Support Spinor Machine

We generalize a support vector machine to a support spinor machine by using the mathematical structure of wedge product over vector machine in order to extend field from vector field to spinor field. The separated hyperplane is extended to Kolmogorov space in time series data which allow us to extend a structure of support vector machine to a support tensor machine and a support tensor machine moduli space. Our performance test on support spinor machine is done over one class classification of end point in physiology state of time series data after empirical mode analysis and compared with support vector machine test. We implement algorithm of support spinor machine by using Holo-Hilbert amplitude modulation for fully nonlinear and nonstationary time series data analysis.Comment: 18 pages, 12 figures, 6 table

Complex Support Vector Machines for Regression and Quaternary Classification

The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for complex-valued data and considers two cases: a) the complex data are split into their real and imaginary parts and a typical real kernel is employed to map the complex data to a complexified feature space and b) a pure complex kernel is used to directly map the data to the induced complex feature space. The recently developed Wirtinger's calculus on complex reproducing kernel Hilbert spaces (RKHS) is employed in order to compute the Lagrangian and derive the dual optimization problem. As one of our major results, we prove that any complex SVM/SVR task is equivalent with solving two real SVM/SVR tasks exploiting a specific real kernel which is generated by the chosen complex kernel. In particular, the case of pure complex kernels leads to the generation of new kernels, which have not been considered before. In the classification case, the proposed framework inherently splits the complex space into four parts. This leads naturally in solving the four class-task (quaternary classification), instead of the typical two classes of the real SVM. In turn, this rationale can be used in a multiclass problem as a split-class scenario based on four classes, as opposed to the one-versus-all method; this can lead to significant computational savings. Experiments demonstrate the effectiveness of the proposed framework for regression and classification tasks that involve complex data.Comment: Manuscript accepted in IEEE Transactions on Neural Networks and Learning System

Applications of Clifford's Geometric Algebra

We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly demonstrate the benefit of developing problem solutions in a unified framework for algebra and geometry with the widest possible scope: from quantum computing and electromagnetism to satellite navigation, from neural computing to camera geometry, image processing, robotics and beyond.Comment: 26 pages, 91 reference

Regularization approaches for support vector machines with applications to biomedical data

The support vector machine (SVM) is a widely used machine learning tool for classification based on statistical learning theory. Given a set of training data, the SVM finds a hyperplane that separates two different classes of data points by the largest distance. While the standard form of SVM uses L2-norm regularization, other regularization approaches are particularly attractive for biomedical datasets where, for example, sparsity and interpretability of the classifier's coefficient values are highly desired features. Therefore, in this paper we consider different types of regularization approaches for SVMs, and explore them in both synthetic and real biomedical datasets

Recognizing Abnormal Heart Sounds Using Deep Learning

The work presented here applies deep learning to the task of automated cardiac auscultation, i.e. recognizing abnormalities in heart sounds. We describe an automated heart sound classification algorithm that combines the use of time-frequency heat map representations with a deep convolutional neural network (CNN). Given the cost-sensitive nature of misclassification, our CNN architecture is trained using a modified loss function that directly optimizes the trade-off between sensitivity and specificity. We evaluated our algorithm at the 2016 PhysioNet Computing in Cardiology challenge where the objective was to accurately classify normal and abnormal heart sounds from single, short, potentially noisy recordings. Our entry to the challenge achieved a final specificity of 0.95, sensitivity of 0.73 and overall score of 0.84. We achieved the greatest specificity score out of all challenge entries and, using just a single CNN, our algorithm differed in overall score by only 0.02 compared to the top place finisher, which used an ensemble approach.Comment: IJCAI 2017 Knowledge Discovery in Healthcare Worksho

Abductive reasoning as the basis to reproduce expert criteria in ECG Atrial Fibrillation identification

Objective: This work aims at providing a new method for the automatic detection of atrial fibrillation, other arrhythmia and noise on short single lead ECG signals, emphasizing the importance of the interpretability of the classification results. Approach: A morphological and rhythm description of the cardiac behavior is obtained by a knowledge-based interpretation of the signal using the \textit{Construe} abductive framework. Then, a set of meaningful features are extracted for each individual heartbeat and as a summary of the full record. The feature distributions were used to elucidate the expert criteria underlying the labeling of the 2017 Physionet/CinC Challenge dataset, enabling a manual partial relabeling to improve the consistency of the classification rules. Finally, state-of-the-art machine learning methods are combined to provide an answer on the basis of the feature values. Main results: The proposal tied for the first place in the official stage of the Challenge, with a combined $F_1$ score of 0.83, and was even improved in the follow-up stage to 0.85 with a significant simplification of the model. Significance: This approach demonstrates the potential of \textit{Construe} to provide robust and valuable descriptions of temporal data even with significant amounts of noise and artifacts. Also, we discuss the importance of a consistent classification criteria in manually labeled training datasets, and the fundamental advantages of knowledge-based approaches to formalize and validate that criteria.Comment: 15 pages, 6 figures, 6 table

An Overview of Machine Learning Approaches in Wireless Mesh Networks

Wireless Mesh Networks (WMNs) have been extensively studied for nearly two decades as one of the most promising candidates expected to power the high bandwidth, high coverage wireless networks of the future. However, consumer demand for such networks has only recently caught up, rendering efforts at optimizing WMNs to support high capacities and offer high QoS, while being secure and fault tolerant, more important than ever. To this end, a recent trend has been the application of Machine Learning (ML) to solve various design and management tasks related to WMNs. In this work, we discuss key ML techniques and analyze how past efforts have applied them in WMNs, while noting some existing issues and suggesting potential solutions. We also provide directions on how ML could advance future research and examine recent developments in the field

Exponential Families for Conditional Random Fields

In this paper we de ne conditional random elds in reproducing kernel Hilbert spaces and show connections to Gaussian Process classi cation. More speci cally, we prove decomposition results for undirected graphical models and we give constructions for kernels. Finally we present e cient means of solving the optimization problem using reduced rank decompositions and we show how stationarity can be exploited e ciently in the optimization process.Comment: Appears in Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI2004

Random Warping Series: A Random Features Method for Time-Series Embedding

Time series data analytics has been a problem of substantial interests for decades, and Dynamic Time Warping (DTW) has been the most widely adopted technique to measure dissimilarity between time series. A number of global-alignment kernels have since been proposed in the spirit of DTW to extend its use to kernel-based estimation method such as support vector machine. However, those kernels suffer from diagonal dominance of the Gram matrix and a quadratic complexity w.r.t. the sample size. In this work, we study a family of alignment-aware positive definite (p.d.) kernels, with its feature embedding given by a distribution of \emph{Random Warping Series (RWS)}. The proposed kernel does not suffer from the issue of diagonal dominance while naturally enjoys a \emph{Random Features} (RF) approximation, which reduces the computational complexity of existing DTW-based techniques from quadratic to linear in terms of both the number and the length of time-series. We also study the convergence of the RF approximation for the domain of time series of unbounded length. Our extensive experiments on 16 benchmark datasets demonstrate that RWS outperforms or matches state-of-the-art classification and clustering methods in both accuracy and computational time. Our code and data is available at { \url{https://github.com/IBM/RandomWarpingSeries}}.Comment: AIStats18, Oral Paper, Add code link for generating RW

Circuit-centric quantum classifiers

The current generation of quantum computing technologies call for quantum algorithms that require a limited number of qubits and quantum gates, and which are robust against errors. A suitable design approach are variational circuits where the parameters of gates are learnt, an approach that is particularly fruitful for applications in machine learning. In this paper, we propose a low-depth variational quantum algorithm for supervised learning. The input feature vectors are encoded into the amplitudes of a quantum system, and a quantum circuit of parametrised single and two-qubit gates together with a single-qubit measurement is used to classify the inputs. This circuit architecture ensures that the number of learnable parameters is poly-logarithmic in the input dimension. We propose a quantum-classical training scheme where the analytical gradients of the model can be estimated by running several slightly adapted versions of the variational circuit. We show with simulations that the circuit-centric quantum classifier performs well on standard classical benchmark datasets while requiring dramatically fewer parameters than other methods. We also evaluate sensitivity of the classification to state preparation and parameter noise, introduce a quantum version of dropout regularisation and provide a graphical representation of quantum gates as highly symmetric linear layers of a neural network.Comment: 17 pages, 9 Figures, 5 Table