In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the unreliability of distances in very high-dimensional spaces. We propose a distance-based iterative method for clustering data in very high-dimensional space, using the $\ell_1$-metric that is less sensitive to high dimensionality than the Euclidean distance. For $K$ clusters in $\mathbb{R}^n$, the problem decomposes to $K$ problems coupled by probabilities, and an iteration reduces to finding $Kn$ weighted medians of points on a line. The complexity of the algorithm is linear in the dimension of the data space, and its performance was observed to improve significantly as the dimension increases.

A century ago, more than 60,000 tigers roamed the wild. Today, the worldwide estimate has dwindled to around 3,200. Poaching is one of the main drivers of this precipitous drop. Whether killed for skins, medicine or trophy hunting, humans have pushed tigers to near-extinction. The same applies to other large animal species like elephants and rhinoceros that play unique and crucial roles in the ecosystems where they live.

Google's parent company Alphabet saw its revenue grow 17% during the first three months of this year, the company said on Thursday, but spent more money on its experimental moonshot projects, engineers, data centers and YouTube shows, causing it to miss investors' profit expectations. Alphabet shares dropped more than 4% in the US during after-hours trading to about 724 a share. The dilemma illustrates Alphabet's key challenge as it seeks to become the technology firm most omnipresent in consumers lives, including search, email, smartphones, maps, self-driving cars, virtual reality and even cancer research. Alphabet's growth has also attracted attention from regulators. On 20 April, the European Union's antitrust regulators charged the company with using its mobile operating system, Android, to block out competitors.

In Arnold Schwarzenegger's 1990 sci-fi classic Total Recall, the protagonist gets into a heated argument with a self-driving cab, driven by an artificial intelligence- challenged automaton. The film takes place in 2084 on Mars. But fully autonomous cars will be a reality right here on Earth by 2021. Their company is best known for inventing a technology to alert drivers to obstacles. Using that proprietary obstacle-sensing sensor system to gather millions of kilometers of driving data, Mobileye is working with many of the world's biggest auto manufacturers to pave the way for self-driving cars and trucks.

Rodney Brooks wasn't willing in 2002 to hazard a guess about when the challenges of robotics would be overcome. "Not in two years or three years," Brooks asserted during an IndustryWeek interview that year. "But is it going to be here in 30 years or 40 years? I'm not quite prepared [to make a prediction]." Still in a book published then and the interview, he gave us a peek at what it would look like when it arrived: "robots that take instruction easily rather than ones that require hours of programming time; robots that can help in small-batch operations rather than ones that only make financial sense in continuous or nearly continuous fixed operation settings with long runs; robots with social interaction skills;" and robots that reduce costs on the factory floor.

The US Army and Marine Corps are set to test tanks with a new version of the iron dome' system developed by the Israeli government. The Trophy Active Protection System (APS) uses sensors to detect an anti tank missile is coming. It then fires small rounds to deflect them, and can also use jammers to mislead the enemy. The system is designed to create a protective field around tanks, shooting down incoming missiles before they detonate. The Trophy Active Protection System (APS) uses sensors to detect an anti tank missile is coming.

How do you get high school students to enjoy studying science? How about by giving them the parts to build a robot and then letting them compete against each other to see who builds the best "bot?"

SAN FRANCISCO -- The cloud may be the future, but the specter of the PC lingers. Microsoft is the latest tech giant whose earnings say that loud and clear. Microsoft on Thursday posted substantial drops in revenue and earnings as it continues to navigate from its legacy PC business into emerging technologies -- a day after chipmaker Intel announced a 11% workforce reduction. The Redmond, Wash.-based company reported a 6% decline in fiscal third-quarter revenue to 20.5 billion. Earnings of 3.8 billion, or 47 cents per share, fell 25%in the same quarter a year ago.

SAN FRANCISCO -- Google parent Alphabet reported first-quarter earnings that fell short of analyst expectations as growing losses from the tech giant's investments in speculative businesses, from self-driving cars to speedy Internet access, overshadowed Google's booming advertising business. Class A shares of Alphabet (GOOGL) fell 6% after hours to 732. They've rallied 44% in the past 12 months. "Alphabet has made it pretty clear they weren't going to stop their investments in other areas, and they spent a little bit more than some people may have liked," said BGC Financial analyst Colin Gillis. "You don't necessarily like to see costs and losses growing faster than revenue, but that's where Alphabet's future is going to be." Chief Financial Officer Ruth Porat, who joined the company last May in a hire investors hoped would curb spending, assured investors that Alphabet is "thoughtfully pursuing big bets."

SAN FRANCISCO -- The cloud may be the future, but the specter of the PC lingers. Microsoft is the latest tech giant to learn that first-hand. Microsoft on Thursday posted substantial drops in revenue and earnings as it continues to navigate from its legacy PC business into emerging technologies -- a day after chip maker Intel announced a 11% workforce reduction. The computing giant reported a 5% decline in fiscal third-quarter revenue to 20.5 billion. Earnings of 3.8 billion, or 47 cents per share, fell from 5 billion, or 61 cents a share, in the same quarter a year ago.