The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch

Recent and forthcoming advances in instrumentation, and giant new surveys, are creating astronomical data sets that are not amenable to the methods of analysis familiar to astronomers. Traditional methods are often inadequate not merely because of the size in bytes of the data sets, but also because of the complexity of modern data sets. Mathematical limitations of familiar algorithms and techniques in dealing with such data sets create a critical need for new paradigms for the representation, analysis and scientific visualization (as opposed to illustrative visualization) of heterogeneous, multiresolution data across application domains. Some of the problems presented by the new data sets have been addressed by other disciplines such as applied mathematics, statistics and machine learning and have been utilized by other sciences such as space-based geosciences. Unfortunately, valuable results pertaining to these problems are mostly to be found only in publications outside of astronomy. Here we offer brief overviews of a number of concepts, techniques and developments, some "old" and some new. These are generally unknown to most of the astronomical community, but are vital to the analysis and visualization of complex datasets and images. In order for astronomers to take advantage of the richness and complexity of the new era of data, and to be able to identify, adopt, and apply new solutions, the astronomical community needs a certain degree of awareness and understanding of the new concepts. One of the goals of this paper is to help bridge the gap between applied mathematics, artificial intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in Astronomy, special issue "Robotic Astronomy

Bispectrum Inversion with Application to Multireference Alignment

We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the signal by aligning and averaging the data. In contrast, we consider a method based on estimating the signal directly, using features of the signal that are invariant under translations. Specifically, we estimate the power spectrum and the bispectrum of the signal from the observations. Under mild assumptions, these invariant features contain enough information to infer the signal. In particular, the bispectrum can be used to estimate the Fourier phases. To this end, we propose and analyze a few algorithms. Our main methods consist of non-convex optimization over the smooth manifold of phases. Empirically, in the absence of noise, these non-convex algorithms appear to converge to the target signal with random initialization. The algorithms are also robust to noise. We then suggest three additional methods. These methods are based on frequency marching, semidefinite relaxation and integer programming. The first two methods provably recover the phases exactly in the absence of noise. In the high noise level regime, the invariant features approach for MRA results in stable estimation if the number of measurements scales like the cube of the noise variance, which is the information-theoretic rate. Additionally, it requires only one pass over the data which is important at low signal-to-noise ratio when the number of observations must be large

Classification Modeling for Malaysian Blooming Flower Images Using Neural Networks

Image processing is a rapidly growing research area of computer science and remains as a challenging problem within the computer vision fields. For the classification of flower images, the problem is mainly due to the huge similarities in terms of colour and texture. The appearance of the image itself such as variation of lights due to different lighting condition, shadow effect on the object’s surface, size, shape, rotation and position, background clutter, states of blooming or budding may affect the utilized classification techniques. This study aims to develop a classification model for Malaysian blooming flowers using neural network with the back propagation algorithms. The flower image is extracted through Region of Interest (ROI) in which texture and colour are emphasized in this study. In this research, a total of 960 images were extracted from 16 types of flowers. Each ROI was represented by three colour attributes (Hue, Saturation, and Value) and four textures attribute (Contrast, Correlation, Energy and Homogeneity). In training and testing phases, experiments were carried out to observe the classification performance of Neural Networks with duplication of difficult pattern to learn (referred to as DOUBLE) as this could possibly explain as to why some flower images were difficult to learn by classifiers. Results show that the overall performance of Neural Network with DOUBLE is 96.3% while actual data set is 68.3%, and the accuracy obtained from Logistic Regression with actual data set is 60.5%. The Decision Tree classification results indicate that the highest performance obtained by Chi-Squared Automatic Interaction Detection(CHAID) and Exhaustive CHAID (EX-CHAID) is merely 42% with DOUBLE. The findings from this study indicate that Neural Network with DOUBLE data set produces highest performance compared to Logistic Regression and Decision Tree. Therefore, NN has been potential in building Malaysian blooming flower model. Future studies can be focused on increasing the sample size and ROI thus may lead to a higher percentage of accuracy. Nevertheless, the developed flower model can be used as part of the Malaysian Blooming Flower recognition system in the future where the colours and texture are needed in the flower identification process

Scene construction impairments in Alzheimer's disease – A unique role for the posterior cingulate cortex

Episodic memory dysfunction represents one of the most prominent and characteristic clinical features of patients with Alzheimer's disease (AD), attributable to the degeneration of medial temporal and posterior parietal regions of the brain. Recent studies have demonstrated marked impairments in the ability to envisage personally relevant events in the future in AD. It remains unclear, however, whether AD patients can imagine fictitious scenes free from temporal constraints, a process that is proposed to rely fundamentally upon the integrity of the hippocampus. The objective of the present study was to investigate the capacity for atemporal scene construction, and its associated neural substrates, in AD. Fourteen AD patients were tested on the scene construction task and their performance was contrasted with 14 age- and education-matched healthy older Control participants. Scene construction performance was strikingly compromised in the AD group, with significant impairments evident for provision of contextual details, spatial coherence, and the overall richness of the imagined experience. Voxel-based morphometry analyses based on structural MRI revealed significant associations between scene construction capacity and atrophy in posterior parietal and lateral temporal brain structures in AD. In contrast, scene construction performance in Controls was related to integrity of frontal, parietal, and medial temporal structures, including the parahippocampal gyrus and posterior hippocampus. The posterior cingulate cortex (PCC) emerged as the common region implicated for scene construction performance across participant groups. Our study highlights the importance of regions specialised for spatial and contextual processing for the construction of atemporal scenes. Damage to these regions in AD compromises the ability to construct novel scenes, leading to the recapitulation of content from previously experienced events