Random projection | EPFL Graph Search

In mathematics and statistics, random projection is a technique used to reduce the dimensionality of a set of points which lie in Euclidean space. Random projection methods are known for their power, simplicity, and low error rates when compared to other methods. According to experimental results, random projection preserves distances well, but empirical results are sparse. They have been applied to many natural language tasks under the name random indexing. Dimensionality reduction Dimensionality reduction Dimensionality reduction, as the name suggests, is reducing the number of random variables using various mathematical methods from statistics and machine learning. Dimensionality reduction is often used to reduce the problem of managing and manipulating large data sets. Dimensionality reduction techniques generally use linear transformations in determining the intrinsic dimensionality of the manifold as well as extracting its principal directions. For this purpose there

Fast Projection Onto Convex Smooth Constraints

Andreas Krause, Ilnura Usmanova

The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on projection problems where the constraints are smooth and the number of constraints is significantly smaller than the dimension. The runtime of existing approaches to solving such problems is either cubic in the dimension or polynomial in the inverse of the target accuracy. Conversely, we propose a simple and efficient primal-dual approach, with a runtime that scales only linearly with the dimension, and only logarithmically in the inverse of the target accuracy. We empirically demonstrate its performance, and compare it with standard baselines.

PMLR2021

Wavelet Density Estimators in Discriminant Analysis

Olivier Renaud

The purpose of discriminant analysis is to predict group membership of an individual on the basis of a set of measurements that have been made on it. In this goal, the availability of a learning sample, for which it is know where each individual came from, is assumed. In this context, the thresholded wavelet density estimator may capture more easily fine structures of group differences than usual linear density estimators (such as kernel-based methods). This does not apply ``as is'' in high dimensional space. However, in the univariate case, the estimator behaves well, and can, therefore, be used in the framework of Projection Pursuit Discriminant Analysis, a method that searches for the one-dimension projection that best separates the groups.

1996

Early Classification of Pathological Heartbeats on Wireless Body Sensor Nodes

Giovanni Ansaloni, David Atienza Alonso, Ivan Beretta, Ruben Braojos Lopez

Smart Wireless Body Sensor Nodes (WBSNs) are a novel class of unobtrusive, battery-powered devices allowing the continuous monitoring and real-time interpretation of a subject's bio-signals, such as the electrocardiogram (ECG). These low-power platforms, while able to perform advanced signal processing to extract information on heart conditions, are usually constrained in terms of computational power and transmission bandwidth. It is therefore essential to identify in the early stages which parts of an ECG are critical for the diagnosis and, only in these cases, activate on demand more detailed and computationally intensive analysis algorithms. In this work, we present a comprehensive framework for real-time automatic classification of normal and abnormal heartbeats, targeting embedded and resource-constrained WBSNs. In particular, we provide a comparative analysis of different strategies to reduce the heartbeat representation dimensionality, and therefore the required computational effort. We then combine these techniques with a neuro-fuzzy classification strategy, which effectively discerns normal and pathological heartbeats with a minimal run time and memory overhead. We prove that, by performing a detailed analysis only on the heartbeats that our classifier identifies as abnormal, a WBSN system can drastically reduce its overall energy consumption. Finally, we assess the choice of neuro-fuzzy classification by comparing its performance and workload with respect to other state-of-the-art strategies. Experimental results using the MIT-BIH Arrhythmia database show energy savings of as much as 60% in the signal processing stage, and 63% in the subsequent wireless transmission, when a neuro-fuzzy classification structure is employed, coupled with a dimensionality reduction technique based on random projections.

MDPI2014

Early Classification of Pathological Heartbeats on Wireless Body Sensor Nodes

Giovanni Ansaloni, David Atienza Alonso, Ivan Beretta, Ruben Braojos Lopez

MDPI2014