Soft clustering analysis of galaxy morphologies: A worked example with SDSS

Context: The huge and still rapidly growing amount of galaxies in modern sky surveys raises the need of an automated and objective classification method. Unsupervised learning algorithms are of particular interest, since they discover classes automatically. Aims: We briefly discuss the pitfalls of oversimplified classification methods and outline an alternative approach called "clustering analysis". Methods: We categorise different classification methods according to their capabilities. Based on this categorisation, we present a probabilistic classification algorithm that automatically detects the optimal classes preferred by the data. We explore the reliability of this algorithm in systematic tests. Using a small sample of bright galaxies from the SDSS, we demonstrate the performance of this algorithm in practice. We are able to disentangle the problems of classification and parametrisation of galaxy morphologies in this case. Results: We give physical arguments that a probabilistic classification scheme is necessary. The algorithm we present produces reasonable morphological classes and object-to-class assignments without any prior assumptions. Conclusions: There are sophisticated automated classification algorithms that meet all necessary requirements, but a lot of work is still needed on the interpretation of the results.Comment: 18 pages, 19 figures, 2 tables, submitted to A

Knee Angles and Axes Crosstalk Correction In Gait, Cycling, and Elliptical Training Exercises

When conducting motion analysis using 3-dimensional motion capture technology, errors in marker placement on the knee results in a widely observed phenomenon known as “crosstalk” [1-18] in calculated knee joint angles (i.e., flexion-extension (FE), adduction-abduction (AA), internal-external rotation (IE)). Principal Component Analysis (PCA) has recently been proposed as a post hoc method to reduce crosstalk errors and operates by minimizing the correlation between the knee angles [1, 2]. However, recent studies that have used PCA have neither considered exercises, such as cycling (C) and elliptical training (E), other than gait (G) nor estimated the corrected knee axes following PCA correction. The hypothesis of this study is that PCA can correct for crosstalk in G, C, and E exercises but that subject-specific PCA corrected axes differ for these exercises. Motion analysis of the selected exercises were conducted on 8 normal weight (body mass index (BMI) = 21.70 +/- 3.20) and 7 overweight participants (BMI = 27.45 +/- 2.45). An enhanced Helen Hayes marker set with 27 markers was used to track kinematics. Knee joint FE, AA, and IE angles were obtained with Cortex (Motion Analysis, Santa Rosa, CA) software and corrected using PCA to obtain corrected angles for each exercise. Exercise-specific corrected knee joint axes were determined by finding axes that reproduced the shank and ankle body vectors taken from Cortex when used with the PCA corrected angles. Then, PCA corrected gait axes were used as a common set of axes for all exercises to find corresponding knee angles. Paired t-tests assessed if FE-AA angle correlations changed with PCA. Multivariate Paired Hotelling’s T-Square tests assessed if the PCA corrected knee joint axes were similar between exercises. ANOVA was used to assess if Cortex angles, PCA corrected angles, and knee angles using PCA corrected gait axes were different. Reduced FE-AA angle correlations existed for G (p\u3c0.001 for Cortex and p=0.85 for PCA corrected), C (p=0.01 for Cortex and p=0.77 for PCA corrected), and E (p\u3c0.001 for Cortex and p=0.77 for PCA corrected). Differences in the PCA corrected knee axes were found between G and C (p\u3c0.0014). Then, differences were found between Cortex, PCA corrected, and C and E knee angles using the PCA corrected G axes (p\u3c0.0056). The results of this study suggest that if PCA is used to reduce crosstalk errors in motions other than G then it is recommended to adopt the use of a PCA corrected axes set determined from G to produce the PCA corrected angles

Dynamic Algorithms and Asymptotic Theory for Lp-norm Data Analysis

The focus of this dissertation is the development of outlier-resistant stochastic algorithms for Principal Component Analysis (PCA) and the derivation of novel asymptotic theory for Lp-norm Principal Component Analysis (Lp-PCA). Modern machine learning and signal processing applications employ sensors that collect large volumes of data measurements that are stored in the form of data matrices, that are often massive and need to be efficiently processed in order to enable machine learning algorithms to perform effective underlying pattern discovery. One such commonly used matrix analysis technique is PCA. Over the past century, PCA has been extensively used in areas such as machine learning, deep learning, pattern recognition, and computer vision, just to name a few. PCA\u27s popularity can be attributed to its intuitive formulation on the L2-norm, availability of an elegant solution via the singular-value-decomposition (SVD), and asymptotic convergence guarantees. However, PCA has been shown to be highly sensitive to faulty measurements (outliers) because of its reliance on the outlier-sensitive L2-norm. Arguably, the most straightforward approach to impart robustness against outliers is to replace the outlier-sensitive L2-norm by the outlier-resistant L1-norm, thus formulating what is known as L1-PCA. Exact and approximate solvers are proposed for L1-PCA in the literature. On the other hand, in this big-data era, the data matrix may be very large and/or the data measurements may arrive in streaming fashion. Traditional L1-PCA algorithms are not suitable in this setting. In order to efficiently process streaming data, while being resistant against outliers, we propose a stochastic L1-PCA algorithm that computes the dominant principal component (PC) with formal convergence guarantees. We further generalize our stochastic L1-PCA algorithm to find multiple components by propose a new PCA framework that maximizes the recently proposed Barron loss. Leveraging Barron loss yields a stochastic algorithm with a tunable robustness parameter that allows the user to control the amount of outlier-resistance required in a given application. We demonstrate the efficacy and robustness of our stochastic algorithms on synthetic and real-world datasets. Our experimental studies include online subspace estimation, classification, video surveillance, and image conditioning, among other things. Last, we focus on the development of asymptotic theory for Lp-PCA. In general, Lp-PCA for p\u3c2 has shown to outperform PCA in the presence of outliers owing to its outlier resistance. However, unlike PCA, Lp-PCA is perceived as a ``robust heuristic\u27\u27 by the research community due to the lack of theoretical asymptotic convergence guarantees. In this work, we strive to shed light on the topic by developing asymptotic theory for Lp-PCA. Specifically, we show that, for a broad class of data distributions, the Lp-PCs span the same subspace as the standard PCs asymptotically and moreover, we prove that the Lp-PCs are specific rotated versions of the PCs. Finally, we demonstrate the asymptotic equivalence of PCA and Lp-PCA with a wide variety of experimental studies

A Survey on Ear Biometrics

Recognizing people by their ear has recently received significant attention in the literature. Several reasons account for this trend: first, ear recognition does not suffer from some problems associated with other non contact biometrics, such as face recognition; second, it is the most promising candidate for combination with the face in the context of multi-pose face recognition; and third, the ear can be used for human recognition in surveillance videos where the face may be occluded completely or in part. Further, the ear appears to degrade little with age. Even though, current ear detection and recognition systems have reached a certain level of maturity, their success is limited to controlled indoor conditions. In addition to variation in illumination, other open research problems include hair occlusion; earprint forensics; ear symmetry; ear classification; and ear individuality. This paper provides a detailed survey of research conducted in ear detection and recognition. It provides an up-to-date review of the existing literature revealing the current state-of-art for not only those who are working in this area but also for those who might exploit this new approach. Furthermore, it offers insights into some unsolved ear recognition problems as well as ear databases available for researchers

HST NIR Snapshot Survey of 3CR Radio Source Counterparts II: An Atlas and Inventory of the Host Galaxies, Mergers and Companions

We present the second part of an H-band (1.6 microns) atlas of z<0.3 3CR radio galaxies, using the Hubble Space Telescope Near Infrared Camera and Multi-Object Spectrometer (HST NICMOS2). We present new imaging for 21 recently acquired sources, and host galaxy modeling for the full sample of 101 (including 11 archival) -- an 87% completion rate. Two different modeling techniques are applied, following those adopted by the galaxy morphology and the quasar host galaxy communities. Results are compared, and found to be in excellent agreement, although the former breaks down in the case of strongly nucleated sources. Companion sources are tabulated, and the presence of mergers, tidal features, dust disks and jets are catalogued. The tables form a catalogue for those interested in the structural and morphological dust-free host galaxy properties of the 3CR sample, and for comparison with morphological studies of quiescent galaxies and quasar host galaxies. Host galaxy masses are estimated, and found to typically lie at around 2*10^11 solar masses. In general, the population is found to be consistent with the local population of quiescent elliptical galaxies, but with a longer tail to low Sersic index, mainly consisting of low-redshift (z<0.1) and low-radio-power (FR I) sources. A few unusually disky FR II host galaxies are picked out for further discussion. Nearby external sources are identified in the majority of our images, many of which we argue are likely to be companion galaxies or merger remnants. The reduced NICMOS data are now publicly available from our website (http://archive.stsci.edu/prepds/3cr/)Comment: ApJS, 177, 148: Final version; includes revised figures 1, 15b, and section 7.5 (and other minor changes from editing process. 65 pages, inc. 17 figure

Image segmentation and pattern classification using support vector machines

Image segmentation and pattern classification have long been important topics in computer science research. Image segmentation is one of the basic and challenging lower-level image processing tasks. Feature extraction, feature reduction, and classifier design based on selected features are the three essential issues for the pattern classification problem. In this dissertation, an automatic Seeded Region Growing (SRG) algorithm for color image segmentation is developed. In the SRG algorithm, the initial seeds are automatically determined. An adaptive morphological edge-linking algorithm to fill in the gaps between edge segments is designed. Broken edges are extended along their slope directions by using the adaptive dilation operation with suitably sized elliptical structuring elements. The size and orientation of the structuring element are adjusted according to local properties. For feature reduction, an improved feature reduction method in input and feature spaces using Support Vector Machines (SVMs) is developed. In the input space, a subset of input features is selected by the ranking of their contributions to the decision function. In the feature space, features are ranked according to the weighted support vectors in each dimension. For object detection, a fast face detection system using SVMs is designed. Twoeye patterns are first detected using a linear SVM, so that most of the background can be eliminated quickly. Two-layer 2nd-degree polynomial SVMs are trained for further face verification. The detection process is implemented directly in feature space, which leads to a faster SVM. By training a two-layer SVM, higher classification rates can be achieved. For active learning, an improved incremental training algorithm for SVMs is developed. Instead of selecting training samples randomly, the k-mean clustering algorithm is applied to collect the initial set of training samples. In active query, a weight is assigned to each sample according to its distance to the current separating hyperplane and the confidence factor. The confidence factor, calculated from the upper bounds of SVM errors, is used to indicate the degree of closeness of the current separating hyperplane to the optimal solution

Robust Orthogonal Complement Principal Component Analysis

Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal subspace estimation. Based on a mathematical formulation of such transformed outliers, a novel robust orthogonal complement principal component analysis (ROC-PCA) is proposed. The framework combines the popular sparsity-enforcing and low rank regularization techniques to deal with row-wise outliers as well as element-wise outliers. A non-asymptotic oracle inequality guarantees the accuracy and high breakdown performance of ROC-PCA in finite samples. To tackle the computational challenges, an efficient algorithm is developed on the basis of Stiefel manifold optimization and iterative thresholding. Furthermore, a batch variant is proposed to significantly reduce the cost in ultra high dimensions. The paper also points out a pitfall of a common practice of SVD reduction in robust PCA. Experiments show the effectiveness and efficiency of ROC-PCA in both synthetic and real data

Bags of Affine Subspaces for Robust Object Tracking

We propose an adaptive tracking algorithm where the object is modelled as a continuously updated bag of affine subspaces, with each subspace constructed from the object's appearance over several consecutive frames. In contrast to linear subspaces, affine subspaces explicitly model the origin of subspaces. Furthermore, instead of using a brittle point-to-subspace distance during the search for the object in a new frame, we propose to use a subspace-to-subspace distance by representing candidate image areas also as affine subspaces. Distances between subspaces are then obtained by exploiting the non-Euclidean geometry of Grassmann manifolds. Experiments on challenging videos (containing object occlusions, deformations, as well as variations in pose and illumination) indicate that the proposed method achieves higher tracking accuracy than several recent discriminative trackers.Comment: in International Conference on Digital Image Computing: Techniques and Applications, 201

Assumption-Free Assessment of Corpus Callosum Shape: Benchmarking and Application

Shape analysis provides a unique insight into biological processes. This paper evaluates the properties, performance, and utility of elliptical Fourier (eFourier) analysis to operationalise global shape, focussing on the human corpus callosum. 8000 simulated corpus callosum contours were generated, systematically varying in terms of global shape (midbody arch, splenium size), local complexity (surface smoothness), and nonshape characteristics (e.g., rotation). 2088 real corpus callosum contours were manually traced from the PATH study. Performance of eFourier was benchmarked in terms of its capacity to capture and then reconstruct shape and systematically operationalise that shape via principal components analysis. We also compared the predictive performance of corpus callosum volume, position in Procrustes-aligned Landmark tangent space, and position in eFourier n-dimensional shape space in relation to the Symbol Digit Modalities Test. Jaccard index for original vs. reconstructed from eFourier shapes was excellent (M=0.98). The combination of eFourier and PCA performed particularly well in reconstructing known n-dimensional shape space but was disrupted by the inclusion of local shape manipulations. For the case study, volume, eFourier, and landmark measures were all correlated. Mixed effect model results indicated all methods detected similar features, but eFourier estimates were most predictive, and of the two shape operationalization techniques had the least error and better model fit. Elliptical Fourier analysis, particularly in combination with principal component analysis, is a powerful, assumption-free and intuitive method of quantifying global shape of the corpus callosum and shows great promise for shape analysis in neuroimaging more broadly.Te study was supported by NHMRC of Australia Grant No. 1002160, 1063907 and ARC Grant 130101705. Tis research was partly undertaken on the National Computational Infrastructure (NCI) facility in Canberra, Australia, which is supported by the Australian Commonwealth Government