nils-herrmann/clean_scirepeval huggingface dataset:
Subspace Learning of Dynamics on a Shape Manifold: A Generative Modeling Approach

In this paper, we propose a novel subspace learning algorithm of shape dynamics. Compared to the previous works, our method is invertible and better characterizes the nonlinear geometry of a shape manifold while retaining a good computational efficiency. In this paper, using a parallel moving frame on a shape manifold, each path of shape dynamics is uniquely represented in a subspace spanned by the moving frame, given an initial condition (the starting point and starting frame). Mathematically, such a representation may be formulated as solving a manifold-valued differential equation, which provides a generative modeling of high-dimensional shape dynamics in a lower dimensional subspace. Given the parallelism and a path on a shape manifold, the parallel moving frame along the path is uniquely determined up to the choice of the starting frame. With an initial frame, we minimize the reconstruction error from the subspace to shape manifold. Such an optimization characterizes well the Riemannian geometry of the manifold by imposing parallelism (equivalent as a Riemannian metric) constraints on the moving frame. The parallelism in this paper is defined by a Levi-Civita connection, which is consistent with the Riemannian metric of the shape manifold. In the experiments, the performance of the subspace learning is extensively evaluated using two scenarios: 1) how the high dimensional geometry is characterized in the subspace and 2) how the reconstruction compares with the original shape dynamics. The results demonstrate and validate the theoretical advantages of the proposed approach.
A New Approach to Global Optimiation by an Adapted Diffusion

In this paper, we study a problem of global optimization of an energy functional by a stochastic dynamics with a general diffusion coefficient. The main result is that adapting the diffusion coefficient to the shape of the functional enables the dynamics to escape wide local minima, and attracts it to narrower global minima that are missed by conventional diffusions. We discuss how to properly choose the diffusion coefficient and show numerically the superior performance of the resulting optimization algorithm.
Node Dominance: Revealing Community and Core-Periphery Structure in Social Networks

This study relates the local property of node dominance to local and global properties of a network. Iterative removal of dominated nodes yields a distributed algorithm for computing a core-periphery decomposition of a social network, where nodes in the network core are seen to be essential in terms of network flow and global structure. Additionally, the connected components in the periphery give information about the community structure of the network, aiding in community detection. A number of explicit results are derived, relating the core and periphery to network flow, community structure, and global network structure, which are corroborated by observational results. The method is illustrated using a real world network (DBLP co-authorship network), with ground-truth communities.
Bridging nonlinear diffusion and multiscale analyses

We revisit the nonlinear diffusion problem of signals/images which has been and remains of great research interest in image analysis and computer vision. We build on a previously reported reformulation of the linear diffusion in a probabilistic setting to address a limitation inherent to nonlinear diffusion, namely a loss of texture particularly noticeable in natural images. In the course of our probabilistic reinterpretation of nonlinear diffusion we have, in addition to gaining much insight into Perona-Malik (1988) equation and its properties, proposed a robust technique which achieved a remarkable noise removal while preserving sharp features like edges. While this has resolved a long standing problem of a required prior knowledge of a stopping time of the evolution, the associated cost was a limitation similar to that of all existing nonlinear diffusion techniques, namely a loss of texture information. Using a method based on frames, we bridge the world of multiscale analysis and that of partial differential equation-based diffusion and effectively address this problem. We give substantiating examples of our approach, particles (pixels or sixels), a reformulation of the linear diffusion in a probabilistic setting and interpret, as a result, the filtering as random motions of particles.
Novel similarity invariant for space curves using turning angles and its application to object recognition

We present a new similarity invariant signature for space curves. This signature is based on the information contained in the turning angles of both the tangent and the binormal vectors at each point on the curve. For an accurate comparison of these signatures, we define a Riemannian metric on the space of the invariant. We show through relevant examples that, unlike classical invariants, the one we define in this paper enjoys multiple important properties at the same time, namely, a high discrimination level, independence of any reference point, uniqueness property, as well as a good preservation of the correspondence between curves. Moreover, we illustrate how to match 3D objects by extracting and comparing the invariant signatures of their curved skeletons.
Bayesian approach to best basis selection

Wavelet packets and local trigonometric bases provide an efficient framework and fast algorithms to obtain a "best basis" or "best representation" of deterministic signals. Applying these deterministic techniques to stochastic processes may, however, lead to variable results. We revisit this problem and introduce a prior model on the underlying signal in noise and account for the contaminating noise model as well. We thus develop a Bayesian-based approach to the best basis problem, while preserving the classical tree search efficiency.
Meaningful 3D shape partitioning using Morse functions

To simplify the matching and recognition of 3D objects, we propose to decompose a complex 3D shape into simpler primitive parts. Our partitioning of objects relies on their topological Reeb graphs. Taking advantage of the properties of Morse theory, we detect the critical points of the global geodesic function. These points define the levels at which the segmentation happens. To preserve the geometry of objects, we choose to use level curves instead of intervals. To proceed with object matching, we propose a kernel-based technique to register Reeb graphs. This optimal positioning of two Reeb graphs prepares for a pairwise comparison of the geometry of their primitives.
Multiresolution analysis of PTCA isopotential maps

The discrete wavelet transform is applied as a joint time/space analysis tool for body surface potential maps. The results of the joint time/space analysis are compared with previous work done by using integral maps. The wavelet transform revealed the close relation between temporal and spatial aspects of cardiac signals. The results of the authors' work suggest that the multiresolution signal decomposition via wavelet transforms provides a new and useful approach to evaluate body surface potential maps.<<ETX>>
Semiparametric skew-symmetric modeling of planar shapes

Shape modeling and template learning form an important area of research in image analysis. The paper addresses the problem from a novel viewpoint /sup s/ing a new class of semiparametric skew distributions. Given several realizations of a shape, we represent its template as a joint distribution of angle and distance from the centroid for all points on the boundary. The shape boundary may be arbitrary and irregular but simple. Its corresponding distribution is learned from the scattered data points of the available boundary realizations. We first obtained a bimodal distribution of the radii distances for given angles and subsequently synthesize the overall joint distributions according to some prior on the angles. We substantiate our proposed methodology with a number of examples.
Squigraphs for Fine and Compact Modeling of 3-D Shapes

We propose to superpose global topological and local geometric 3-D shape descriptors in order to define one compact and discriminative representation for a 3-D object. While a number of available 3-D shape modeling techniques yield satisfactory object classification rates, there is still a need for a refined and efficient identification/recognition of objects among the same class. In this paper, we use Morse theory in a two-phase approach. To ensure the invariance of the final representation to isometric transforms, we choose the Morse function to be a simple and intrinsic global geodesic function defined on the surface of a 3-D object. The first phase is a coarse representation through a reduced topological Reeb graph. We use it for a meaningful decomposition of shapes into primitives. During the second phase, we add detailed geometric information by tracking the evolution of Morse function's level curves along each primitive. We then embed the manifold of these curves into ¿3, and obtain a single curve. By combining phase one and two, we build new graphs rich in topological and geometric information that we refer to as squigraphs. Our experiments show that squigraphs are more general than existing techniques. They achieve similar classification rates to those achieved by classical shape descriptors. Their performance, however, becomes clearly superior when finer classification and identification operations are targeted. Indeed, while other techniques see their performances dropping, squigraphs maintain a performance rate of the order of 97%.
An independent component analysis approach to perfusion weighted imaging

In dynamic susceptibility contrast perfusion weighted imaging, the recirculation effect is normally removed by gamma-variate fitting from concentration curves before estimating hemodynamic parameters. At lower SNR, however, many fitting failures may result. Moreover, when cerebral hemodynamics is compromised e.g., cerebral ischemia, a substantially broadened concentration curve is anticipated, resulting in the first passage overlapping with recirculation, which again causes a gamma-fit to fail to consistently discern recirculation contributions from the first passage. We propose to exploit independent component analysis to obviate the recirculation effect. We demonstrate that such a technique can remove recirculation in normal and ischemic brain tissues while preserving the first passage. This in turn allows for accurate recirculation elimination and hence improved estimation of cerebral blood volume particularly when overlapping between first passage and recirculation is suspected as in the case of an ischemic lesion.
3D curve interpolation and object reconstruction

Three dimensional objects viewed as surfaces or volumes embedded in /spl Ropf//sup 3/, are usually sampled along the z-dimension by planes for rendering or modeling purposes. The resulting intersections are curves or planar shapes which may in turn be modeled for parsimony of representation. Each curve or planar shape may be viewed as a point in a high dimensional manifold, thereby providing the notion of interpolation between two curves or two points on this manifold to reconstruct the subsurface that lies between the two slices. We exploit some recent results in formulating this interpolation problem as an optimization problem in /spl Ropf//sup 3/ to yield a simple interpolating spline, known as elasticae, which when evaluated at intermediate points yields curves which can in turn be instrumental in 3D reconstruction. The approach is particularly suited for interpolation between MRI slices and for modeling and reconstruction of 3D shapes.
Multiscale detection of nonstationary signals

A statistical method for detecting and/or localizing nonstationarities in a process observed over a time interval T is presented. Stationarity is induced by taking a wavelet transform of the process. A parametric model is fitted to the result. The error incurred in fitting the model is shown to preserve the singularity manifested in the transform. The error is then used to establish a statistical detection test that is free of any prior knowledge about the class of signals being analyzed, and of any user input.<<ETX>>
Statistical Analysis of the Global Geodesic Function for 3D Object Classification

This paper presents a novel classification strategy for 3D objects. Our technique is based on using a global geodesic function to intrinsically describe the surface of an object. The choice of the global geodesic function ensures the invariance of the classification procedure to scaling and all isometric transformations. Using the Jensen-Shannon divergence, feature parameters are extracted from the probability distribution functions of the global geodesic function for each one of the classes. These parameters are used in the decision of a class membership of an object. This approach demonstrates low computational cost, efficiency, and robustness to resolution over many different data sets.
A nonlinear diffusion-based three-band filter bank

In this letter, we revisit a number of concepts that have recently proven to be useful in multiresolution signal analysis, specifically by replacing the now classical linear-scale transition operators by nonlinear ones. More precisely, we address the problem of designing appropriate operators associated to nonlinear filter banks using multiscale analysis. We first establish a connection between nonlinear filter banks and partial differential equations operators used in scale-space theory. Toward this end, we propose specific structures of nonlinear three-band decompositions ensuring a perfect reconstruction. The behavior of the proposed structures is analyzed for a step-like signal in a high SNR scenario, and a simulation is proposed for a more complex scenario.
Rotation invariant topology coding of 2D and 3D objects using Morse theory

In this paper, we propose a numerical algorithm for extracting the topology of a three-dimensional object (2 dimensional surface) embedded in a three-dimensional space /spl Ropf//sup 3/. The method is based on capturing the topology of a modified Reeb graph by tracking the critical points of a distance function. As such, the approach employs Morse theory in the study of translation, rotation, and scale invariant skeletal graphs. The latter are useful in the representation and classification of objects in /spl Ropf//sup 3/.
On denoising and best signal representation

We propose a best basis algorithm for signal enhancement in white Gaussian noise. The best basis search is performed in families of orthonormal bases constructed with wavelet packets or local cosine bases. We base our search for the "best" basis on a criterion of minimal reconstruction error of the underlying signal. This approach is intuitively appealing, because the enhanced or estimated signal has an associated measure of performance, namely, the resulting mean-square error. Previous approaches in this framework have focused on obtaining the most "compact" signal representations, which consequently contribute to effective denoising. These approaches, however, do not possess the inherent measure of performance which our algorithm provides. We first propose an estimator of the mean-square error, based on a heuristic argument and subsequently compare the reconstruction performance based upon it to that based on the Stein (1981) unbiased risk estimator. We compare the two proposed estimators by providing both qualitative and quantitative analyses of the bias term. Having two estimators of the mean-square error, we incorporate these cost functions into the search for the "best" basis, and subsequently provide a substantiating example to demonstrate their performance.
Capturing human activity by a curve

One of the main challenges of human behavior analysis is the high dimensionality of the representation space. In shape representation, however, a specific human behavior may naturally be described by a 1D path which lies in shape space. According to Whitney Embedding Theorem, such a 1D manifold may be embedded in R3. Motivated by the potential of reducing the dimensionality of behavior representation, we construct an embedding to map the path of evolution of the silhouette in shape space to a representational curve in R3. In contrast to other behavioral embedding, where each point of the path in shape space is projected to lower dimension, we embed the homotopy function of the whole path to be a planar curve function. The proposed embedding utilizes sampling theory to provide computational efficiency and simple reconstruction from the embedding space. Upon validating such a representation, we proceed to model different activities by an AR model of the representative curve. Experiments are provided to illustrate our technique and to demonstrate its viability.
Bridging scale-space to multiscale frame analyses

We address a well known problem of nonlinear image diffusion techniques, namely the loss of texture information. We do so by first determining that it is due to unaccounted correlation structure in the image which we subsequently mitigate by proposing a wavelet frame-based technique. This, by the same token, establishes a theoretical bridge between the scale space methodology and the multiscale analysis approach. We provide examples to illustrate the effectiveness of the proposed approach.
Stabilized inverse diffusion equations and segmentation of vector-valued images

We further investigate and generalize the stabilized inverse diffusion equations (SIDEs), which were introduced and analyzed by Pollak, Willsky and Krim (see Technical Report LIDSP-2368, Laboratory for Information and Decision Systems, MIT, 1996, and Scale-Space Theory in Computer Vision, Springer, 1997). We demonstrate their robustness and applicability to the segmentation of color images.
Discovering the Whole by the Coarse: A topological paradigm for data analysis

The increasing interest in big data applications is ushering in a large effort in seeking new, efficient, and adapted data models to reduce complexity, while preserving maximal intrinsic information. Graph-based models have recently been getting a lot of attention on account of their intuitive and direct connection to the data [43]. The cost of these models, however, is to some extent giving up geometric insight as well as algebraic flexibility.
Information Diffusion of Topic Propagation in Social Media

Real-world social and/or operational networks consist of agents with associated states, whose connectivity forms complex topologies. This complexity is further compounded by interconnected information layers, consisting, for instance, documents/resources of the agents which mutually share topical similarities. Our goal in this paper is to predict the specific states of the agents, as their observed resources evolve in time and get updated. The information diffusion among the agents and the publications themselves effectively result in a dynamic process which we capture by an interconnected system of networks (i.e., layered). More specifically, we use a notion of a supra-Laplacian matrix to address such a generalized diffusion of an interconnected network starting with the classical “graph Laplacian.” The auxiliary and external input update is modeled by a multidimensional Brownian process, yielding two contributions to the variations in the states of the agents: one that is due to the intrinsic interactions in the network system, and the other due to the external inputs or innovations. A variation on this theme, a priori knowledge of a fraction of the agents' states is shown to lead to a Kalman predictor problem. This helps us refine the predicted states exploiting the estimation error in the agents' states. Three real-world datasets are used to evaluate and validate the information diffusion process in this novel-layered network approach. Our results demonstrate a lower prediction error when using the interconnected network rather than the single connectivity layer between the agents. The prediction error is further improved by using the estimated diffusion connection and by applying the Kalman approach with partial observations.
A invertible dimension reduction of curves on a manifold

In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential geometry tools such as moving frame and parallel transportation are successfully adapted into the dimension reduction problem of high dimensional curves. Intuitively, instead of searching for a global flat subspace for curve embedding, we deployed a sequence of local flat subspaces adaptive to the geometry of both of the curve and the manifold it lies on. In practice, the experimental results of the dimension reduction and reconstruction algorithms well illustrate the advantages of the proposed theoretical innovation.
A stochastic flow for feature extraction

Over the years the evolution of level sets of two-dimensional functions or images in time through a partial differential equation has emerged as an important tool in image processing. Curve evolution, which may be viewed as an evolution of a single level curve, has been applied to a wide variety of problems such as smoothing of shapes, shape analysis and shape recovery. We give a stochastic interpretation of the basic curve smoothing equation, the so called geometric heat equation, and show that this evolution amounts to a rotational diffusion movement of the particles along the contour. Moreover, assuming that a priori information about the orientation of objects to be preserved is known, we present new flows which amount to weighting the geometric heat equation nonlinearly as a function of the angle of the normal to the curve at each point.
Control and prediction of beliefs on social network

In this paper we propose a belief flow model for social networks and evaluate its application on estimation of public converged beliefs. The model reveals that the control of beliefs in a social network heavily depends on its degree centralities and clustering coefficients. The application of this model to social network belief flow simulation leads to a capacity to control and predict the converged beliefs in a social network. Two different network models, preferential attachment model and generalized Markov Graph model, are applied to the belief flow model. Experiments with published real social network data are provided and demonstrate very good performance of the belief flow model as well as a comparison between different network models.
Emergence of core-periphery structure from local node dominance in social networks

There has been growing evidence recently for the view that social networks can be divided into a well connected core, and a sparse periphery. This paper describes how such a global description can be obtained from local "dominance" relation ships between vertices, to naturally yield a distributed algorithm for such a decomposition. It is shown that the resulting core describes the global structure of the network, while also preserving shortest paths, and displaying "expander-like" properties. Moreover, the periphery obtained from this de composition consists of a large number of connected com ponents, which can be used to identify communities in the network. These are used for a `divide-and-conquer' strategy for community detection, where the peripheral components are obtained as a pre-processing step to identify the small sets most likely to contain communities. The method is illustrated using a real world network (DBLP co-authorship network), with ground-truth communities.