This paper presents a novel time series clustering method, the self-organising eigenspace map (SOEM), based on a generalisation of the well-known self-organising feature map (SOFM). The SOEM operates on the eigenspaces of the embedded covariance structures of time series which are related directly to modes in those time series. Approximate joint diagonalisation acts as a pseudo-metric across these spaces allowing us to generalise the SOFM to a neural network with matrix input. The technique is empirically validated against three sets of experiments; univariate and multivariate time series clustering, and application to (clustered) multi-variate time series forecasting. Results indicate that the technique performs a valid topologically ordered clustering of the time series. The clustering is superior in comparison to standard benchmarks when the data is non-aligned, gives the best clustering stage for when used in forecasting, and can be used with partial/non-overlapping time series, multivariate clustering and produces a topological representation of the time series objects.

This paper deals with estimating model parameters in graphical models. We reformulate it as an information geometric optimization problem and introduce a natural gradient descent strategy that incorporates additional meta parameters. We show that our approach is a strong alternative to the celebrated EM approach for learning in graphical models. Actually, our natural gradient based strategy leads to learning optimal parameters for the final objective function without artificially trying to fit a distribution that may not correspond to the real one. We support our theoretical findings with the question of trend detection in financial markets and show that the learned model performs better than traditional practitioner methods and is less prone to overfitting.

For text analysis, one often resorts to a lossy representation that either completely ignores word order or embeds each word as a low-dimensional dense feature vector. In this paper, we propose convolutional Poisson factor analysis (CPFA) that directly operates on a lossless representation that processes the words in each document as a sequence of high-dimensional one-hot vectors. To boost its performance, we further propose the convolutional Poisson gamma belief network (CPGBN) that couples CPFA with the gamma belief network via a novel probabilistic pooling layer. CPFA forms words into phrases and captures very specific phrase-level topics, and CPGBN further builds a hierarchy of increasingly more general phrase-level topics. For efficient inference, we develop both a Gibbs sampler and a Weibull distribution based convolutional variational auto-encoder. Experimental results demonstrate that CPGBN can extract high-quality text latent representations that capture the word order information, and hence can be leveraged as a building block to enrich a wide variety of existing latent variable models that ignore word order.

Tactile enhanced multimedia is generated by synchronizing traditional multimedia clips, to generate hot and cold air effect, with an electric heater and a fan. This objective is to give viewers a more realistic and immersing feel of the multimedia content. The response to this enhanced multimedia content (mulsemedia) is evaluated in terms of the appreciation/emotion by using human brain signals. We observe and record electroencephalography (EEG) data using a commercially available four channel MUSE headband. A total of 21 participants voluntarily participated in this study for EEG recordings. We extract frequency domain features from five different bands of each EEG channel. Four emotions namely: happy, relaxed, sad, and angry are classified using a support vector machine in response to the tactile enhanced multimedia. An increased accuracy of 76:19% is achieved when compared to 63:41% by using the time domain features. Our results show that the selected frequency domain features could be better suited for emotion classification in mulsemedia studies.

Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte Carlo, but these can be expensive when the data set is large and/or the model is complex, so more efficient variational approximations have recently received considerable attention. The traditional variational methods, that seek to minimize the Kullback--Leibler divergence between the posterior and a relatively simple parametric family, provide accurate and efficient estimation of the posterior mean, but often does not capture other moments, and have limitations in terms of the models to which they can be applied. Here we propose the construction of variational approximations based on minimizing the Fisher divergence, and develop an efficient computational algorithm that can be applied to a wide range of models without conjugacy or potentially unrealistic mean-field assumptions. We demonstrate the superior performance of the proposed method for the benchmark case of logistic regression.

Support vector machine (SVM) is one of the most widely used classification methods. In this paper, we consider soft margin support vector machine used on data points with independent features, where the sample size $n$ and the feature dimension $p$ grows to $\infty$ in a fixed ratio $p/n\rightarrow \delta$. We propose a set of equations that exactly characterizes the asymptotic behavior of support vector machine. In particular, we give exact formula for (1) the variability of the optimal coefficients, (2) proportion of data points lying on the margin boundary (i.e. number of support vectors), (3) the final objective function value, and (4) expected misclassification error on new data points, which in particular implies exact formula for the optimal tuning parameter given a data generating mechanism. The global null case is considered first, where the label $y\in\{+1,-1\}$ is independent of the feature $x$. Then the signaled case is considered, where the label $y\in\{+1,-1\}$ is allowed to have a general dependence on the feature $x$ through a linear combination $a_0^Tx$. These results for the non-smooth hinge loss serve as an analogue to the recent results in \citet{sur2018modern} for smooth logistic loss. Our approach is based on heuristic leave-one-out calculations.

Many optimization problems can be cast into the maximum satisfiability (MAX-SAT) form, and many solvers have been developed for tackling such problems. To evaluate the performance of a MAX-SAT solver, it is convenient to generate difficult MAX-SAT instances with solutions known in advance. Here, we propose a method of generating weighted MAX-2-SAT instances inspired by the frustrated-loop algorithm used by the quantum annealing community to generate Ising spin-glass instances with nearest-neighbor coupling. Our algorithm is extended to instances whose underlying coupling graph is general, though we focus here on the case of bipartite coupling, with the associated energy being the restricted Boltzmann machine (RBM) energy. It is shown that any MAX-2-SAT problem can be reduced to the problem of minimizing an RBM energy over the nodal values. The algorithm is designed such that the difficulty of the generated instances can be tuned through a central parameter known as the frustration index. Two versions of the algorithm are presented: the random- and structured-loop algorithms. For the random-loop algorithm, we provide a thorough theoretical and empirical analysis on its mathematical properties from the perspective of frustration, and observe empirically, using simulated annealing, a double phase transition behavior in the difficulty scaling behavior driven by the frustration index. For the structured-loop algorithm, we show that it offers an improvement in difficulty of the generated instances over the random-loop algorithm, with the improvement factor scaling super-exponentially with respect to the frustration index for instances at high loop density. At the end of the paper, we provide a brief discussion of the relevance of this work to the pre-training of RBMs.

A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory shows these optimization methods can converge by using an unbiased gradient estimator. However, in practice biased gradient estimation can allow more efficient convergence to the vicinity since an unbiased approach is computationally more expensive. To produce fast convergence there are two trade-offs of these optimization strategies which are between stochastic/batch, and between biased/unbiased. This paper proposes an integrated approach which can control the nature of the stochastic element in the optimizer and can balance the trade-off of estimator between the biased and unbiased by using a hyper-parameter. It is shown theoretically and experimentally that this hyper-parameter can be configured to provide an effective balance to improve the convergence rate.

We present a navigation system that combines ideas from hierarchical planning and machine learning. The system uses a traditional global planner to compute optimal paths towards a goal, and a deep local trajectory planner and velocity controller to compute motion commands. The latter components of the system adjust the behavior of the robot through attention mechanisms such that it moves towards the goal, avoids obstacles, and respects the space of nearby pedestrians. Both the structure of the proposed deep models and the use of attention mechanisms make the system's execution interpretable. Our simulation experiments suggest that the proposed architecture outperforms baselines that try to map global plan information and sensor data directly to velocity commands. In comparison to a hand-designed traditional navigation system, the proposed approach showed more consistent performance.

In this paper, we present an experimental study for the classification of perceived human stress using non-invasive physiological signals. These include electroencephalography (EEG), galvanic skin response (GSR), and photoplethysmography (PPG). We conducted experiments consisting of steps including data acquisition, feature extraction, and perceived human stress classification. The physiological data of $28$ participants are acquired in an open eye condition for a duration of three minutes. Four different features are extracted in time domain from EEG, GSR and PPG signals and classification is performed using multiple classifiers including support vector machine, the Naive Bayes, and multi-layer perceptron (MLP). The best classification accuracy of 75% is achieved by using MLP classifier. Our experimental results have shown that our proposed scheme outperforms existing perceived stress classification methods, where no stress inducers are used.