Locality-sensitive hashing converts high-dimensional feature vectors, such as image and speech, into bit arrays and allows high-speed similarity calculation with the Hamming distance. There is a hashing scheme that maps feature vectors to bit arrays depending on the signs of the inner products between feature vectors and the normal vectors of hyperplanes placed in the feature space. This hashing can be seen as a discretization of the feature space by hyperplanes. If labels for data are given, one can determine the hyperplanes by using learning algorithms. However, many proposed learning methods do not consider the hyperplanes' offsets. Not doing so decreases the number of partitioned regions, and the correlation between Hamming distances and Euclidean distances becomes small. In this paper, we propose a lift map that converts learning algorithms without the offsets to the ones that take into account the offsets. With this method, the learning methods without the offsets give the discretizations of spaces as if it takes into account the offsets. For the proposed method, we input several high-dimensional feature data sets and studied the relationship between the statistical characteristics of data, the number of hyperplanes, and the effect of the proposed method.

In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems (or, more generally, nested systems) offer a way to generate complex mappings using simple stages. Each layer performs a different operation and achieves an ever more sophisticated representation of the input, as, for example, in an deep artificial neural network, an object recognition cascade in computer vision or a speech front-end processing. Joint estimation of the parameters of all the layers and selection of an optimal architecture is widely considered to be a difficult numerical nonconvex optimization problem, difficult to parallelize for execution in a distributed computation environment, and requiring significant human expert effort, which leads to suboptimal systems in practice. We describe a general mathematical strategy to learn the parameters and, to some extent, the architecture of nested systems, called the method of auxiliary coordinates (MAC). This replaces the original problem involving a deeply nested function with a constrained problem involving a different function in an augmented space without nesting. The constrained problem may be solved with penalty-based methods using alternating optimization over the parameters and the auxiliary coordinates. MAC has provable convergence, is easy to implement reusing existing algorithms for single layers, can be parallelized trivially and massively, applies even when parameter derivatives are not available or not desirable, and is competitive with state-of-the-art nonlinear optimizers even in the serial computation setting, often providing reasonable models within a few iterations.

Self-Organizing Maps (SOM) are popular unsupervised artificial neural network used to reduce dimensions and visualize data. Visual interpretation from Self-Organizing Maps (SOM) has been limited due to grid approach of data representation, which makes inter-scenario analysis impossible. The paper proposes a new way to structure SOM. This model reconstructs SOM to show strength between variables as the threads of a cobweb and illuminate inter-scenario analysis. While Radar Graphs are very crude representation of spider web, this model uses more lively and realistic cobweb representation to take into account the difference in strength and length of threads. This model allows for visualization of highly unstructured dataset with large number of dimensions, common in Bigdata sources.

A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse Gaussian distribution. This approach is mathematically elegant and relatively computationally straightforward. Our novel mixture modelling approach is demonstrated on both simulated and real data to illustrate clustering and classification applications. In these analyses, our mixture of shifted asymmetric Laplace distributions performs favourably when compared to the popular Gaussian approach. This work, which marks an important step in the non-Gaussian model-based clustering and classification direction, concludes with discussion as well as suggestions for future work.

We discuss a general technique that can be used to form a differentiable bound on the optima of non-differentiable or discrete objective functions. We form a unified description of these methods and consider under which circumstances the bound is concave. In particular we consider two concrete applications of the method, namely sparse learning and support vector classification.

In this note, we present a new averaging technique for the projected stochastic subgradient method. By using a weighted average with a weight of t+1 for each iterate w_t at iteration t, we obtain the convergence rate of O(1/t) with both an easy proof and an easy implementation. The new scheme is compared empirically to existing techniques, with similar performance behavior.

Topic models provide a useful method for dimensionality reduction and exploratory data analysis in large text corpora. Most approaches to topic model inference have been based on a maximum likelihood objective. Efficient algorithms exist that approximate this objective, but they have no provable guarantees. Recently, algorithms have been introduced that provide provable bounds, but these algorithms are not practical because they are inefficient and not robust to violations of model assumptions. In this paper we present an algorithm for topic model inference that is both provable and practical. The algorithm produces results comparable to the best MCMC implementations while running orders of magnitude faster.

Cryo-electron microscopy (cryo-EM) studies using single particle reconstruction are extensively used to reveal structural information on macromolecular complexes. Aiming at the highest achievable resolution, state of the art electron microscopes automatically acquire thousands of high-quality micrographs. Particles are detected on and boxed out from each micrograph using fully- or semi-automated approaches. However, the obtained particles still require laborious manual post-picking classification, which is one major bottleneck for single particle analysis of large datasets. We introduce MAPPOS, a supervised post-picking strategy for the classification of boxed particle images, as additional strategy adding to the already efficient automated particle picking routines. MAPPOS employs machine learning techniques to train a robust classifier from a small number of characteristic image features. In order to accurately quantify the performance of MAPPOS we used simulated particle and non-particle images. In addition, we verified our method by applying it to an experimental cryo-EM dataset and comparing the results to the manual classification of the same dataset. Comparisons between MAPPOS and manual post-picking classification by several human experts demonstrated that merely a few hundred sample images are sufficient for MAPPOS to classify an entire dataset with a human-like performance. MAPPOS was shown to greatly accelerate the throughput of large datasets by reducing the manual workload by orders of magnitude while maintaining a reliable identification of non-particle images.

We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order operations (e.g., certain optimizations) are considered primitive for the purposes of measuring complexity. We consider classes of information operators and algorithms made up of scaled families, and investigate the utility of scaling the complexities to minimize error. We look at the division of statistical learning into information and algorithmic components, at the complexities of each, and at applications to support vector machine (SVM) and more general machine learning algorithms. We give applications to SVM algorithms graded into linear and higher order components, and give an example in biomedical informatics.

We propose a generative model of a group EEG analysis, based on appropriate kernel assumptions on EEG data. We derive the variational inference update rule using various approximation techniques. The proposed model outperforms the current state-of-the-art algorithms in terms of common pattern extraction. The validity of the proposed model is tested on the BCI competition dataset.