Analysis of Irregular Spatial Data with Machine Learning: Classification of Building Patterns with a Graph Convolutional Neural Network (Short Paper)

Machine learning methods such as Convolutional Neural Network (CNN) are becoming an integral part of scientific research in many disciplines, the analysis of spatial data often failed to these powerful methods because of its irregularity. By using the graph Fourier transform and convolution theorem, we try to convert the convolution operation into a point-wise product in Fourier domain and build a learning architecture of graph CNN for the classification of building patterns. Experiments showed that this method has achieved outstanding results in identifying regular and irregular patterns, and has significantly improved in comparing with other methods

"Selection of Input Parameters for Multivariate Classifiersin Proactive Machine Health Monitoring by Clustering Envelope Spectrum Harmonics"

In condition monitoring (CM) signal analysis the inherent problem of key characteristics being masked by noise can be addressed by analysis of the signal envelope. Envelope analysis of vibration signals is effective in extracting useful information for diagnosing different faults. However, the number of envelope features is generally too large to be effectively incorporated in system models. In this paper a novel method of extracting the pertinent information from such signals based on multivariate statistical techniques is developed which substantialy reduces the number of input parameters required for data classification models. This was achieved by clustering possible model variables into a number of homogeneous groups to assertain levels of interdependency. Representatives from each of the groups were selected for their power to discriminate between the categorical classes. The techniques established were applied to a reciprocating compressor rig wherein the target was identifying machine states with respect to operational health through comparison of signal outputs for healthy and faulty systems. The technique allowed near perfect fault classification. In addition methods for identifying seperable classes are investigated through profiling techniques, illustrated using Andrew’s Fourier curves

Moment-Matching Polynomials

We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem and deviate significantly from known Fourier-based methods, which require the underlying distribution to have some product structure. Our main application is the first polynomial-time algorithm for agnostically learning any function of a constant number of halfspaces with respect to any log-concave distribution (for any constant accuracy parameter). This result was not known even for the case of learning the intersection of two halfspaces without noise. Additionally, we show that in the "smoothed-analysis" setting, the above results hold with respect to distributions that have sub-exponential tails, a property satisfied by many natural and well-studied distributions in machine learning. Given that our algorithms can be implemented using Support Vector Machines (SVMs) with a polynomial kernel, these results give a rigorous theoretical explanation as to why many kernel methods work so well in practice

Selection of Input Parameters for Multivariate Classifiers in Proactive Machine Health Monitoring by Clustering Envelope Spectrum Harmonics

In condition monitoring (CM) signal analysis the inherent problem of key characteristics being masked by noise can be addressed by analysis of the signal envelope. Envelope analysis of vibration signals is effective in extracting useful information for diagnosing different faults. However, the number of envelope features is generally too large to be effectively incorporated in system models. In this paper a novel method of extracting the pertinent information from such signals based on multivariate statistical techniques is developed which substantialy reduces the number of input parameters required for data classification models. This was achieved by clustering possible model variables into a number of homogeneous groups to assertain levels of interdependency. Representatives from each of the groups were selected for their power to discriminate between the categorical classes. The techniques established were applied to a reciprocating compressor rig wherein the target was identifying machine states with respect to operational health through comparison of signal outputs for healthy and faulty systems. The technique allowed near perfect fault classification. In addition methods for identifying seperable classes are investigated through profiling techniques, illustrated using Andrew’s Fourier curves

Automatic microscopic image analysis by moving window local Fourier Transform and Machine Learning

Analysis of microscope images is a tedious work which requires patience and time, usually done manually by the microscopist after data collection. The results obtained in such a way might be biased by the human who performed the analysis. Here we introduce an approach of automatic image analysis, which is based on locally applied Fourier Transform and Machine Learning methods. In this approach, a whole image is scanned by a local moving window with defined size and the 2D Fourier Transform is calculated for each window. Then, all the Local Fourier Transforms are fed into Machine Learning processing. Firstly, a number of components in the data is estimated from Principal Component Analysis (PCA) Scree Plot performed on the data. Secondly, the data are decomposed blindly by Non-Negative Matrix Factorization (NMF) into interpretable spatial maps (loadings) and corresponding Fourier Transforms (factors). As a result, the microscopic image is analyzed and the features on the image are automatically discovered, based on the local changes in Fourier Transform, without human bias. The user selects only a size and movement of the scanning local window which defines the final analysis resolution. This automatic approach was successfully applied to analysis of various microscopic images with and without local periodicity i.e. atomically resolved High Angle Annular Dark Field (HAADF) Scanning Transmission Electron Microscopy (STEM) image of Au nanoisland of fcc and Au hcp phases, Scanning Tunneling Microscopy (STM) image of Au-induced reconstruction on Ge(001) surface, Scanning Electron Microscopy (SEM) image of metallic nanoclusters grown on GaSb surface, and Fluorescence microscopy image of HeLa cell line of cervical cancer. The proposed approach could be used to automatically analyze the local structure of microscopic images within a time of about a minute for a single image on a modern desktop/notebook computer and it is freely available as a Python analysis notebook and Python program for batch processing

Application of several methods for determining transfer functions and frequency response of aircraft from flight data

In the process of analyzing the longitudinal frequency-response characteristics of aircraft, information on some of the methods of analysis has been obtained by the Langley Aeronautical Laboratory of the National Advisory Committee for Aeronautics. In the investigation of these methods, the practical applications and limitations were stressed. In general, the methods considered may be classed as: (1) analysis of sinusoidal response, (2) analysis of transient response as to harmonic content through determination of the Fourier integral by manual or machine methods, and (3) analysis of the transient through the use of least-squares solutions of the coefficients of an assumed equation for either the transient time response or frequency response (sometimes referred to as curve-fitting methods). (author

MCMC Learning

The theory of learning under the uniform distribution is rich and deep, with connections to cryptography, computational complexity, and the analysis of boolean functions to name a few areas. This theory however is very limited due to the fact that the uniform distribution and the corresponding Fourier basis are rarely encountered as a statistical model. A family of distributions that vastly generalizes the uniform distribution on the Boolean cube is that of distributions represented by Markov Random Fields (MRF). Markov Random Fields are one of the main tools for modeling high dimensional data in many areas of statistics and machine learning. In this paper we initiate the investigation of extending central ideas, methods and algorithms from the theory of learning under the uniform distribution to the setup of learning concepts given examples from MRF distributions. In particular, our results establish a novel connection between properties of MCMC sampling of MRFs and learning under the MRF distribution.Comment: 28 pages, 1 figur

Optimal Rates for Random Fourier Features

Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show good versatility, they are computationally intensive and have poor scalability to large data as they require operations on Gram matrices. In order to mitigate this serious computational limitation, recently randomized constructions have been proposed in the literature, which allow the application of fast linear algorithms. Random Fourier features (RFF) are among the most popular and widely applied constructions: they provide an easily computable, low-dimensional feature representation for shift-invariant kernels. Despite the popularity of RFFs, very little is understood theoretically about their approximation quality. In this paper, we provide a detailed finite-sample theoretical analysis about the approximation quality of RFFs by (i) establishing optimal (in terms of the RFF dimension, and growing set size) performance guarantees in uniform norm, and (ii) presenting guarantees in $L^r$ ($1\le r<\infty$) norms. We also propose an RFF approximation to derivatives of a kernel with a theoretical study on its approximation quality.Comment: To appear at NIPS-201