In this paper a new completely unsupervised mesh segmentation algorithm is proposed, which is based on the PCA interpretation of the Laplacian eigenvectors of the mesh and on parametric clustering using Gaussian mixtures. We analyse the geometric properties of these vectors and we devise a practical method that combines single-vector analysis with multiple-vector analysis. We attempt to characterize the projection of the graph onto each one of its eigenvectors based on PCA properties of the eigenvectors. We devise an unsupervised probabilistic method, based on one-dimensional Gaussian mixture modeling with model selection, to reveal the structure of each eigenvector. Based on this structure, we select a subset of eigenvectors among the set of the smallest non-null eigenvectors and we embed the mesh into the isometric space spanned by this selection of eigenvectors. The final clustering is performed via unsupervised classification based on learning a multi-dimensional Gaussian mixture model of the embedded graph.

We present a new framework for semi-supervised learning with sparse eigenfunction bases of kernel matrices. It turns out that when the cluster assumption holds, that is, when the high density regions are sufficiently separated by low density valleys, each high density area corresponds to a unique representative eigenvector. Linear combination of such eigenvectors (or, more precisely, of their Nystrom extensions) provide good candidates for good classification functions. By first choosing an appropriate basis of these eigenvectors from unlabeled data and then using labeled data with Lasso to select a classifier in the span of these eigenvectors, we obtain a classifier, which has a very sparse representation in this basis. Importantly, the sparsity appears naturally from the cluster assumption. Experimental results on a number of real-world datasets show that our method is competitive with the state of the art semi-supervised learning algorithms and out-performs the natural base-line algorithm (Lasso in the Kernel PCA basis).

We present a novel approach for estimating the intrinsic dimensionality of certain point clouds: we assume that the points are sampled from a manifold M of dimension k , with k << D, and corrupted by D -dimensional noise. When M is linear, one may analyze this situation by SVD: with no noise one would obtain a rank k matrix, and noise may be treated as a perturbation of the covariance matrix. When M is a nonlinear manifold, global SVD may dramatically overestimate the intrinsic dimensionality. We introduce a multiscale version SVD and discuss how one can extract estimators for the intrinsic dimensionality that are highly robust to noise, while require a smaller sample size than current estimators.

We propose a generative model for high dimensional data consisting of intrinsically low dimensional clusters that are noisily sampled. The proposed model is a mixture of probabilistic principal surfaces (MiPPS) optimized using expectation maximization. We use a Bayesian prior on the model parameters to maximize the corresponding marginal likelihood. We also show empirically that this optimization can be biased towards a good local optimum by using our prior intuition to guide the initialization phase The proposed unsupervised algorithm naturally handles cases where the data lies on multiple connected components of a single manifold and where the component manifolds intersect. In addition to clustering, we learn a functional model for the underlying structure of each component cluster as a parameterized hyper-surface in ambient noise.This model is used to learn a global embedding that we use for visualization of the entire dataset. We demonstrate the performance of MiPPS in separating and visualizing land cover types in a hyperspectral dataset.

We present an interactive learning method that enables a user to iteratively refine a regression model. The user examines the output of the model, visualized as the vertical axis of a 2D scatterplot, and provides corrections by repositioning individual data points to the correct output level. Each repositioned data point acts as a control point for altering the learned model, using the geometry underlying the data. We capture the underlying structure of the data as a manifold, on which we compute a set of basis functions as the foundation for learning. Our results show that manifold-based interactive learning achieves dramatic improvement over alternative approaches.

In this paper we propose a new distance metric for signals that admit a sparse representation in a known basis or dictionary. The metric is derived as the length of the sparse geodesic path between two points, by which we mean the shortest path between the points that is itself sparse. We show that the distance can be computed via a simple formula and that the entire geodesic path can be easily generated. The distance provides a natural similarity measure that can be exploited as a perceptually meaningful distance metric for natural images. Furthermore, the distance has applications in supervised, semi-supervised, and unsupervised learning settings.

PMRFSim is a proof of concept geospatial social agent-based simulation capable of examining the interactions of 60,000+ agents over a simulated year within a few minutes. PMRFSim utilizes real world data from sources ranging from the U.S. Census Bureau, a regional sociologist, and base security. PMRFSim models two types of agents, normal and adverse agents. Adverse agents have harmful intent and goals to spread negative sentiment and acquire intelligence. All agents are endowed with demographic and geospatial attributes. Agents interact with each other and respond to events. PMRFSim allows an analyst to construct various what-if scenarios and generates numerous graphs that characterize the social landscape. This analysis is intended to aid public affairs officers understand the social landscape.

The propagation of blood flow along the fetoplacental arterial system has been hypothesized to have a compensatory response to placental anomalies that may result in fetal stress. When the placenta generates increased resistance, the umbilical artery blood flow would decrease and in the worst scenario become absent, which will lead to fetal asphyxia and hypoxia. To compensate for the decreased oxygen supply from maternal placenta, the fetal middle cerebral arteries would become dilated leading to an increased diastolic flow, hence more oxygen. This compensatory phase , however, only lasts for a certain period of time, after which the hypoxia may lead to fetal demise or long term irreversible organ damages. In high-risk pregnancies, Doppler ultrasound technology is commonly used to monitor the fetoplacental arterial blood flow to assess fetal well being. If the anomalies occur prior to the end of the 40-week of gestation, surgical or aggressive medical intervention might be necessary to save the fetal life. Timing this intervention, however, is complex due to the fine balancing act to minimize potential risks from prematurity and organ damage vs. rescuing a fetal life through cesarean section or aggressive medical treatment or natural delivery at the earliest possible gestational age. A reasonable goal is to allow the pregnancy to continue to the point just before fetal damage occurs. To achieve that goal, various testing criteria, e.g. venous Doppler and fetal heart rate, have been used to identify de-compensation. In this work, we conducted computer simulation of the fetoplacental arterial blood flow of a Systemic Lupus Erythematosus (SLE) pregnancy based on Doppler blood flow readings taken during the 10-day period prior to the delivery. The simulation suggests that timing the delivery based on either Doppler waveform readings or fetal heart rates give similar pregnancy outcome.

A form of categorical perception occurs constantly outside the laboratory, as when different The history of research on speech perception is speakers produce the "same" word or when a speaker says replete with examples of nonlinearities, or threshold the "same" word quickly or slowly. This means that phenomena, relating acoustics to perception. These speech perception cannot be a simple concatenation of nonlinearities are essential in that they allow stable sound elements to yield syllables, syllables to yield communication despite variation in the acoustic signal words, or words to yield sentences. The interdependency across speakers, emphasis, background noise, etc. across scales reveals a complex system with nonlinearly Furthermore, the range of acoustic signals perceived as interacting elements that somehow allow veridical equivalent is much larger for speech sounds than for communication.

A peloton is a group of cyclists whose individual and collective energy expenditures are reduced when cyclists ride behind others in zones of reduced air pressure; this effect is known in cycling as ‘drafting’. As an aggregate of biological agents (human), a peloton is a complex dynamical system from which patterns of collective behaviour emerge, including phases and transitions between phases, through which pelotons oscillate. Coupling of cyclists’ energy expenditures when drafting is the basic peloton property from which self-organized collective behaviours emerge. Shown here are equations that model coupling behaviours. Environmental constraints are further parameters that affect peloton dynamics. Phases are defined by thresholds of aggregate energy expenditure; shown here are two different, but consistent, conceptual descriptions of these phase transitions. The first is an energetic model that describes phases in terms of individual, bi-coupled and globally-coupled energy output thresholds that define four observable changes in peloton behaviour. A second, economic model incorporates competition and cooperation dynamics: cooperation increases as power outputs and course constraints increase and population diminishes, and where competition and cooperation for resources results in peloton divisions into sub-pelotons whose average fitness levels are more closely homogeneous.