The main focus here is on finding the point that minimizes the sum of the "distances" to n points in a d-dimensional space, called centroid or center, especially in the presence of outliers. We also discuss an interesting physics problem: finding the point of maximum or minimum light, sound, radioactivity, or heat intensity, in the presence of an energy field produced by n energy source points. Both problems are closely related and use the same algorithm to find solutions. The sum of "distances" between an arbitrary point (u, v) and a set S { (x(1), y(1)) ... (x(n), y(n)) } of n points is defined as follows: The function H has one parameter p called power, and when p 2, we are facing the traditional problem of finding the centroid of a cloud of points: in this case, the solution is the classic average of the n points. This solution is notoriously sensitive to outliers.

Tax season is around the corner, and for most Americans, it involves dealing with the complex tax code, an accountant, and maybe friends who claim to be tax experts. According to IRS statistics, there were 507 million visitors to the irs.gov website in 2016, a 3 percent increase when compared to 2015. Furthermore, Americans spend 6.1 billion hours and $233.8 billion complying with the tax code. With complexity comes confusion and frustration, leading many taxpayers to turn to tax preparers or tax preparation software. Those who don't are at a disadvantage because most Americans are unaware of which deductions to consider, dependents to claims, student loan amounts to deduct, or where to file.

Hassaan Ahmed is co-founder of Intellisense Solutions. Machine learning is not new. We have witnessed it since the 1990s, when Amazon introduced a new "recommended for you" section for its users to display more personalized results. When we search for something on Google, machine learning is behind those search results. The "Friends" recommendations or the suggested pages on Facebook or a product recommendation on any e-commerce site all depend on machine learning.

One of the major differentiators between Apache Spark and the prior generation of Apache Hadoop–based and MapReduce-based technologies is the built-in Spark machine-learning library (MLlib). The motivation behind including these capabilities is to make practical machine learning scalable and understandable for data engineers and data scientists. MLlib also leverages Spark's distributed, in-memory execution model to yield significant performance benefits over preceding technologies such as R and Apache Mahout. While the capabilities in MLlib are powerful in the abstract, one still needs to identify a practical application, implement a technical solution and productionalize the analysis for its downstream consumers. As I discussed in the post, Spark: The operating system for big data analytics, Spark makes the implementation and productionalization of advanced data analysis significantly less challenging than the aforementioned technologies.

When Michael Litt and Devon Galloway launched Vidyard, they knew the market in which they wanted to compete--but, as often happens with start-ups, they didn't yet know the best way to do it. Back in 2009, Litt was interning at Cypress Semiconductor in California while pursuing an engineering degree at the University of Waterloo. It was his job to find production studios that could create customer-service videos for Cypress's website, but he found that the studios charged exorbitant prices for low-quality product. Litt's idea was simple: make better and cheaper videos for corporate clients. To continue reading this article, you must be a Globe Unlimited subscriber. Click here to get full access to Globe Unlimited.

In many respects, 2016 was the year of artificial intelligence (AI). Innovations such as big data, advances in machine learning and computing power, and algorithms capable of hearing and seeing with beyond-human accuracy have brought the benefits of AI to bear on our daily lives. By working together with machines, people can now accomplish more by doing less. Yet the power of AI can address far bigger challenges than helping organise our calendars, order our groceries or play games. In collaboration with AI, people can help to solve some of the world's most urgent and difficult problems.

A survey by Personetics shows that the financial services industry is getting a closer to supporting conversational commerce, supporting projects that use chatbots to improve the overall customer experience. Research reveals that most banking providers will be using automated chatbots to handle a significant volume of customer conversations in the near future. Some are doing it already. Powered by chatbots, conversational commerce (Voice-First Banking) allows organizations to interact with customers over digital and messaging platforms, providing answers to questions, advice and offers in real-time. A survey conducted by Personetics shows that over three quarters of financial institution respondents view chatbots as a viable commercial solution now or within the next 1-2 years, and almost half of the companies already have active chatbot projects in place. A majority of the respondents see a substantial share of customer conversations handled by bots within 3-5 years.

In the Marvel universe, billionaire Tony Stark/Iron Man has Jarvis, a personal AI to anticipate his needs and streamline his life. When I mention this to Collie Brown, founder and CEO of Arghon, a personal AI company, he gives a knowing smile. A moment before he described his AI product as a "life assistant." "There's the Watsons of the world, geared towards large scale data and the like," Brown said. "Arghon's about you, what's happening in your life from the time you wake up to the time you go to bed. Our goal is to manage what happens in between that."

If the basics of retail are elementary, then it should be no surprise that a technology named Watson is leading what may be one of the biggest trends in 2017. Watson is the name of an artificial intelligence technology (AI) by IBM; many may remember Watson for its $1 million winning streak on "Jeopardy." Today, several major retailers -- from Macy's to 1-800-Flowers.Com -- are using or testing the supercomputer's cognitive computing capabilities to more acutely predict (and serve) customer wishes. Most recently, Staples announced plans to implement Watson technology to bring to life its Easy Button. Infused with the technology, the button can now take Staples orders by voice, text, email, messaging app or mobile app.

Consider the tragedy of a child killed by neglect and abuse. Now consider the tragedy of a child taken from parents who would not have criminally abused her. Computer algorithms might soon help humans make such difficult decisions -- but only if we recognize the myriad ways in which they can go wrong. In countless cities across the nation, child welfare services make extremely tough calls every day. With limited resources and information, they must often rely on gut instinct in predicting who is most vulnerable.