SOM-VAE: Interpretable Discrete Representation Learning on Time Series

High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most representation learning algorithms for time series data are difficult to interpret. This is due to non-intuitive mappings from data features to salient properties of the representation and non-smoothness over time. To address this problem, we propose a new representation learning framework building on ideas from interpretable discrete dimensionality reduction and deep generative modeling. This framework allows us to learn discrete representations of time series, which give rise to smooth and interpretable embeddings with superior clustering performance. We introduce a new way to overcome the non-differentiability in discrete representation learning and present a gradient-based version of the traditional self-organizing map algorithm that is more performant than the original. Furthermore, to allow for a probabilistic interpretation of our method, we integrate a Markov model in the representation space. This model uncovers the temporal transition structure, improves clustering performance even further and provides additional explanatory insights as well as a natural representation of uncertainty. We evaluate our model in terms of clustering performance and interpretability on static (Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST images, a chaotic Lorenz attractor system with two macro states, as well as on a challenging real world medical time series application on the eICU data set. Our learned representations compare favorably with competitor methods and facilitate downstream tasks on the real world data.Comment: Accepted for publication at the Seventh International Conference on Learning Representations (ICLR 2019

3D reconstruction of medical images from slices automatically landmarked with growing neural models

In this study, we utilise a novel approach to segment out the ventricular system in a series of high resolution T1-weighted MR images. We present a brain ventricles fast reconstruction method. The method is based on the processing of brain sections and establishing a fixed number of landmarks onto those sections to reconstruct the ventricles 3D surface. Automated landmark extraction is accomplished through the use of the self-organising network, the growing neural gas (GNG), which is able to topographically map the low dimensionality of the network to the high dimensionality of the contour manifold without requiring a priori knowledge of the input space structure. Moreover, our GNG landmark method is tolerant to noise and eliminates outliers. Our method accelerates the classical surface reconstruction and filtering processes. The proposed method offers higher accuracy compared to methods with similar efficiency as Voxel Grid

A Detailed Investigation into Low-Level Feature Detection in Spectrogram Images

Being the first stage of analysis within an image, low-level feature detection is a crucial step in the image analysis process and, as such, deserves suitable attention. This paper presents a systematic investigation into low-level feature detection in spectrogram images. The result of which is the identification of frequency tracks. Analysis of the literature identifies different strategies for accomplishing low-level feature detection. Nevertheless, the advantages and disadvantages of each are not explicitly investigated. Three model-based detection strategies are outlined, each extracting an increasing amount of information from the spectrogram, and, through ROC analysis, it is shown that at increasing levels of extraction the detection rates increase. Nevertheless, further investigation suggests that model-based detection has a limitation—it is not computationally feasible to fully evaluate the model of even a simple sinusoidal track. Therefore, alternative approaches, such as dimensionality reduction, are investigated to reduce the complex search space. It is shown that, if carefully selected, these techniques can approach the detection rates of model-based strategies that perform the same level of information extraction. The implementations used to derive the results presented within this paper are available online from http://stdetect.googlecode.com

A Graph-Based Semi-Supervised k Nearest-Neighbor Method for Nonlinear Manifold Distributed Data Classification

$k$ Nearest Neighbors ($k$NN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially when a very limited amount of labeled samples are available. In this paper, we propose a new graph-based $k$NN algorithm which can effectively handle both Gaussian distributed data and nonlinear manifold distributed data. To achieve this goal, we first propose a constrained Tired Random Walk (TRW) by constructing an $R$-level nearest-neighbor strengthened tree over the graph, and then compute a TRW matrix for similarity measurement purposes. After this, the nearest neighbors are identified according to the TRW matrix and the class label of a query point is determined by the sum of all the TRW weights of its nearest neighbors. To deal with online situations, we also propose a new algorithm to handle sequential samples based a local neighborhood reconstruction. Comparison experiments are conducted on both synthetic data sets and real-world data sets to demonstrate the validity of the proposed new $k$NN algorithm and its improvements to other version of $k$NN algorithms. Given the widespread appearance of manifold structures in real-world problems and the popularity of the traditional $k$NN algorithm, the proposed manifold version $k$NN shows promising potential for classifying manifold-distributed data.Comment: 32 pages, 12 figures, 7 table

The Parameter-Less Self-Organizing Map algorithm

The Parameter-Less Self-Organizing Map (PLSOM) is a new neural network algorithm based on the Self-Organizing Map (SOM). It eliminates the need for a learning rate and annealing schemes for learning rate and neighbourhood size. We discuss the relative performance of the PLSOM and the SOM and demonstrate some tasks in which the SOM fails but the PLSOM performs satisfactory. Finally we discuss some example applications of the PLSOM and present a proof of ordering under certain limited conditions.Comment: 29 pages, 27 figures. Based on publication in IEEE Trans. on Neural Network

FPGA-based Anomalous trajectory detection using SOFM

A system for automatically classifying the trajectory of a moving object in a scene as usual or suspicious is presented. The system uses an unsupervised neural network (Self Organising Feature Map) fully implemented on a reconfigurable hardware architecture (Field Programmable Gate Array) to cluster trajectories acquired over a period, in order to detect novel ones. First order motion information, including first order moving average smoothing, is generated from the 2D image coordinates (trajectories). The classification is dynamic and achieved in real-time. The dynamic classifier is achieved using a SOFM and a probabilistic model. Experimental results show less than 15\% classification error, showing the robustness of our approach over others in literature and the speed-up over the use of conventional microprocessor as compared to the use of an off-the-shelf FPGA prototyping board

Unsupervised machine learning clustering and data exploration of radio-astronomical images

In this thesis, I demonstrate a novel and efficient unsupervised clustering and data exploration method with the combination of a Self-Organising Map (SOM) and a Convolutional Autoencoder, applied to radio-astronomical images from the Radio Galaxy Zoo (RGZ) dataset. The rapidly increasing volume and complexity of radio-astronomical data have ushered in a new era of big-data astronomy which has increased the demand for Machine Learning (ML) solutions. In this era, the sheer amount of image data produced with modern instruments and has resulted in a significant data deluge. Furthermore, the morphologies of objects captured in these radio-astronomical images are highly complex and challenging to classify conclusively due to their intricate and indiscrete nature. Additionally, major radio-astronomical discoveries are unplanned and found in the unexpected, making unsupervised ML highly desirable by operating with few assumptions and without labelled training data. In this thesis, I developed a novel unsupervised ML approach as a practical solution to these astronomy challenges. Using this system, I demonstrated the use of convolutional autoencoders and SOM’s as a dimensionality reduction method to delineate the complexity and volume of astronomical data. My optimised system shows that the coupling of these methods is a powerful method of data exploration and unsupervised clustering of radio-astronomical images. The results of this thesis show this approach is capable of accurately separating features by complexity on a SOM manifold and unified distance matrix with neighbourhood similarity and hierarchical clustering of the mapped astronomical features. This method provides an effective means to explore the high-level topological relationships of image features and morphology in large datasets automatically with minimal processing time and computational resources. I achieved these capabilities with a new and innovative method of SOM training using the autoencoder compressed latent feature vector representations of radio-astronomical data, rather than raw images. Using this system, I successfully investigated SOM affine transformation invariance and analysed the true nature of rotational effects on this manifold using autoencoder random rotation training augmentations. Throughout this thesis, I present my method as a powerful new approach to data exploration technique and contribution to the field. The speed and effectiveness of this method indicates excellent scalability and holds implications for use on large future surveys, large-scale instruments such as the Square Kilometre Array and in other big-data and complexity analysis applications

Stochastic Vector Quantisers

In this paper a stochastic generalisation of the standard Linde-Buzo-Gray (LBG) approach to vector quantiser (VQ) design is presented, in which the encoder is implemented as the sampling of a vector of code indices from a probability distribution derived from the input vector, and the decoder is implemented as a superposition of reconstruction vectors, and the stochastic VQ is optimised using a minimum mean Euclidean reconstruction distortion criterion, as in the LBG case. Numerical simulations are used to demonstrate how this leads to self-organisation of the stochastic VQ, where different stochastically sampled code indices become associated with different input subspaces. This property may be used to automate the process of splitting high-dimensional input vectors into low-dimensional blocks before encoding them.Comment: 22 pages, 12 figure

Classification of ordered texture images using regression modelling and granulometric features

Structural information available from the granulometry of an image has been used widely in image texture analysis and classification. In this paper we present a method for classifying texture images which follow an intrinsic ordering of textures, using polynomial regression to express granulometric moments as a function of class label. Separate models are built for each individual moment and combined for back-prediction of the class label of a new image. The methodology was developed on synthetic images of evolving textures and tested using real images of 8 different grades of cut-tear-curl black tea leaves. For comparison, grey level co-occurrence (GLCM) based features were also computed, and both feature types were used in a range of classifiers including the regression approach. Experimental results demonstrate the superiority of the granulometric moments over GLCM-based features for classifying these tea images