonged positive-going responses found in some autistic participants may account for prior research findings of attenuated N2 amplitudes in autism. However, there was also considerable overlap between groups, with participants of both groups appearing in all clusters. These results emphasize the utility of using clustering to explore individual differences in brain responses, which can expand on and clarify the results of analyses of group mean differences.

Exploratory Data Analysis (EDA) approaches are adopted to address the difficult extreme-K categorical sample problem. Due to observed data's categorical nature, all comparisons among populations ar...

The notion of dominance is ubiquitous across the animal kingdom, wherein some species/groups such relationships are strictly hierarchical and others are not. Modern approaches for measuring dominance have emerged in recent years taking advantage of increased computational power. One such technique, named Percolation and Conductance (Perc), uses both direct and indirect information about the flow of dominance relationships to generate hierarchical rank order that makes no assumptions about the linearity of these relationships. It also provides a new metric, known as ‘dominance certainty’, which is a complimentary measure to dominance rank that assesses the degree of ambiguity of rank relationships at the individual, dyadic and group levels. In this focused review, we will (i) describe how Perc measures dominance rank while accounting for both nonlinear hierarchical structure as well as sparsity in data—here we also provide a metric of dominance certainty estimated by Perc, which can be used to compliment the information dominance rank supplies; (ii) summarize a series of studies by our research team reflecting the importance of ‘dominance certainty’ on individual and societal health in large captive rhesus macaque breeding groups; and (iii) provide some concluding remarks and suggestions for future directions for dominance hierarchy research.This article is part of the theme issue ‘The centennial of the pecking order: current state and future prospects for the study of dominance hierarchies’.

Electroencephalography (EEG) is a brain imaging approach that has been widely used in neuroscience and clinical settings. The conventional EEG analyses usually require pre-defined frequency bands when characterizing neural oscillations and extracting features for classifying EEG signals. However, neural responses are naturally heterogeneous by showing variations in frequency bands of brainwaves and peak frequencies of oscillatory modes across individuals. Fail to account for such variations might result in information loss and classifiers with low accuracy but high variation across individuals. To address these issues, we present a systematic time-frequency analysis approach for analyzing scalp EEG signals. In particular, we propose a data-driven method to compute the subject-specific frequency bands for brain oscillations via Hilbert-Huang Transform, lifting the restriction of using fixed frequency bands for all subjects. Then, we propose two novel metrics to quantify the power and frequency aspects of brainwaves represented by sub-signals decomposed from the EEG signals. The effectiveness of the proposed metrics are tested on two scalp EEG datasets and compared with four commonly used features sets extracted from wavelet and Hilbert-Huang Transform. The validation results show that the proposed metrics are more discriminatory than other features leading to accuracies in the range of 94.93% to 99.84%. Besides classification, the proposed metrics show great potential in quantification of neural oscillations and serving as biomarkers in the neuroscience research.

Volatility of financial stock is referring to the degree of uncertainty or risk embedded within a stock's dynamics. Such risk has been received huge amounts of attention from diverse financial researchers. By following the concept of regime-switching model, we proposed a non-parametric approach, named encoding-and-decoding, to discover multiple volatility states embedded within a discrete time series of stock returns. The encoding is performed across the entire span of temporal time points for relatively extreme events with respect to a chosen quantile-based threshold. As such the return time series is transformed into Bernoulli-variable processes. In the decoding phase, we computationally seek for locations of change points via estimations based on a new searching algorithm in conjunction with the information criterion applied on the observed collection of recurrence times upon the binary process. Besides the independence required for building the Geometric distributional likelihood function, the proposed approach can functionally partition the entire return time series into a collection of homogeneous segments without any assumptions of dynamic structure and underlying distributions. In the numerical experiments, our approach is found favorably compared with parametric models like Hidden Markov Model. In the real data applications, we introduce the application of our approach in forecasting stock returns. Finally, volatility dynamic of every single stock of S&P500 is revealed, and a stock network is consequently established to represent dependency relations derived through concurrent volatility states among S&P500.

Targeted color-dots with varying shapes and sizes in images are first exhaustively identified, and then their multiscale 2D geometric patterns are extracted for testing spatial uniformness in a progressive fashion. Based on color theory in physics, we develop a new color-identification algorithm relying on highly associative relations among the three color-coordinates: RGB or HSV. Such high associations critically imply low color-complexity of a color image, and renders potentials of exhaustive identification of targeted color-dots of all shapes and sizes. Via heterogeneous shaded regions and lighting conditions, our algorithm is shown being robust, practical and efficient comparing with the popular Contour and OpenCV approaches. Upon all identified color-pixels, we form color-dots as individually connected networks with shapes and sizes. We construct minimum spanning trees (MST) as spatial geometries of dot-collectives of various size-scales. Given a size-scale, the distribution of distances between immediate neighbors in the observed MST is extracted, so do many simulated MSTs under the spatial uniformness assumption. We devise a new algorithm for testing 2D spatial uniformness based on a Hierarchical clustering tree upon all involving MSTs. Our developments are illustrated on images obtained by mimicking chemical spraying via drone in Precision Agriculture., 21 pages, 21 figures

Background Autistic individuals exhibit atypical patterns of sensory processing that are known to be related to quality of life, but which are also highly heterogeneous. Previous investigations of this heterogeneity have ordinarily used questionnaires and have rarely investigated sensory processing in typical development (TD) alongside autism spectrum development (ASD). Methods The present study used hierarchical clustering in a large sample to identify subgroups of young autistic and typically developing children based on the normalized global field power (GFP) of their event-related potentials (ERPs) to auditory stimuli of four different loudness intensities (50, 60, 70, 80 dB SPL): that is, based on an index of the relative strengths of their neural responses across these loudness conditions. Results Four clusters of participants were defined. Normalized GFP responses to sounds of different intensities differed strongly across clusters. There was considerable overlap in cluster assignments of autistic and typically developing participants, but autistic participants were more likely to display a pattern of relatively linear increases in response strength accompanied by a disproportionately strong response to 70 dB stimuli. Autistic participants displaying this pattern trended towards obtaining higher scores on assessments of cognitive abilities. There was also a trend for typically developing participants to disproportionately fall into a cluster characterized by disproportionately/nonlinearly strong 60 dB responses. Greater auditory distractibility was reported among autistic participants in a cluster characterized by disproportionately strong responses to the loudest (80 dB) sounds, and furthermore, relatively strong responses to loud sounds were correlated with auditory distractibility. This appears to provide evidence of coinciding behavioral and neural sensory atypicalities. Limitations Replication may be needed to verify exploratory results. This analysis does not address variability related to classical ERP latencies and topographies. The sensory questionnaire employed was not specifically designed for use in autism. Hearing acuity was not measured. Variability in sensory responses unrelated to loudness is not addressed, leaving room for additional research. Conclusions Taken together, these data demonstrate the broader benefits of using electrophysiology to explore individual differences. They illuminate different neural response patterns and suggest relationships between sensory neural responses and sensory behaviors, cognitive abilities, and autism diagnostic status.

All features of any data type are universally equipped with categorical nature revealed through histograms. A contingency table framed by two histograms affords directional and mutual associations based on rescaled conditional Shannon entropies for any feature-pair. The heatmap of the mutual association matrix of all features becomes a roadmap showing which features are highly associative with which features. We develop our data analysis paradigm called categorical exploratory data analysis (CEDA) with this heatmap as a foundation. CEDA is demonstrated to provide new resolutions for two topics: multiclass classification (MCC) with one single categorical response variable and response manifold analytics (RMA) with multiple response variables. We compute visible and explainable information contents with multiscale and heterogeneous deterministic and stochastic structures in both topics. MCC involves all feature-group specific mixing geometries of labeled high-dimensional point-clouds. Upon each identified feature-group, we devise an indirect distance measure, a robust label embedding tree (LET), and a series of tree-based binary competitions to discover and present asymmetric mixing geometries. Then, a chain of complementary feature-groups offers a collection of mixing geometric pattern-categories with multiple perspective views. RMA studies a system’s regulating principles via multiple dimensional manifolds jointly constituted by targeted multiple response features and selected major covariate features. This manifold is marked with categorical localities reflecting major effects. Diverse minor effects are checked and identified across all localities for heterogeneity. Both MCC and RMA information contents are computed for data’s information content with predictive inferences as by-products. We illustrate CEDA developments via Iris data and demonstrate its applications on data taken from the PITCHf/x database.

Additional file 1. Supporting Information.

Based on the same databases, we computationally address two seemingly highly related, in fact drastically distinct, questions via computational data-driven algorithms: 1) how to precisely achieve the big task of differentiating gait signatures of many individuals and 2) how to reconstruct an individual’s complex gait dynamics in full. Our brains can “effortlessly” resolve the first question, but will definitely fail in the second one because many fine temporal scale gait patterns surely escape our eyes. Based on accelerometers’ 3D gait time series databases, we link the answers toward both questions via multiscale structural dependency within gait dynamics of our musculoskeletal system. Two types of dependency manifestations are explored. We first develop simple algorithmic computing called Principle System-State Analysis for the coarse dependency in implicit forms. Principle System-State Analysis is shown to be able to efficiently classifying among many subjects. We then develop a multiscale Local-1st-Global-2nd Coding Algorithm and a landmark computing algorithm. With both algorithms, we can precisely dissect rhythmic gait cycles, and then decompose each cycle into a series of cyclic gait phases. With proper color-coding and stacking, we reconstruct and represent an individual’s gait dynamics via a 3D cylinder to collectively reveal universal deterministic and stochastic structural patterns on centisecond (10 milliseconds) scale across all rhythmic cycles. This 3D cylinder can serve as “passtensor” for authentication purposes related to clinical diagnoses and cybersecurity.

Clustering large and complex data sets whose partitions may adopt arbitrary shapes remains a difficult challenge. Part of this challenge comes from the difficulty in defining a similarity measure between the data points that captures the underlying geometry of those data points. In this paper, we propose an algorithm, DCG++ that generates such a similarity measure that is data-driven and ultrametric. DCG++ uses Markov Chain Random Walks to capture the intrinsic geometry of data, scans possible scales, and combines all this information using a simple procedure that is shown to generate an ultrametric. We validate the effectiveness of this similarity measure within the context of clustering on synthetic data with complex geometry, on a real-world data set containing segmented audio records of frog calls described by mel-frequency cepstral coefficients, as well as on an image segmentation problem. The experimental results show a significant improvement on performance with the DCG-based ultrametric compared to using an empirical distance measure.

Electroencephalography (EEG) is an electrophysiological monitoring method to record electrical activity of the brain using different electrodes, which are considered as the EEG channels that are placed on scalp. In this paper, we propose an effective information processing approach to explore the association among EEG channels under different circumstances. Particularly, we design four different experimental scenarios and record the EEG signals under motions of eye-opening and body-movement. With sequences of data collected in time order, we first compute the mutual conditional entropy to measure the association between two electrodes. Using the hierarchical clustering tree and data mechanics algorithm, we could effectively identify the association between particular EEG channels under certain motion scenarios. We also implement the weighted random forest to further classify the classes (experimental scenarios) of the EEG time series. Our evaluation results show that we could successfully classify the particular motions with given EEG data series.

Discrete combinatorial optimization problems in the real world are typically defined via an ensemble of potentially high dimensional measurements pertaining to all subjects of a system under study. We point out that such a data ensemble in fact embeds with system's information content that is not directly used in defining the combinatorial optimization problems. Can machine learning algorithms extract such information content and make combinatorial optimizing tasks more efficient? Would such algorithmic computations bring new perspectives into this classic topic of Applied Mathematics and Theoretical Computer Science? We show that answers to both questions are positive. One key reason is due to permutation invariance. That is, the data ensemble of subjects' measurement vectors is permutation invariant when it is represented through a subject-vs.-measurement matrix. An unsupervised machine learning algorithm, called Data Mechanics (DM), is applied to find optimal permutations on row and column axes such that the permuted matrix reveals coupled deterministic and stochastic structures as the system's information content. The deterministic structures are shown to facilitate geometry-based divide-and-conquer scheme that helps optimizing task, while stochastic structures are used to generate an ensemble of mimicries retaining the deterministic structures, and then reveal the robustness pertaining to the original version of optimal solution. Two simulated systems, Assignment problem and Traveling Salesman problem, are considered. Beyond demonstrating computational advantages and intrinsic robustness in the two systems, we propose brand new robust optimal solutions. We believe such robust versions of optimal solutions are potentially more realistic and practical in real world settings.

Can a popular real-world competition system indeed be fragile? To address this question, we represent such a system by a directed binary network. Upon observed network data, typically in a form of win-and-loss matrix, our computational developments begin with collectively extracting network's information flows. And then we compute and discover network's macrostate. This computable macrostate is further shown to contain deterministic structures embedded with randomness mechanisms. Such coupled deterministic and stochastic components becomes the basis for generating the microstate ensemble. Specifically a network mimicking algorithm is proposed to generate a microstate ensemble by subject to the statistical mechanics principle: All generated microscopic states have to conform to its macrostate of the target system. We demonstrate that such a microstate ensemble is an effective platform for exploring systemic sensitivity. Throughout our computational developments, we employ the NCAA Football Bowl Subdivision (FBS) as an illustrating example system. Upon this system, its macrostate is discovered by having a nonlinear global ranking hierarchy as its deterministic component, while its constrained randomness component is embraced within the nearly completely recovered conference schedule . Based on the computed microstate ensemble, we are able to conclude that the NCAA FBS is overall a fragile competition system because it retains highly heterogeneous degrees of sensitivity with its ranking hierarchy.

ObjectivesPolicing is a conflict-limiting mechanism observed in many primate species. It is thought to require a skewed distribution of social power for some individuals to have sufficiently high social power to stop others' fights, yet social power has not been examined in most species with policing behavior. We examined networks of subordination signals as a source of social power that permits policing behavior in rhesus macaques.Materials and methodsFor each of seven captive groups of rhesus macaques, we (a) examined the structure of subordination signal networks and used GLMs to examine the relationship between (b) pairwise dominance certainty and subordination network pathways and (c) policing frequency and social power (group-level convergence in subordination signaling pathways).ResultsNetworks of subordination signals had perfect linear transitivity, and pairs connected by both direct and indirect pathways of signals had more certain dominance relationships than pairs with no such network connection. Social power calculated using both direct and indirect network pathways showed a heavy-tailed distribution and positively predicted conflict policing.ConclusionsOur results empirically substantiate that subordination signaling is associated with greater dominance relationship certainty and further show that pairs who signal rarely (or not at all) may use information from others' signaling interactions to infer or reaffirm the relative certainty of their own relationships. We argue that the network of formal dominance relationships is central to societal stability because it is important for relationship stability and also supports the additional stabilizing mechanism of policing.

The construction of dominance hierarchies for animal societies is an important aspect of understanding the nature of social relationships, and the models to calculate dominance ranks are many. However, choosing the appropriate model for a given data set may appear daunting to the average behaviourist, especially when many of these models assume linearity of dominance. Here, we present a method to test whether or not a data set fits the assumption of linearity using the Bradley–Terry model as a representative of the class of models that assume linearity. Our method uses the geometry of a posterior distribution of possible rankings given the data by using a random walk on this distribution. This test is intuitive, efficient, particularly for large number of individuals, and represents an improvement over previous linearity tests because it takes into account all information (i.e. both linear and apparently circular or nonlinear information) from the data with few restrictions due to high dimensionality. Such a test is not only useful in determining whether a linear hierarchy is relevant to a given animal society, but is necessary in justifying the results of any analysis for which the assumption of linearity is made, such as the Bradley–Terry model. If the assumption of linearity is not met, other methods for ranking, such as the beta random field method proposed by Fushing et al. (2011 , PLoS One , 6 , e17817) should be considered.

There are many compelling accounts of the ways in which the emotions of 1 member of a romantic relationship should influence and be influenced by the partner. However, there are relatively few methodological tools available for representing the alleged complexity of dyad level emotional experiences. In this article, we present an algorithm for examining such affective dynamics based on patterns of variability. The algorithm identifies periods of stability based on length of time and amplitude of emotional fluctuations. The patterns of variability and stability are quantified at the individual and dyadic level, and the approach is illustrated using data of the daily emotional experiences of individuals in romantic couples. With this technique, we examine the fluctuations of the emotions for each person and inspect the overlap fluctuations between both individuals in the dyad. The individual and dyadic indices of variability are then used to predict the status of the dyads (i.e., together, apart) 1 year later.

Foraging niche overlap between attendant species and the nuclear species of mixed-species flocks may induce competition as well as facilitation. In this study, we hypothesized that canopy species would appear more frequently in flocks where nuclear species foraged in the canopy and that species with greater niche overlap with nuclear species would have lower departure rates. Flocking and foraging behaviors of flocks led by the Grey-cheeked Fulvetta Alcippe morrisonia were studied in northeastern Taiwan for two consecutive non-breeding seasons from 1998 to 2000. The foraging height spectrum increased with increasing group size of fulvettas because more fulvettas were found foraging across different strata. The number of species and number of individuals of canopy attendants in a flock increased more rapidly than understory attendants as the group size of fulvettas increased. The more the foraging height of an attendant species overlapped with that of the nuclear species, the lower its departure rate. Specifically, canopy attendant species that usually had a lower niche overlap with the nuclear species dropped out of the flock more frequently than understory attendant species. These observations indicate that foraging niche overlap between attendant species and the nuclear species may facilitate the formation of mixed-species bird flocks. It is therefore important to incorporate the role of positive interactions when trying to understand the formation and maintenance of biological communities.

We present an approach for evaluating coherence in multivariate systems that considers all the variables simultaneously. We operationalize the multivariate system as a network and define coherence as the efficiency with which a signal is transmitted throughout the network. We illustrate this approach with time series data from 15 psychophysiological signals representing individuals’ moment-by-moment emotional reactions to emotional films. First, we summarize the time series through nonparametric Receiver Operating Characteristic (ROC) curves. Second, we use Spearman rank correlations to calculate relationships between each pair of variables. Third, based on the obtained associations, we construct a network using the variables as nodes. Finally, we examine signal transmission through all the nodes in the network. Our results indicate that the network consisting of the 15 psychophysiological signals has a small-world structure, with three clusters of variables and strong within-cluster connections. This structure supports an effective signal transmission across the entire network. When compared across experimental conditions, our results indicate that coherence is relatively stronger for intense emotional stimuli than for neutral stimuli. These findings are discussed in relation to multivariate methods and emotion theories.

We propose a new way of constructing dynamic decision-making model and a non-likelihood based statistical approach for analyzing a new data type: longitudinal distribution data. This longitudinal data records a trajectory of an animal’s dynamic decision-making when continuously exploiting a relative large, but close environment. The ensemble of all hosts contained in the environment is postulated to constitute a manifold of species-specific fitness-gains at any time point, and traverses through two major distinct phases: abundance vs. scarcity of pristine hosts. As such a manifold provides the relative potentials to all possible hosts available for selection, we construct a phase-dependent dynamic decision-making mechanism in a form of a self-adaptive conditional probabilistic model. We devise a Minimum Sum of Chi-squared approach to simultaneously evaluate individual cognitive capability within the two distinct phases and address the validity of the manifold based dynamic decision-making model on the longitudinal distribution data. We analyze three real data sets of seed beetle Callosobruchus maculatus collected from three experimental designs with different degrees of resource heterogeneity. Our statistical inferences are shown to successfully resolve the behavioral ecology issue of whether animal adaptively employs a dynamic decision-making mechanism in response to gradual environmental changes.