CUR Decompositions, Similarity Matrices, and Subspace Clustering

A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces $\mathscr{U}=\underset{i=1}{\overset{M}\bigcup}S_i$. The similarity matrices thus constructed give the exact clustering in the noise-free case. Additionally, this decomposition gives rise to many distinct similarity matrices from a given set of data, which allow enough flexibility to perform accurate clustering of noisy data. We also show that two known methods for subspace clustering can be derived from the CUR decomposition. An algorithm based on the theoretical construction of similarity matrices is presented, and experiments on synthetic and real data are presented to test the method. Additionally, an adaptation of our CUR based similarity matrices is utilized to provide a heuristic algorithm for subspace clustering; this algorithm yields the best overall performance to date for clustering the Hopkins155 motion segmentation dataset.Comment: Approximately 30 pages. Current version contains improved algorithm and numerical experiments from the previous versio

Assessing the quality of a student-generated question repository

We present results from a study that categorizes and assesses the quality of questions and explanations authored by students, in question repositories produced as part of the summative assessment in introductory physics courses over the past two years. Mapping question quality onto the levels in the cognitive domain of Bloom's taxonomy, we find that students produce questions of high quality. More than three-quarters of questions fall into categories beyond simple recall, in contrast to similar studies of student-authored content in different subject domains. Similarly, the quality of student-authored explanations for questions was also high, with approximately 60% of all explanations classified as being of high or outstanding quality. Overall, 75% of questions met combined quality criteria, which we hypothesize is due in part to the in-class scaffolding activities that we provided for students ahead of requiring them to author questions.Comment: 24 pages, 5 figure

Conformal symmetry and light flavor baryon spectra

The degeneracy among parity pairs systematically observed in the N and Delta spectra is interpreted to hint on a possible conformal symmetry realization in the light flavor baryon sector in line with AdS_5/CFT_4. The case is made by showing that all the observed N and Delta resonances with masses below 2500 MeV distribute fairly well each over the first levels of a unitary representation of the conformal group, a representation that covers the spectrum of a quark-diquark system, placed directly on the AdS_5 cone, conformally compactified to R^1*S^3. The free geodesic motion on the S^3 manifold is described by means of the scalar conformal equation there, which is of the Klein-Gordon type. The equation is then gauged by the "curved" Coulomb potential that has the form of a cotangent function. Conformal symmetry is not exact, this because the gauge potential slightly modifies the conformal centrifugal barrier of the free geodesic motion. Thanks to this, the degeneracy between P11-S11 pairs from same level is relaxed, while the remaining states belonging to same level remain practically degenerate. The model describes the correct mass ordering in the P11-S11 pairs through the nucleon spectrum as a combined effect of the above conformal symmetry breaking, on the one side, and a parity change of the diquark from a scalar at low masses, to a pseudoscalar at higher masses, on the other. The quality of the wave functions is illustrated by calculations of realistic mean-square charge radii and electric charge form-factors on the examples of the proton, and the protonic P11(1440), and S11(1535) resonances. The scheme also allows for a prediction of the dressing function of an effective instantaneous gluon propagator from the Fourier transform of the gauge potential. We find a dressing function that is finite in the infrared and tends to zero at infinity.Comment: Latex, 5 figures, 2 tables; Paper upgraded in accord with the published version. Discussion on the meson sector include

Posing 3D Models from Drawing

Inferring the 3D pose of a character from a drawing is a complex and under-constrained problem. Solving it may help automate various parts of an animation production pipeline such as pre-visualisation. In this paper, a novel way of inferring the 3D pose from a monocular 2D sketch is proposed. The proposed method does not make any external assumptions about the model, allowing it to be used on different types of characters. The inference of the 3D pose is formulated as an optimisation problem and a parallel variation of the Particle Swarm Optimisation algorithm called PARAC-LOAPSO is utilised for searching the minimum. Testing in isolation as well as part of a larger scene, the presented method is evaluated by posing a lamp, a horse and a human character. The results show that this method is robust, highly scalable and is able to be extended to various types of models

Automated Classification of Airborne Laser Scanning Point Clouds

Making sense of the physical world has always been at the core of mapping. Up until recently, this has always dependent on using the human eye. Using airborne lasers, it has become possible to quickly "see" more of the world in many more dimensions. The resulting enormous point clouds serve as data sources for applications far beyond the original mapping purposes ranging from flooding protection and forestry to threat mitigation. In order to process these large quantities of data, novel methods are required. In this contribution, we develop models to automatically classify ground cover and soil types. Using the logic of machine learning, we critically review the advantages of supervised and unsupervised methods. Focusing on decision trees, we improve accuracy by including beam vector components and using a genetic algorithm. We find that our approach delivers consistently high quality classifications, surpassing classical methods

Analytic Framework for Students' Use of Mathematics in Upper-Division Physics

Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and researchers in characterizing students' difficulties with specific mathematical tools when solving the long and complex problems that are characteristic of upper-division. In this paper, we present this framework, including its motivation and development. We also describe an application of the framework to investigations of student difficulties with direct integration in electricity and magnetism (i.e., Coulomb's Law) and approximation methods in classical mechanics (i.e., Taylor series). These investigations provide examples of the types of difficulties encountered by advanced physics students, as well as the utility of the framework for both researchers and instructors.Comment: 17 pages, 4 figures, 3 tables, in Phys. Rev. - PE

Sparse and low rank approximations for action recognition

Action recognition is crucial area of research in computer vision with wide range of applications in surveillance, patient-monitoring systems, video indexing, Human- Computer Interaction and many more. These applications require automated action recognition. Robust classification methods are sought-after despite influential research in this field over past decade. The data resources have grown tremendously owing to the advances in the digital revolution which cannot be compared to the meagre resources in the past. The main limitation on a system when dealing with video data is the computational burden due to large dimensions and data redundancy. Sparse and low rank approximation methods have evolved recently which aim at concise and meaningful representation of data. This thesis explores the application of sparse and low rank approximation methods in the context of video data classification with the following contributions. 1. An approach for solving the problem of action and gesture classification is proposed within the sparse representation domain, effectively dealing with large feature dimensions, 2. Low rank matrix completion approach is proposed to jointly classify more than one action 3. Deep features are proposed for robust classification of multiple actions within matrix completion framework which can handle data deficiencies. This thesis starts with the applicability of sparse representations based classifi- cation methods to the problem of action and gesture recognition. Random projection is used to reduce the dimensionality of the features. These are referred to as compressed features in this thesis. The dictionary formed with compressed features has proved to be efficient for the classification task achieving comparable results to the state of the art. Next, this thesis addresses the more promising problem of simultaneous classifi- cation of multiple actions. This is treated as matrix completion problem under transduction setting. Matrix completion methods are considered as the generic extension to the sparse representation methods from compressed sensing point of view. The features and corresponding labels of the training and test data are concatenated and placed as columns of a matrix. The unknown test labels would be the missing entries in that matrix. This is solved using rank minimization techniques based on the assumption that the underlying complete matrix would be a low rank one. This approach has achieved results better than the state of the art on datasets with varying complexities. This thesis then extends the matrix completion framework for joint classification of actions to handle the missing features besides missing test labels. In this context, deep features from a convolutional neural network are proposed. A convolutional neural network is trained on the training data and features are extracted from train and test data from the trained network. The performance of the deep features has proved to be promising when compared to the state of the art hand-crafted features

Computer Vision without Vision : Methods and Applications of Radio and Audio Based SLAM

The central problem of this thesis is estimating receiver-sender node positions from measured receiver-sender distances or equivalent measurements. This problem arises in many applications such as microphone array calibration, radio antenna array calibration, mapping and positioning using ultra-wideband and mapping and positioning using round-trip-time measurements between mobile phones and Wi-Fi-units. Previous research has explored some of these problems, creating minimal solvers for instance, but these solutions lack real world implementation. Due to the nature of using different media, finding reliable receiver-sender distances is tough, with many of the measurements being erroneous or to a worse extent missing. Therefore in this thesis, we explore using minimal solvers to create robust solutions, that encompass small erroneous measurements and work around missing and grossly erroneous measurements.This thesis focuses mainly on Time-of-Arrival measurements using radio technologies such as Two-way-Ranging in Ultra-Wideband and a new IEEE standard 802.11mc found on many WiFi modules. The methods investigated, also related to Computer Vision problems such as Stucture-from-Motion. As part of this thesis, a range of new commercial radio technologies are characterised in terms of ranging in real world enviroments. In doing so, we have shown how these technologies can be used as a more accurate alternative to the Global Positioning System in indoor enviroments. Further to these solutions, more methods are proposed for large scale problems when multiple users will collect the data, commonly known as Big Data. For these cases, more data is not always better, so a method is proposed to try find the relevant data to calibrate large systems