nils-herrmann/clean_scirepeval huggingface dataset:
A unifying approach to hard and probabilistic clustering

We derive the clustering problem from first principles showing that the goal of achieving a probabilistic, or "hard", multi class clustering result is equivalent to the algebraic problem of a completely positive factorization under a doubly stochastic constraint. We show that spectral clustering, normalized cuts, kernel K-means and the various normalizations of the associated affinity matrix are particular instances and approximations of this general principle. We propose an efficient algorithm for achieving a completely positive factorization and extend the basic clustering scheme to situations where partial label information is available.
Gene Selection via a Spectral Approach

Array technologies have made it possible to record simultaneously the expression pattern of thousands of genes. A fundamental problem in the analysis of gene expression data is the identification of highly relevant genes that either discriminate between phenotypic labels or are important with respect to the cellular process studied in the experiment. Examples include: cell cycle or heat shock in yeast experiments, chemical or genetic perturbations of mammalian cell lines, and genes involved in class discovery for human tumors. We focus on the task of unsupervised gene selection. Selecting a small subset of genes is particularly challenging as the data sets involved are typically characterized by a small sample size and a very large feature space. We propose a model independent approach which scores candidate gene selections using spectral properties of the candidate af?nity matrix. The algorithm is simple to implement, yet contains a number of remarkable properties which guarantee consistent sparse selections. We applied our algorithm on five different data sets. The first consists of time course data from four well studied Hematopoietic cell lines (HL-60, Jurkat, NB4, and U937). The other four data sets include three well studied treatment outcomes (large cell lymphoma, childhood medulloblastomas, breast tumors) and one unpublished data set (lymph status). We compared our approach both with other unsupervised methods (SOM,PCA,GS) and with supervised methods (SNR,RMB,RFE). The results show that our approach considerably outperforms all the other unsupervised approaches in our study, is competitive with supervised methods and in some cases even outperforms supervised approaches.
Non-negative tensor factorization with applications to statistics and computer vision

We derive algorithms for finding a non-negative n-dimensional tensor factorization (n-NTF) which includes the non-negative matrix factorization (NMF) as a particular case when n = 2. We motivate the use of n-NTF in three areas of data analysis: (i) connection to latent class models in statistics, (ii) sparse image coding in computer vision, and (iii) model selection problems. We derive a "direct" positive-preserving gradient descent algorithm and an alternating scheme based on repeated multiple rank-1 problems.
Sparse image coding using a 3D non-negative tensor factorization

We introduce an algorithm for a non-negative 3D tensor factorization for the purpose of establishing a local parts feature decomposition from an object class of images. In the past, such a decomposition was obtained using non-negative matrix factorization (NMF) where images were vectorized before being factored by NMF. A tensor factorization (NTF) on the other hand preserves the 2D representations of images and provides a unique factorization (unlike NMF which is not unique). The resulting "factors" from the NTF factorization are both sparse (like with NMF) but also separable allowing efficient convolution with the test image. Results show a superior decomposition to what an NMF can provide on all fronts - degree of sparsity, lack of ghost residue due to invariant parts and efficiency of coding of around an order of magnitude better. Experiments on using the local parts decomposition for face detection using SVM and Adaboost classifiers demonstrate that the recovered features are discriminatory and highly effective for classification.
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A Monocular Vision Advance Warning System for the Automotive Aftermarket

Driver inattention and poor judgment are the major causes of motor vehicle accidents (MVA). Extensive research has shown that intelligent driver assistance systems can significantly reduce the number and severity of these accidents. The driver’s visual perception abilities are a key factor in the design of the driving environment. This makes image processing a natural candidate in any effort to impact MVAs. The vision system described here encompasses 3 major capabilities: (i) Lane Departure Warning (ii) Headway Monitoring and Warning (iii) Forward Collision Warning. This paper describes in detail the different warning features, the HMI (visual and acoustic) application design rules, and results of a study in which the system was installed in a commercial fleet and passenger vehicles.
Algebraic Set Kernels with Application to Inference Over Local Image Representations

This paper presents a general family of algebraic positive definite similarity functions over spaces of matrices with varying column rank. The columns can represent local regions in an image (whereby images have varying number of local parts), images of an image sequence, motion trajectories in a multibody motion, and so forth. The family of set kernels we derive is based on a group invariant tensor product lifting with parameters that can be naturally tuned to provide a cook-book of sorts covering the possible "wish lists" from similarity measures over sets of varying cardinality. We highlight the strengths of our approach by demonstrating the set kernels for visual recognition of pedestrians using local parts representations.
Solid or not solid: vision for radar target validation

In the context of combining radar and vision sensors for a fusion application in dense city traffic situations, one of the major challenges is to be able to validate radar targets. We take a high-level fusion approach assuming that both sensor modalities have the capacity to independently locate and identify targets of interest. In this context, radar targets can either correspond to a vision target- in which case the target is validated without further processing- or not. It is the latter case that drives the focus of this paper. A non-matched radar target can correspond to some solid object which is not part of the objects of interest of the vision sensor (such as a guard-rail) or can be caused by reflections in which case it is a ghost target which does not match any physical object in the real world. We describe a number of computational steps for the decision making of non-matched radar targets. The computations combine both direct motion parallax measurements and indirect motion analysis- which are not sufficient for computing parallax but are nevertheless quite effective- and pattern classification steps for covering situations which motion analysis are weak or ineffective. One of the major advantages of our high-level fusion approach is that it allows the use of simpler (low cost) radar technology to create a combined high performance system.
Dynamic P n to P n Alignment

We introduce in this chapter A generalization of the classical collineation of P n. The generalization allows for a certain degree of freedom in the local-ization of points in P n at the expense of using multiple m > 2 views. The degree of freedom per point is governed by an additional parameter 1 ≤ k < n which stands for the dimension of the subspace in which the indvidual points are allowed to move while the projective change of coordinates take place. In other words, the point set is not necessarily stationary allowing the configuration to change while the entire coordinate system undergoes a projective change of coordinates. If we denote a change of coordinates as a " view " of the physical set of points, then in this chapter we discuss the multi-view relations that can be determined from observations (views) of a dynamically changing point-configuration —-the underlying transformations and how they can be recovered. For example, for a point set in P 2 (planar configuration) undergoing linear motion the multiple views of the point set generate a multilinear constraint across three views governed by a 3 × 3 × 3 contravariant tensor H. The tensor, referred to as homography tensor, can be recovered linearly from 26 observations (matching points across three views) and once recovered can be unfolded to yield the global coordinate change (the individual pair of homography matrices). A point set in P 3 (3D configuration) can undergo motion in a plane or along a line (each point independently). For the line motion, the multi-view constraints are governed by a 4 × 4 × 4 family of contravariant tensors J that capture the dynamic 3D-to-3D alignment problem. More generally, the family of homography tensors is captured by three parameters: the dimension n of the observation space, the dimension k < n of the subspace along which each point of the point set is allowed to move, and the number of " views " m. Formally , the homography tensors form a GL(V) module, denoted by V (n, m, k), defined by the set of all tensors v 1 ⊗· · ·⊗v m ∈ V ⊗m where v i are n-dimensional vectors and dim Span{v 1 ,. .. , v m } ≤ k. We will be interested in the structure and dimension of V (n, m, k). The notion of using mutli-view analysis for non-rigid …
Pedestrian detection for driving assistance systems: single-frame classification and system level performance

We describe the functional and architectural breakdown of a monocular pedestrian detection system. We describe in detail our approach for single-frame classification based on a novel scheme of breaking down the class variability by repeatedly training a set of relatively simple classifiers on clusters of the training set. Single-frame classification performance results and system level performance figures for daytime conditions are presented with a discussion about the remaining gap to meet a daytime normal weather condition production system.
Kernel Feature Selection with Side Data Using a Spectral Approach

We address the problem of selecting a subset of the most relevant features from a set of sample data in cases where there are multiple (equally reasonable) solutions. In particular, this topic includes on one hand the introduction of hand-crafted kernels which emphasize certain desirable aspects of the data and, on the other hand, the suppression of one of the solutions given “side” data, i.e., when one is given information about undesired aspects of the data. Such situations often arise when there are several, even conflicting, dimensions to the data. For example, documents can be clustered based on topic, authorship or writing style; images of human faces can be clustered based on illumination conditions, facial expressions or by person identity, and so forth.
On the Relationship Between the Support Vector Machine for Classification and Sparsified Fisher's Linear Discriminant

We show that the orientation and location of the separating hyperplane for 2-class supervised pattern classification obtained by the Support Vector Machine (SVM) proposed by Vapnik and his colleagues, is equivalent to the solution obtained by Fisher's Linear Discriminant on the set of Support Vectors. In other words, SVM can be seen as a way to ‘sparsify’ Fisher's Linear Discriminant in order to obtain the most generalizing classification from the training set.
On Projection Matrices 
$$\mathcal{P}^k \to \mathcal{P}^2 ,k = 3,...,6, $$
 and their Applications in Computer Vision

AbstractProjection matrices from projective spaces 
$${\mathcal{P}}^3 {\text{ to }}{\mathcal{P}}^2 $$
 have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings 
$${\mathcal{P}}^k \to {\mathcal{P}}^2 ,k = 3,4,5,6$$
 for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices (where k > 3) and methods for extracting the (non-rigid) structure and motion for each application.
Multiple View Geometry of General Algebraic Curves

We introduce a number of new results in the context of multi-view geometry from general algebraic curves. We start with the recovery of camera geometry from matching curves. We first show how one can compute, without any knowledge on the camera, the homography induced by a single planar curve. Then we continue with the derivation of the extended Kruppa's equations which are responsible for describing the epipolar constraint of two projections of a general algebraic curve. As part of the derivation of those constraints we address the issue of dimension analysis and as a result establish the minimal number of algebraic curves required for a solution of the epipolar geometry as a function of their degree and genus.We then establish new results on the reconstruction of general algebraic curves from multiple views. We address three different representations of curves: (i) the regular point representation in which we show that the reconstruction from two views of a curve of degree d admits two solutions, one of degree d and the other of degree d(d − 1). Moreover using this representation, we address the problem of homography recovery for planar curves, (ii) dual space representation (tangents) for which we derive a lower bound for the number of views necessary for reconstruction as a function of the curve degree and genus, and (iii) a new representation (to computer vision) based on the set of lines meeting the curve which does not require any curve fitting in image space, for which we also derive lower bounds for the number of views necessary for reconstruction as a function of curve degree alone.
On Photometric Issues in 3D Visual Recognition from a Single 2D Image

We describe the problem of recognition under changing illumination conditions and changing viewing positions from a computational and human vision perspective. On the computational side we focus on the mathematical problems of creating an equivalence class for images of the same 3D object undergoing certain groups of transformations—mostly those due to changing illumination, and briefly discuss those due to changing viewing positions. The computational treatment culminates in proposing a simple scheme for recognizing, via alignment, an image of a familiar object taken from a novel viewing position and a novel illumination condition. On the human vision aspect, the paper is motivated by empirical evidence inspired by Mooney images of faces that suggest a relatively high level of visual processing is involved in compensating for photometric sources of variability, and furthermore, that certain limitations on the admissible representations of image information may exist. The psychophysical observations and the computational results that follow agree in several important respects, such as the same (apparent) limitations on image representations.
Selecting Relevant Genes with a Spectral Approach

Array technologies have made it possible to record simultaneously the expression pattern of thousands of genes. A fundamental problem in the analysis of gene expression data is the identificat ion of highly relevant genes that either discriminate between phenotypic labels or are important with respect to the cellular process studied in the experiment: for example cell cycle or heat shock in yeast experiments, chemical or genetic perturbations of mammalian cell lines, and genes involved in class discovery for human tumors. In this paper we focus on the task of unsupervised gene selection. The problem of selecting a small subset of genes is particularly chal lenging as the datasets involved are typically characterized by a ve ry small sample size — in the order of few tens of tissue samples — and by a very large feature space as the number of genes tend to be in the high thousands. We propose a model independent approach which scores candidate gene selections using spectral properties of the candidate affinity matrix. The algorithm is very straigh tforward to implement yet contains a number of remarkable properties which guarantee consistent sparse selections. To illustrate the value of our approach we applied our algorithm on five different datasets . The first consists of time course data from four well studied Hema topoietic cell lines (HL-60, Jurkat, NB4, and U937). The other four datasets include three well studied treatment outcomes (large cell lymphoma, childhood medulloblastomas, breast tumors) and one unpublished dataset (lymph status). We compared our approach both with other unsupervised methods (SOM,PCA,GS) and with supervised methods (SNR,RMB,RFE). The results clearly show that our approach considerably outperforms all the other unsupervised approaches in our study, is competitive with supervised methods and in some case even outperforms supervised approaches.
Guest Editorial

• advances in multi-view stereo reconstruction have led to impressive results in recovering geometricallyand photometrically-complex shapes from large collections of photographs; • image-based modeling and rendering techniques have demonstrated the potential of creating photo-realistic simulations of real scenes; and • the area of structure-from-motion has evolved into a body of results related to the representation of 3D space and its camera views in terms of collections of functions representing both the geometric and photometric variability of image space.
The Quadric Reference Surface: Theory and Applications

The conceptual component of this work is about “reference surfaces” which are the analogous to reference frames often used for shape representation purposes. The theoretical component of this work involves the question of whether one can find a unique (and simple) mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3D, given (i) few corresponding points in the two views, or (ii) the outline conic of the surface in one view (only) and few corresponding points in the two views. The practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects.
Forward collision warning with a single camera

The large number of rear end collisions due to driver inattention has been identified as a major automotive safety issue. Even a short advance warning can significantly reduce the number and severity of the collisions. This paper describes a vision based forward collision warning (FCW) system for highway safety. The algorithm described in this paper computes time to contact (TTC) and possible collision course directly from the size and position of the vehicles in the image - which are the natural measurements for a vision based system - without having to compute a 3D representation of the scene. The use of a single low cost image sensor results in an affordable system which is simple to install. The system has been implemented on real-time hardware and has been test driven on highways. Collision avoidance tests have also been performed on test tracks.
Feature selection for unsupervised and supervised inference: the emergence of sparsity in a weighted-based approach

The problem of selecting a subset of relevant features in a potentially overwhelming quantity of data is classic and found in many branches of science including - examples in computer vision, text processing and more recently bioinformatics are abundant. We present a definition of "relevancy" based on spectral properties of the Affinity (or Laplacian) of the features' measurement matrix. The feature selection process is then based on a continuous ranking of the features defined by a least-squares optimization process. A remarkable property of the feature relevance function is that sparse solutions for the ranking values naturally emerge as a result of a "biased nonnegativity" of a key matrix in the process. As a result, a simple least-squares optimization process converges onto a sparse solution, i.e., a selection of a subset of features which form a local maxima over the relevance function. The feature selection algorithm can be embedded in both unsupervised and supervised inference problems and empirical evidence shows that the feature selections typically achieve high accuracy even when only a small fraction of the features are relevant.
Kernel Feature Selection

We address the problem of using a kernel spectral criterion function for feature selection. A feature selection paradigm using spectral properties of the affinity matrix of the input data was recently introduced in  and which leads to a bilinear interaction between entries of the data sample. Our goal in this paper is to extend the idea of spectral criteria for feature selection to higher order interactions among the data by introducing a kernel operation through which high-order mappings of the original feature vectors can be made possible.
Learning over Sets using Kernel Principal Angles

We consider the problem of learning with instances defined over a space of sets of vectors. We derive a new positive definite kernel f(A,B) defined over pairs of matrices A,B based on the concept of principal angles between two linear subspaces. We show that the principal angles can be recovered using only inner-products between pairs of column vectors of the input matrices thereby allowing the original column vectors of A,B to be mapped onto arbitrarily high-dimensional feature spaces.We demonstrate the usage of the matrix-based kernel function f(A,B) with experiments on two visual tasks. The first task is the discrimination of "irregular" motion trajectory of an individual or a group of individuals in a video sequence. We use the SVM approach using f(A,B) where an input matrix represents the motion trajectory of a group of individuals over a certain (fixed) time frame. We show that the classification (irregular versus regular) greatly outperforms the conventional representation where all the trajectories form a single vector. The second application is the visual recognition of faces from input video sequences representing head motion and facial expressions where f(A,B) is used to compare two image sequences.
Kernel principal angles for classification machines with applications to image sequence interpretation

We consider the problem of learning with instances defined over a space of sets of vectors. We derive a new positive definite kernel f(A, B) defined over pairs of matrices A, B based on the concept of principal angles between two linear subspaces. We show that the principal angles can be recovered using only inner-products between pairs of column vectors of the input matrices thereby allowing the original column vectors of A, B to be mapped onto arbitrarily high-dimensional feature spaces. We apply this technique to inference over image sequences applications of face recognition and irregular motion trajectory detection.