Dimensionality reduction is a critical component of any solution dealing with massive data collections. Being able to sift through a mountain of data efficiently in order to find the key descriptive, predictive and explanatory features of the collection is a fundamental required capability for coping with the avalanche of data that all organizations are collecting. Identifying the most interesting dimensions of data is especially critical when integrating high-dimensional (high-variety) complex data sources, then attempting to visualize the most insightful patterns in the data, and then telling the data's story to your stakeholders. There is a "good news, bad news" angle here. First, the bad news: the human capacity for visualizing multiple dimensions is very limited: 3 or 4 dimensions are manageable; 5 or 6 dimensions are possible (e.g., with colors and symbols); but more dimensions are difficult-to-impossible to assimilate.

The implied semantics of direct manipulation is that when a user drags an UI element (in this case, an axis handle), they are signaling to the system that they wished that the corresponding data point had been projected to the location where the UI element was dropped, rather than where it was dragged from. In our case the overall projection is a rotation (originally determined by the Grand Tour), and an arbitrary user manipulation might not necessarily generate a new projection that is also a rotation. Our goal, then, is to find a new rotation which satisfies the user request and is close to the previous state of the Grand Tour projection, so that the resulting state satisfies the user request. In a nutshell, when user drags the ithi {th}ith axis handle by (dx,dy)(dx, dy)(dx,dy), we add them to the first two entries of the ithi {th}ith row of the Grand Tour matrix, and then perform Gram-Schmidt orthonormalization on the rows of the new matrix. Rows have to be reordered such that the ithi {th}ith row is considered first in the Gram-Schmidt procedure.

Dimensionality reduction is a critical component of any solution dealing with massive data collections. Being able to sift through a mountain of data efficiently in order to find the key descriptive, predictive and explanatory features of the collection is a fundamental required capability for coping with the Big Data avalanche. Identifying the most interesting dimensions of data is especially valuable when visualizing high-dimensional (high-variety) big data and when telling your data's story. There is a "good news, bad news" angle here. First, the bad news: the human capacity for visualizing multiple dimensions is very limited: 3 or 4 dimensions are manageable; 5 or 6 dimensions are possible; but more dimensions are difficult-to-impossible to assimilate. Now for the good news: the human cognitive ability to detect patterns, anomalies, changes, or other "features" in a large complex "scene" surpasses most computer algorithms for speed and effectiveness.

Dimensionality reduction is a critical component of any solution dealing with massive data collections. Being able to sift through a mountain of data efficiently in order to find the key descriptive, predictive and explanatory features of the collection is a fundamental required capability for coping with the Big Data avalanche. Identifying the most interesting dimensions of data is especially valuable when visualizing high-dimensional (high-variety) big data and when telling your data's story. There is a "good news, bad news" angle here. First, the bad news: the human capacity for visualizing multiple dimensions is very limited: 3 or 4 dimensions are manageable; 5 or 6 dimensions are possible; but more dimensions are difficult-to-impossible to assimilate.

It's the home to North Korea's space program, and a cover for testing the technology that could one day send a nuclear-warhead-bearing missile hurtling towards the US mainland. Now thanks to some publicity photographs, modeling software, and the efforts of an enterprising video game developer, you can tour its command center without fear of arrest. The North Korea specialist website 38 North has released a 3-D model of the control room at the Sohae Satellite Launching Station, the building from which the North launches its satellites and test rocket engines. The model makes for a nifty virtual experience, showing viewers the heart of the facility in rich enough detail to spot the curvature of the rubber seals on the windows. You can see several of the renders in the gallery above.

The three men who anchored the massively successful "Top Gear" automotive TV show will bring their large personalities back to the small screen Nov. 18, when Amazon Prime debuts the new series "The Grand Tour." Starring Jeremy Clarkson, James May and Richard Hammond, the first season will include 12 one-hour episodes, shot in exotic locations, where the three men drive, discuss and destroy various motor vehicles to comic effect. As in "Top Gear," which ended a 12-year syndicated run when the BBC declined to renew Clarkson's contract following a series of friction-causing incidents involving the outspoken former auto journalist, "The Grand Tour" features globe-trotting hi-jinks laced with boyish jibes. It will be different from "Top Gear," the men said during a visit to The Times -- but not much. "Well, it has us three hosting it," Clarkson said. "(May) is slow and lost and (Hammond) is short and I am bombastic and tall, and fat," Clarkson concluded.

Jeremy Clarkson and James May, former hosts of BBC 2's Top Gear program, are consummate car-guys. And they reinforced that fact during a recent chat at a Hollywood hotel ahead of the debut of their new car show, Grand Tour, on Amazon. SEE ALSO: Jeremy Clarkson's new driving show has an epic teaser trailer (and a launch date) More than bemoan the death of "interesting" mass-market cars, the two greying Brits analyzed the merits of self-driving cars, crossovers and -- of all things -- swearing on TV. Though they admit there's nothing much the Grand Tour can do that Top Gear couldn't, based upon their enthusiasm, witticisms and chemistry, I am confident the new show will be as pleasurable (if not more so) as Top Gear. You'll have to wait and see for yourself on November 18, though, when Grand Tour premiers on Amazon Prime.

Dimensionality reduction is a critical component of any solution dealing with massive data collections. Being able to sift through a mountain of data efficiently in order to find the key descriptive, predictive, and explanatory features of the collection is a fundamental required capability for coping with the Big Data avalanche. Identifying the most interesting dimensions of data is especially valuable when visualizing high-dimensional (high-variety) big data. There is a "good news, bad news" angle here. First, the bad news: the human capacity for seeing multiple dimensions is very limited: 3 or 4 dimensions are manageable; 5 or 6 dimensions are possible; but more dimensions are difficult-to-impossible to assimilate.