The most well known and ubiquitous clustering problem encountered in nearly every branch of science is undoubtedly $k$-means: given a set of data points and a parameter $k$, select $k$ centres and partition the data points into $k$ clusters around these centres so that the sum of squares of distances of the points to their cluster centre is minimized. Typically these data points lie $\mathbb{R}^d$ for some $d\geq 2$. $k$-means and the first algorithms for it were introduced in the 1950's. Since then, hundreds of papers have studied this problem and many algorithms have been proposed for it. The most commonly used algorithm is known as Lloyd-Forgy, which is also referred to as "the" $k$-means algorithm, and various extensions of it often work very well in practice. However, they may produce solutions whose cost is arbitrarily large compared to the optimum solution. Kanungo et al. [2004] analyzed a simple local search heuristic to get a polynomial-time algorithm with approximation ratio $9+\epsilon$ for any fixed $\epsilon>0$ for $k$-means in Euclidean space. Finding an algorithm with a better approximation guarantee has remained one of the biggest open questions in this area, in particular whether one can get a true PTAS for fixed dimension Euclidean space. We settle this problem by showing that a simple local search algorithm provides a PTAS for $k$-means in $\mathbb{R}^d$ for any fixed $d$. More precisely, for any error parameter $\epsilon>0$, the local search algorithm that considers swaps of up to $\rho=d^{O(d)}\cdot{\epsilon}^{-O(d/\epsilon)}$ centres at a time finds a solution using exactly $k$ centres whose cost is at most a $(1+\epsilon)$-factor greater than the optimum. Finally, we provide the first demonstration that local search yields a PTAS for the uncapacitated facility location problem and $k$-median with non-uniform opening costs in doubling metrics.

Constructing activity budgets for marine animals when they are at sea and cannot be directly observed is challenging, but recent advances in bio-logging technology offer solutions to this problem. Accelerometers can potentially identify a wide range of behaviours for animals based on unique patterns of acceleration. However, when analysing data derived from accelerometers, there are many statistical techniques available which when applied to different data sets produce different classification accuracies. We investigated a selection of supervised machine learning methods for interpreting behavioural data from captive otariids (fur seals and sea lions). We conducted controlled experiments with 12 seals, where their behaviours were filmed while they were wearing 3-axis accelerometers.

Here's a conversation I had recently with Cleverbot. What are your views on the future of chatbots in language learning? User: What are your views on the future of chatbots in language learning? User: Do you think there is a future for chatbots in language education? Cleverbot: Sure, if you are talking about the moon. I also tried to have a conversation with Alice, the avatar from EFL Classroom Bot, listed by Larry Ferlazzo as one of'the best online chatbots for practicing English'.

A 2017 Chrysler Pacifica hybrid minivan equipped with Waymo's self-driving vehicle technology. Waymo, the company born from Alphabet's Google Self-Driving Car research project, faces mounting competition to perfect technology needed for fully autonomous vehicles. After staying low key about its progress, the latest indications from the new company are that it's far along the path to making such vehicles a reality by taking cost out of the components and boosting overall performance and reliability. John Krafcik, Waymo's chief executive officer, said at the Automobili-D conference in Detroit that the latest sensors, software, artificial intelligence and other components -- all developed and built in-house -- are being used for a fleet of 100 Chrysler Pacifica minivans, the first batch of which will begin public road tests in California and Arizona this month, he said. Keeping development and production in-house has led to major cost savings, including a 90% reduction for the laser Lidar sensor riding atop the new Pacificas.

It was actually about when technology goes wrong: In many ways, 2016 was the year of the exploding batteries. A little over a year ago, hoverboards topped many holiday wish lists. By December 2015, they were being recalled by the thousands. According to Popular Science, "…cheaply made hoverboards have exploded and caught fire, forcing Amazon to stop selling specific models and Overstock to discontinue all sales." Rolling into 2016, major computer companies recalled batteries for fire hazards, baby monitors were pulled from shelves and major airlines diverted flights for emergency landings when tablets caught fire onboard.

SYS-CON Events announced today that Fusion, a leading provider of cloud services, will exhibit at SYS-CON's 20th International Cloud Expo, which will take place on June 6-8, 2017, at the Javits Center in New York City, NY. Fusion, a leading provider of integrated cloud solutions to small, medium and large businesses, is the industry's single source for the cloud. Fusion's advanced, proprietary cloud service platform enables the integration of leading edge solutions in the cloud, including cloud communications, cloud connectivity, and cloud computing. Fusion's innovative, yet proven cloud solutions lower our customers' cost of ownership, and deliver new levels of security, flexibility, scalability, and speed of deployment. For more information, please visit http://www.fusionconnect.com.

IBM (NYSE:IBM) jointly announced with the German conglomerate Siemens (OTCPK:SIEGY) that they are planning to include IBM's Watson in Siemens's industry analytics platform MindSphere. Siemens is Europe's largest manufacturing and electronics company with a worldwide presence. Siemens operates in the industrial sector with lots of on-premises software suites, which the company is willing to send to cloud. As a result, IBM's Watson will get a significant boost. This article investigates how IBM's Watson platform will benefit from the development.

To process an image, for example, the lowest layer is fed the raw images. It notes things like the brightness and colours of individual pixels, and how those properties are distributed across the image. The next layer combines these observations into more abstract categories, identifying edges, shadows and the like. The layer after that will analyse those edges and shadows in turn, looking for combinations that signify features such as eyes, lips and ears. And these can then be combined into a representation of a face--and indeed not just any face, but even a new image of a particular face that the network has seen before.

If you came across an animal in the wild and wanted to learn more about it, there are a few things you might do: You might watch what it eats, poke it to see how it reacts, and even dissect it if you got the chance. Mathematicians are not so different from naturalists. Rather than studying organisms, they study equations and shapes using their own techniques. They twist and stretch mathematical objects, translate them into new mathematical languages, and apply them to new problems. As they find new ways to look at familiar things, the possibilities for insight multiply.

Deep learning is the new big trend in machine learning. It had many recent successes in computer vision, automatic speech recognition and natural language processing. The goal of this blog post is to give you a hands-on introduction to deep learning. To do this, we will build a Cat/Dog image classifier using a deep learning algorithm called convolutional neural network (CNN) and a Kaggle dataset. This post is divided into 2 main parts. The first part covers some core concepts behind deep learning, while the second part is structured in a hands-on tutorial format. In the first part of the hands-on tutorial (section 4), we will build a Cat/Dog image classifier using a convolutional neural network from scratch.