Customisable arithmetic hardware designs

Imperial Users onl

Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck operators

This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all points, we define a diffusion distance between any two data points and show that the low dimensional representation of the data by the first few eigenvectors of the corresponding Markov matrix is optimal under a certain mean squared error criterion. Furthermore, assuming that data points are random samples from a density p(\x) = e^{-U(\x)} we identify these eigenvectors as discrete approximations of eigenfunctions of a Fokker-Planck operator in a potential 2U(\x) with reflecting boundary conditions. Finally, applying known results regarding the eigenvalues and eigenfunctions of the continuous Fokker-Planck operator, we provide a mathematical justification for the success of spectral clustering and dimensional reduction algorithms based on these first few eigenvectors. This analysis elucidates, in terms of the characteristics of diffusion processes, many empirical findings regarding spectral clustering algorithms.Comment: submitted to NIPS 200

Synthesising 3D solid models of natural heterogeneous materials from single sample image, using encoding deep convolutional generative adversarial networks

Three-dimensional solid computational representations of natural heterogeneous materials are challenging to generate due to their high degree of randomness and varying scales of patterns, such as veins and cracks, in different sizes and directions. In this regard, this paper introduces a new architecture to synthesise 3D solid material models by using encoding deep convolutional generative adversarial networks (EDCGANs). DCGANs have been useful in generative tasks in relation to image processing by successfully recreating similar results based on adequate training. While concentrating on natural heterogeneous materials, this paper uses an encoding and a decoding DCGAN combined in a similar way to auto-encoders to convert a given image into marble, based on patches. Additionally, the method creates an input dataset from a single 2D high-resolution exemplar. Further, it translates of 2D data, used as a seed, into 3D data to create material blocks. While the results on the Z-axis do not have size restrictions, the X- and Y-axis are constrained by the given image. Using the method, the paper explores possible ways to present 3D solid textures. The modelling potentials of the developed approach as a design tool is explored to synthesise a 3D solid texture of leaf-like material from an exemplar of a leaf image

Stochastic model for the 3D microstructure of pristine and cyclically aged cathodes in Li-ion batteries

It is well-known that the microstructure of electrodes in lithium-ion batteries strongly affects their performance. Vice versa, the microstructure can exhibit strong changes during the usage of the battery due to aging effects. For a better understanding of these effects, mathematical analysis and modeling has turned out to be of great help. In particular, stochastic 3D microstructure models have proven to be a powerful and very flexible tool to generate various kinds of particle-based structures. Recently, such models have been proposed for the microstructure of anodes in lithium-ion energy and power cells. In the present paper, we describe a stochastic modeling approach for the 3D microstructure of cathodes in a lithium-ion energy cell, which differs significantly from the one observed in anodes. The model for the cathode data enhances the ideas of the anode models, which have been developed so far. It is calibrated using 3D tomographic image data from pristine as well as two aged cathodes. A validation based on morphological image characteristics shows that the model is able to realistically describe both, the microstructure of pristine and aged cathodes. Thus, we conclude that the model is suitable to generate virtual, but realistic microstructures of lithium-ion cathodes

kk-MLE: A fast algorithm for learning statistical mixture models

We describe $k$-MLE, a fast and efficient local search algorithm for learning finite statistical mixtures of exponential families such as Gaussian mixture models. Mixture models are traditionally learned using the expectation-maximization (EM) soft clustering technique that monotonically increases the incomplete (expected complete) likelihood. Given prescribed mixture weights, the hard clustering $k$-MLE algorithm iteratively assigns data to the most likely weighted component and update the component models using Maximum Likelihood Estimators (MLEs). Using the duality between exponential families and Bregman divergences, we prove that the local convergence of the complete likelihood of $k$-MLE follows directly from the convergence of a dual additively weighted Bregman hard clustering. The inner loop of $k$-MLE can be implemented using any $k$-means heuristic like the celebrated Lloyd's batched or Hartigan's greedy swap updates. We then show how to update the mixture weights by minimizing a cross-entropy criterion that implies to update weights by taking the relative proportion of cluster points, and reiterate the mixture parameter update and mixture weight update processes until convergence. Hard EM is interpreted as a special case of $k$-MLE when both the component update and the weight update are performed successively in the inner loop. To initialize $k$-MLE, we propose $k$-MLE++, a careful initialization of $k$-MLE guaranteeing probabilistically a global bound on the best possible complete likelihood.Comment: 31 pages, Extend preliminary paper presented at IEEE ICASSP 201

High Level Trigger Using ALICE ITS Detector

The high $P_T$ trigger capabilities of the ALICE inner tracking system (ITS) as a standalone detector have been investigated. Since the high $P_T$ charged particles mostly lead to the linear trajectories within this ITS sector, it is possible to select tracks of $P_T$ of the order of 2 GeV and above by confining to a narrow search window in the ($\theta,\phi$) space. Also shown that by performing a principal component transformation, it is possible to rotate from a 12 dimensional ($\theta$-$\phi$) space (in this space, a good ITS track has 6 pairs of hit co-ordinates) into a parametric space characterized by only two independent components when the track momentum exceeds a particular limit. This independent component analysis (ICA) has been uitilised further to reduce the false track contribution to an acceptable level particularly when the charged multiplicity is large. Finally, it is shown that with a narrow bin width of $\Delta \theta = \Delta \phi \sim 0.008$ radian and with PCA or ICA cut, the ITS can be used to trigger the jet particles with $P_T \ge 2$ GeV. Apart from triggering these high $P_T$ particles, this method can also be used to estimate the initial momentum of the high $P_T$ tracks for seeding which can be further prolonged into the TPC detector both for offline and online Kalman tracking or even to detect those high $P_T$ tracks of rare events which might get lost in the TPC-TRD dead zone.Comment: 20 pages, 10 figure

Unsupervised Superpixel Generation using Edge-Sparse Embedding

Partitioning an image into superpixels based on the similarity of pixels with respect to features such as colour or spatial location can significantly reduce data complexity and improve subsequent image processing tasks. Initial algorithms for unsupervised superpixel generation solely relied on local cues without prioritizing significant edges over arbitrary ones. On the other hand, more recent methods based on unsupervised deep learning either fail to properly address the trade-off between superpixel edge adherence and compactness or lack control over the generated number of superpixels. By using random images with strong spatial correlation as input, \ie, blurred noise images, in a non-convolutional image decoder we can reduce the expected number of contrasts and enforce smooth, connected edges in the reconstructed image. We generate edge-sparse pixel embeddings by encoding additional spatial information into the piece-wise smooth activation maps from the decoder's last hidden layer and use a standard clustering algorithm to extract high quality superpixels. Our proposed method reaches state-of-the-art performance on the BSDS500, PASCAL-Context and a microscopy dataset

A Hardware Efficient Random Number Generator for Nonuniform Distributions with Arbitrary Precision

Nonuniform random numbers are key for many technical applications, and designing efficient hardware implementations of non-uniform random number generators is a very active research field. However, most state-of-the-art architectures are either tailored to specific distributions or use up a lot of hardware resources. At ReConFig 2010, we have presented a new design that saves up to 48% of area compared to state-of-the-art inversion-based implementation, usable for arbitrary distributions and precision. In this paper, we introduce a more flexible version together with a refined segmentation scheme that allows to further reduce the approximation error significantly. We provide a free software tool allowing users to implement their own distributions easily, and we have tested our random number generator thoroughly by statistic analysis and two application tests