State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with $\ell_1$, $\ell_2$ or nuclear norms. $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad theoretical conditions, but the clusters may not be connected. $\ell_2$ and nuclear norm regularization often improve connectivity, but give a subspace-preserving affinity only for independent subspaces. Mixed $\ell_1$, $\ell_2$ and nuclear norm regularizations offer a balance between the subspace-preserving and connectedness properties, but this comes at the cost of increased computational complexity. This paper studies the geometry of the elastic net regularizer (a mixture of the $\ell_1$ and $\ell_2$ norms) and uses it to derive a provably correct and scalable active set method for finding the optimal coefficients. Our geometric analysis also provides a theoretical justification and a geometric interpretation for the balance between the connectedness (due to $\ell_2$ regularization) and subspace-preserving (due to $\ell_1$ regularization) properties for elastic net subspace clustering. Our experiments show that the proposed active set method not only achieves state-of-the-art clustering performance, but also efficiently handles large-scale datasets.

We revisit the problem of inferring the overall ranking among entities in the framework of Bradley-Terry-Luce (BTL) model, based on available empirical data on pairwise preferences. By a simple transformation, we can cast the problem as that of solving a noisy linear system, for which a ready algorithm is available in the form of the randomized Kaczmarz method. This scheme is provably convergent, has excellent empirical performance, and is amenable to on-line, distributed and asynchronous variants. Convergence, convergence rate, and error analysis of the proposed algorithm are presented and several numerical experiments are conducted whose results validate our theoretical findings.

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regression. Through computer simulations and analysis of magnetoencephalographic data, we demonstrate the efficacy of the method in identifying meaningful modulations of oscillatory signals corrupted by structured temporal and spatiotemporal noise. These results suggest that the method is particularly suitable for the analysis and interpretation of complex temporal and spatiotemporal neural signals.

This article addresses the problem of derivative-free (single- or multi-objective) optimization subject to multiple inequality constraints. Both the objective and constraint functions are assumed to be smooth, non-linear and expensive to evaluate. As a consequence, the number of evaluations that can be used to carry out the optimization is very limited, as in complex industrial design optimization problems. The method we propose to overcome this difficulty has its roots in both the Bayesian and the multi-objective optimization literatures. More specifically, an extended domination rule is used to handle objectives and constraints in a unified way, and a corresponding expected hyper-volume improvement sampling criterion is proposed. This new criterion is naturally adapted to the search of a feasible point when none is available, and reduces to existing Bayesian sampling criteria---the classical Expected Improvement (EI) criterion and some of its constrained/multi-objective extensions---as soon as at least one feasible point is available. The calculation and optimization of the criterion are performed using Sequential Monte Carlo techniques. In particular, an algorithm similar to the subset simulation method, which is well known in the field of structural reliability, is used to estimate the criterion. The method, which we call BMOO (for Bayesian Multi-Objective Optimization), is compared to state-of-the-art algorithms for single- and multi-objective constrained optimization.

As a result, users are forced to wade through pages and pages of listings to find the exact item they're looking for. That could push a lot of customers to rivals like Amazon.com, Inc., which is why eBay has finally done something about it. On Thursday, eBay announced that it's agreed to acquire Swedish software make Expertmaker, which specializes in AI and machine learning systems that can help to analyze and organize massive sets of data. It's just what the doctor ordered for eBay, which hosts an average of 900 million listings at any one time. Expertmaker has actually been working with eBay since 2010, most recently helping out with a "structured data" project aimed at making eBay's site less cluttered than it currently is.

The scikit-learn library is the premiere library for machine learning in Python. The online documentation is quite good but sometimes can feel fragmented or limited by narrow examples. In this post you will discover the book Scikit-Learn Cookbook by Trent Hauck that provides a desktop reference to supplement the online documentation and help you get started with scikit-learn quickly. The Scikit-Learn Cookbook is a focused book written by Trent Hauck and published by Packt Publishing. Over 50 recipes to incorporate scikit-learn into every step of the data science pipeline, from feature extraction to model building and model evaluation.

Everyone has an AI in their pocket these days -- Siri, Cortana, Google Now and Amazon's Alexa have given everyone easy access to virtual assistants. But one promising startup could wind up beating them all: Viv. Viv is still in its early stages, but it has caused a lot of excitement in the tech community, and according to a profile in The Washington Post, it has drawn bids from some major players. Here's what you need to know about Viv. Viv is poised to be the next big AI assistant.

Today, telepresence robots are priced for purchase or rent anywhere between 5,000 to 200,000, Chun says. While his research suggests the telepresence market is valued at 4 billion, he estimates that it's actually about half when factoring in conservative assumptions. Still, there is a lot of promise in the near future. Chun recorded 20 telepresence robot patents in 2014, and projected 36 patents for 2015. Additionally, the United States remains the dominant market, but Chun is seeing expansion in countries in Asia and the Middle East.

Nasa has announced that it has found evidence of flowing water on Mars. Scientists have long speculated that Recurring Slope Lineae -- or dark patches -- on Mars were made up of briny water but the new findings prove that those patches are caused by liquid water, which it has established by finding hydrated salts. Several hundred camped outside the London store in Covent Garden. The 6s will have new features like a vastly improved camera and a pressure-sensitive "3D Touch" display

In the previous blog we have seen the theory and mathematics behind the Maximum Entropy and Logistic Regression Classifiers. Logistic Regression is one of the most powerful classification methods within machine learning and can be used for a wide variety of tasks. Think of pre-policing or predictive analytics in health; it can be used to aid tuberculosis patients, aid breast cancer diagnosis, etc. Think of modeling urban growth, analysing mortgage pre-payments and defaults, forecasting the direction and strength of stock market movement, and even sports. Reading all of this, the theory[1] of Maximum Entropy Classification might look difficult. In my experience, the average Developer does not believe they can design a proper Maximum Entropy / Logistic Regression Classifier from scratch.