AI News, DrSkippy/Data-Science-45min-Intros


We'll pull in data from Twitter's public api, parse out the tweet text, separate

Let's grab some json records from Twitter's public api that we'll grab using

Two steps: To choose the appropriate number of svd components, we need to explore the amount of variance explained with each component.

We'll now apply kmeans to find the centroids that will be used to predict a cluster for each tweet.

Those tweets nearest the cluster centers are used as an approximation for their meanings.


The record was broken again when 3,085 tweets per second were posted after the Los Angeles Lakers' victory in the 2010 NBA Finals on June 17,[44] and then again at the close of Japan's victory over Denmark in the World Cup when users published 3,283 tweets per second.[45] The record was set again during the 2011 FIFA Women's World Cup Final between Japan and the United States, when 7,196 tweets per second were published.[46] When American singer Michael Jackson died on June 25, 2009, Twitter servers crashed after users were updating their status to include the words 'Michael Jackson' at a rate of 100,000 tweets per hour.[47] The current record as of August 3, 2013 was set in Japan, with 143,199 tweets per second during a television screening of the movie Castle in the Sky[48] (beating the previous record of 33,388, also set by Japan for the television screening of the same movie).[49] Twitter acquired application developer Atebits on April 11, 2010.

Twitter hit 100 million monthly active users in September 2011.[66] On January 28, 2013, Twitter acquired Crashlytics in order to build out its mobile developer products.[67] On April 18, 2013, Twitter launched a music app called Twitter Music for the iPhone.[68] On August 28, 2013, Twitter acquired Trendrr,[69] followed by the acquisition of MoPub on September 9, 2013.[70] As of September 2013, the company's data showed that 200 million users send over 400 million tweets daily, with nearly 60% of tweets sent from mobile devices.[71] On June 4, 2014, Twitter announced that it will acquire Namo Media, a technology firm specializing in 'native advertising' for mobile devices.[72] On June 19, 2014, Twitter announced that it has reached an undisclosed deal to buy SnappyTV, a service that helps edit and share video from television broadcasts.[73][74] The company was helping broadcasters and rights holders to share video content both organically across social and via Twitter's Amplify program.[75] In July 2014, Twitter announced that it intends to buy a young company called CardSpring for an undisclosed sum.

The partnership is intended to help businesses use Twitter data to understand their customers, businesses and other trends.[78] On February 11, 2015, Twitter announced that it had acquired Niche, an advertising network for social media stars, founded by Rob Fishman and Darren Lachtman.[79] The acquisition price was reportedly $50 million.[80] On March 13, 2015, Twitter announced its acquisition of Periscope, an app that allows live streaming of video.[81] In April 2015, the desktop homepage changed.[82] Twitter announced that it has acquired TellApart, a commerce ads tech firm, with $532 million stock.[83][84] Later in the year it became apparent that growth had slowed, according to Fortune,[85] Business Insider,[86] Marketing Land[87] and other news websites including Quartz (in 2016).[88] In June 2016, Twitter acquired an artificial intelligence startup called Magic Pony for $150 million.[89][90] On September 12, 2013, Twitter announced that it had filed papers with the U.S. Securities and Exchange Commission (SEC) ahead of a planned stock market listing.[91] It revealed its prospectus in an 800-page filing.[92] Twitter planned to raise US$1 billion as the basis for its stock market debut.[93] The IPO filing states that '200,000,000+ monthly active users' access Twitter and '500,000,000+ tweets per day' are posted.[31][94] In an October 15, 2013 amendment to their SEC S-1 filing,[95] Twitter declared that they would list on the New York Stock Exchange (NYSE), quashing speculation that their stock would trade on the NASDAQ exchange.

This decision was widely viewed to be a reaction to the botched initial public offering of Facebook.[96] On November 6, 2013, 70 million shares[97] were priced at US$26 and issued by lead underwriter Goldman Sachs.[98] On November 7, 2013, the first day of trading on the NYSE, Twitter shares opened at $26.00 and closed at US$44.90, giving the company a valuation of around US$31 billion.[99] The paperwork from November 7 shows that among the founders, Williams received a sum of US$2.56 billion and Dorsey received US$1.05 billion, while Costolo's payment was US$345 million.[100] On February 5, 2014, Twitter published its first results as a public company, showing a net loss of $511 million in the fourth quarter of 2013.[101] On January 5, 2016, CEO Jack Dorsey commented on a report that Twitter planned to expand its character limit to 10,000 (private messages already had the longer limit as of July), requiring users to click to see anything beyond 140 characters.

He said while Twitter would 'never lose that feeling' of speed, users could do more with the text.[102] In September 2016, Twitter shares rose 20% after a report that it had received takeover approaches.[103] Potential buyers were Alphabet (parent company of Google),[103] Microsoft,[104][105][106],[103][107] Verizon,[107] and The Walt Disney Company.[108][109] Twitter's board of directors were open to a deal, which could have come by the end of 2016.[103][110] However, no deal was made, with reports in October stating that all the potential buyers dropped out partly due to concerns over abuse and harassment on the service.[111][112][113] In June of 2017, Twitter revamped its dashboard to improve the new user experience.[114][115] As chief executive officer, Dorsey saw the startup through two rounds of capital funding by the venture capitalists who backed the company.[116] On October 16, 2008,[117] Williams took over the role of CEO, and Dorsey became chairman of the board.[118] On October 4, 2010, Williams announced that he was stepping down as CEO.

As of 2009[update], fewer than half of tweets posted were posted using the web user interface with most users using third-party applications (based on an analysis of 500 million tweets by Sysomos).[172] In June 2009, after being criticized by Kanye West and sued by Tony La Russa over unauthorized accounts run by impersonators, Twitter launched their 'Verified Accounts' program.[173][174] Twitter stated that an account with a verification badge indicates 'we've been in contact with the person or entity the account is representing and verified that it is approved.'[175] After the beta period, Twitter stated in their FAQ that the company 'proactively verifies accounts on an ongoing basis to make it easier for users to find who they’re looking for' and that they 'do not accept requests for verification from the general public.'[176] In July 2016, Twitter announced a public application process to grant verified status to an account 'if it is determined to be of public interest' and that verification 'does not imply an endorsement.'[177][178][179] As of November 2017, Twitter continued to deny verification of Julian Assange despite his requests.[180] In November 2017, the company suspended the verification process and announced plans to refine it in response to backlash after white nationalist Jason Kessler had his account verified on Twitter.[181][182][183] Verified status allows access to some features unavailable to other users, such as only seeing mentions from other verified accounts.[184] In a March 8, 2018 live-stream on Twitter's Periscope, Dorsey discussed the idea of allowing any user to get a verified account.

Polls are open for up to 7 days, and voters are not personally identified.[195] In 2016, Twitter began to place a larger focus on live streaming video programming, hosting various events including streams of the Republican and Democratic conventions during the U.S. presidential campaign as part of a partnership with CBS News,[196] Dreamhack and ESL eSports events,[197] and winning a bid for non-exclusive streaming rights to ten NFL Thursday Night Football games in the 2016 season.[198][197] During an event in New York in May 2017, Twitter announced that it planned to construct a 24-hour streaming video channel hosted within the service, featuring content from various partners.[199][197] CEO Jack Dorsey stated that the digital video strategy was part of a goal for Twitter to be 'the first place that anyone hears of anything going on that matters to them';

Twitter's first A round of funding was for an undisclosed amount that is rumored to have been between US$1 million and US$5 million.[227] Its second B round of funding in 2008 was for US$22 million[228] and its third C round of funding in 2009 was for US$35 million from Institutional Venture Partners and Benchmark Capital along with an undisclosed amount from other investors including Union Square Ventures, Spark Capital, and Insight Venture Partners.[227] Twitter is backed by Union Square Ventures, Digital Garage, Spark Capital, and Bezos Expeditions.[229] In May 2008, The Industry Standard remarked that Twitter's long-term viability is limited by a lack of revenue.[230] Twitter board member Todd Chaffee forecast that the company could profit from e-commerce, noting that users may want to buy items directly from Twitter since it already provides product recommendations and promotions.[231] By March 2009 communications consultant Bill Douglass predicted in an interview that Twitter would be worth $1 billion within six months,[232] which came to pass when the company closed a financing round valuing it at $1 billion in September of that year.[233] The company raised US$200 million in new venture capital in December 2010, at a valuation of approximately US$3.7 billion.[234] In March 2011, 35,000 Twitter shares sold for US$34.50 each on Sharespost, an implied valuation of US$7.8 billion.[235] In August 2010 Twitter announced a 'significant' investment led by Digital Sky Technologies that, at US$800 million, was reported to be the largest venture round in history.[236] In December 2011, the Saudi prince Alwaleed bin Talal invested US$300 million in Twitter.

The people creating the 'bots' are often from Eastern Europe and Asia.[295][296] In 2013, two Italian researchers calculated 10 percent of total accounts on Twitter are 'bots' however, other estimates have placed the figure even higher.[297] After a number of high-profile hacks of official accounts, including those of the Associated Press and The Guardian,[298] in April 2013, Twitter announced a two-factor login verification as an added measure against hacking.[299] In August Twitter announced plans to introduce a 'report abuse' button for all versions of the site following uproar, including a petition with 100,000 signatures, over Tweets that included rape and death threats to historian Mary Beard, feminist campaigner Caroline Criado Perez and the member of parliament Stella Creasy.[300][301][302] Followed the sharing of images showing the killing of American journalist James Foley in 2014, Twitter said that in certain cases it would delete pictures of people who had died after requests from family members and 'authorized individuals'.[303][304] Twitter announced new reporting and blocking policies in December 2014,[305][306][307][308] including a blocking mechanism devised by Randi Harper, a target of GamerGate.[309][310][311] In February 2015, CEO Dick Costolo said he was 'frankly ashamed' at how poorly Twitter handled trolling and abuse, and admitted Twitter had lost users as a result.[312] In 2015, following an updated terms of service and privacy policy, Twitter users outside of the United States are legally served by the Ireland-based Twitter International Company instead of Twitter, Inc.

[315] Twitter has a history of both using and releasing open source software while overcoming technical challenges of their service.[316] A page in their developer documentation thanks dozens of open source projects which they have used, from revision control software like Git to programming languages such as Ruby and Scala.[317] Software released as open source by the company includes the Gizzard Scala framework for creating distributed datastores, the distributed graph database FlockDB, the Finagle library for building asynchronous RPC servers and clients, the TwUI user interface framework for iOS, and the Bower client-side package manager.[318] The popular Twitter Bootstrap web design library was also started at Twitter and is the second most popular repository on GitHub.[319] On April 17, 2012, Twitter announced it would implement an 'Innovators Patent Agreement' which would obligate Twitter to only use its patents for defensive purposes.

These fake accounts are often used to build large follower populations quickly for advertisers, while others respond to tweets that include a certain word or phrase.[326] Twitter's wide-open application programming interface and cloud servers make it possible for twitterbots' existence within the social networking site.[327] Twitter is recognized for having one of the most open and powerful developer APIs of any major technology company.[328] Developer interest in Twitter began immediately following its launch, prompting the company to release the first version of its public API in September 2006.[329] The API quickly became iconic as a reference implementation for public REST APIs and is widely cited in programming tutorials.[330] From 2006 until 2010, Twitter's developer platform experienced strong growth and a highly favorable reputation.

Between 2010 and 2012, however, Twitter made a number of decisions that were received unfavorably by the developer community.[331] In 2010, Twitter mandated that all developers adopt OAuth authentication with just 9 weeks of notice.[332] Later that year, Twitter launched its own URL shortener, in direct competition with some of its most well-known 3rd-party developers.[333] And in 2012, Twitter introduced strict usage limits for its API, 'completely crippling' some developers.[334] While these moves successfully increased the stability and security of the service, they were broadly perceived as hostile to developers, causing them to lose trust in the platform.[335] In an effort to reset its relationship with developers, Twitter acquired Crashlytics on January 28, 2013 for over USD $100 million, its largest acquisition to date.[336] Founded by Jeff Seibert and Wayne Chang, Crashlytics had rapidly gained popularity as a tool to help mobile developers identify and fix bugs in their apps.[337] Twitter committed to continue supporting and expanding the service.[338] In October 2014, Twitter announced Fabric, a suite of mobile developer tools built around Crashlytics.[339] Fabric brought together Crashlytics, Answers (mobile app analytics), Beta (mobile app distribution), Digits (mobile app identity and authentication services), MoPub, and TwitterKit (login with Twitter and Tweet display functionality) into a single, modular SDK, allowing developers to pick and choose which features they needed while guaranteeing ease of installation and compatibility.

For example, it has been used to organize protests, sometimes referred to as 'Twitter Revolutions',[344] which include April 2009 Moldovan parliamentary election protests, 2009 student protests in Austria, 2009 Gaza–Israel conflict, 2009 Iran green revolution, 2009 Toronto G20, 2010 Bolivarian Revolution, 2010 Germany Stuttgart21, 2011 Egypt Revolution, 2011 England riots, 2011 United States Occupy movement, 2011 Anti-austerity movement in Spain, 2011 Greece Aganaktismenoi movements, 2011 Italy Rome demonstration, 2011 Wisconsin labor protests, 2012 Gaza–Israel conflict, 2013 protests in Brazil, 2013 Gezi Park protests.[345] A result of the Iranian election protests saw the government of Iran block Twitter in censorship.[346] The service is also used as a form of civil disobedience: In 2010, users expressed outrage over the Twitter Joke Trial by copying a controversial joke about bombing an airport and attaching the hashtag #IAmSpartacus, a reference to the Spartacus film and a sign of solidarity and support to a man controversially prosecuted after posting a tweet joking about bombing an airport if they cancelled his flight.

#IAmSpartacus became the number one trending topic on Twitter worldwide.[347] Another case of civil disobedience happened in the 2011 British privacy injunction debate, where several celebrities who had taken out anonymized injunctions were identified by thousands of users in protest to traditional journalism being censored.[348] During the Arab Spring in early 2011, the number of hashtags mentioning the uprisings in Tunisia and Egypt increased.[349] A study by the Dubai School of Government found that only 0.26% of the Egyptian population, 0.1% of the Tunisian population and 0.04% of the Syrian population are active on Twitter.[350] In January 2016, Twitter was sued by the widow of a U.S. man killed in the 2015 Amman shooting attack, claiming that allowing the Islamic State of Iraq and the Levant (ISIL) to continually use the platform, including direct messages in particular,[351] constituted the provision of material support to a terrorist organization, which is illegal under U.S. federal law.

Twitter disputed the claim, stating that 'violent threats and the promotion of terrorism deserve no place on Twitter and, like other social networks, our rules make that clear.'[352][353] The lawsuit was dismissed by the United States District Court for the Northern District of California, upholding the Section 230 safe harbor, which dictates that the operators of an interactive computer service are not liable for the content published by its users.[353][354] The lawsuit was revised in August 2016, providing comparisons to other telecommunications devices.[351] Twitter suspended multiple parody accounts that satirized Russian politics in May 2016, sparking protests and raising questions about where the company stands on freedom of speech.[355] Following public outcry, Twitter restored the accounts the next day without explaining why the accounts had been suspended.[356] The same day, Twitter, along with Facebook, Google, and Microsoft, jointly agreed to a European Union code of conduct obligating them to review '[the] majority of valid notifications for removal of illegal hate speech' posted on their services within 24 hours.[357] In August 2016, Twitter stated that it had banned 235,000 accounts over the past six months, bringing the overall number of suspended accounts to 360,000 accounts in the past year, for violating policies banning use of the platform to promote extremism.[358] In October 2017, actress Rose McGowan said that Twitter had suspended her account for 12 hours after she repeatedly tweeted about former film studio executive Harvey Weinstein's alleged sexual misconduct toward her and others.

The boycott was joined by activists, celebrities and journalists.[361] In November 2017, the Paradise Papers, a set of confidential electronic documents relating to offshore investment, revealed that Twitter is among the corporations that avoided paying taxes using offshore companies.[362] Later The New York Times reported that Russian-American billionaire Yuri Milner had strong Kremlin backing for his investments in Facebook and Twitter.[363] In May 2018, in response to scrutiny over the misuse of Twitter by those seeking to maliciously influence elections, Twitter announced that it would partner with the nonprofit organization Ballotpedia to add special labels verifying the authenticity of political candidates running for election in the U.S.[364][365] Twitter is banned completely in Iran, China and North Korea,[366] and has been intermittently blocked in numerous countries including Egypt, Iraq, Turkey and Venezuela on different bases.[367][368][369][370] In 2016, Twitter cooperated with the Israeli government to remove certain content originating outside Israel from tweets seen in Israel.[371] In the 11th biannual transparency report published on September 19, 2017, Twitter said that Turkey was the first among countries where about 90 percent of removal requests came from, followed by Russia, France and Germany.[372] As part of evidence to a US Senate Enquiry, the company admitted that their systems 'detected and hid' several hundred thousand tweets relating to the 2016 Democratic National Committee email leak.[373] After claims in the media that the hashtags #wikileaks and #occupywallstreet were being censored because they did not show up on the site's list of trending topics, Twitter responded by stating that it does not censor hashtags unless they contain obscenities.[374][375][376] In 2016, at the same time as Twitter executives paid to attend a political fundraiser by Hillary Clinton, the Twitter platform banned a pro-Bernie Sanders account that had started a hashtag critical of Clinton's fundraising from wealthy donors.[377] The announcement of Twitter's 'Trust &

It was neither intended nor designed for high-performance communication, but the idea that it could be used for emergency communication was not lost on the creators, who knew that the service could have wide-reaching effects early on when the company used it to communicate during earthquakes.[384] Another practical use that is being studied is Twitter's ability to track epidemics and how they spread.[385] In addition, Twitter has acted as a sensor for automatic response to natural disasters such as bush fires.[386][387] Twitter has been adopted as a communication and learning tool in educational and research[388] settings mostly in colleges and universities.[389][390] It has been used as a backchannel to promote student interactions, especially in large-lecture courses.[391] Research has found that using Twitter in college courses helps students communicate with each other and faculty, promotes informal learning, allows shy students a forum for increased participation, increases student engagement, and improves overall course grades.[392][393][394] Twitter has been an increasingly growing in the field of education, as an effective tool that can be used to encourage learning and idea, or knowledge sharing, in and outside the classroom.[395] By using or creating hashtags, students and educators are able to communicate under specific categories of their choice, to enhance and promote education.

Tech writer Bruce Sterling commented in 2007 that using Twitter for 'literate communication' is 'about as likely as firing up a CB radio and hearing some guy recite the Iliad'.[397] In September 2008, the journalist Clive Thompson mused in a New York Times Magazine editorial that the service had expanded narcissism into 'a new, supermetabolic extreme—the ultimate expression of a generation of celebrity-addled youths who believe their every utterance is fascinating and ought to be shared with the world'.[398] One of the earliest documented forms of celebrity-related Twitter-like disclosures dates from 1980, when real estate mogul William Desmond Ryan made round-the-clock press releases about his relationship with comedian Phyllis Diller, even revealing what she was making him for dinner on a nightly basis.[399] Conversely, Vancouver Sun columnist Steve Dotto opined that part of Twitter's appeal is the challenge of trying to publish such messages in tight constraints,[400] and Jonathan Zittrain, professor of Internet law at Harvard Law School, said that 'the qualities that make Twitter seem inane and half-baked are what makes it so powerful.'[401] The novelist Rick Moody wrote a short story for Electric Literature called 'Some Contemporary Characters,' composed entirely of tweets.[402] In 2009, Nielsen Online reported that Twitter had a user-retention rate of forty percent.

As of April 2016, his successor, Pope Francis, has 9.06 million followers of his Twitter account (@Pontifex).[421] In a 2015 European Foundation for Democracy-European Policy Centre policy dialogue panel in Brussels, Mark Wallace, CEO of the 'CounterExtremism Project' and former U.S ambassador to the United Nations, said: “Twitter is currently the ´gateway drug´ for those seeking to recruit fighters for Islamic terrorism and this must be stopped.” [422] Twitterbots are capable of influencing public opinion about culture, products and political agendas by automatically generating mass amounts of tweets through imitating human communication.[423] The New York Times states, 'They have sleep-wake cycles so their fakery is more convincing, making them less prone to repetitive patterns that flag them as mere programs.'[424] The tweets generated vary anywhere from a simple automated response to content creation and information sharing, all of which depends on the intention of the person purchasing or creating the bot.

This practice of obtaining mass amounts of twitterbots as followers is not permitted on Twitter.[429] The emphasis on followers and likes as a measure of social capital has urged people to extend their circle to weak and latent ties to promote the idea of popularity for celebrities, politicians, musicians, public figures, and companies alike.[430] According to The New York Times, bots amass significant influence and have been noted to sway elections, influence the stock market, public appeal, and attack governments.[431] According to documents leaked by Edward Snowden and published in July 2014, the United Kingdom's GCHQ has a tool named BIRDSONG for 'automated posting of Twitter updates', and a tool named BIRDSTRIKE for 'Twitter monitoring and profile collection'.[432][433] Twitter is also increasingly used for making TV more interactive and social.[434] This effect is sometimes referred to as the second screen,[435] 'virtual watercooler' or social television—the practice has been called 'chatterboxing'.[436] Twitter has been successfully used to encourage people to watch live TV events, such as the Oscars, the Super Bowl[437] and the MTV Video Music Awards;

With the additional analytic tools, Twitter was able to improve the firm's offering to advertisers, allowing them to, for instance, only promote a tweet onto the timelines of users who were watching a certain programme.[450] By February 2014, all four major U.S. TV networks had signed up to the Amplify program, bringing a variety of premium TV content onto the social platform in the form of in-tweet real-time video clips.[451] In March 2014, ITV became the first major broadcaster in the UK to sign up to Twitter Amplify[452] and Twitter introduced one-tap video playback across its mobile apps to further enhance the consumer experience.[453] In June 2014, Twitter acquired its Amplify partner in the U.S., SnappyTV.[454] In Europe, Twitter's Amplify partner is London-based Grabyo, which has also struck numerous deals with broadcasters and rights holders[75] to share video content across Facebook and Twitter.[455] In July 2017, Twitter announced that it would wind down SnappyTV as a separate company, and integrate its features into the Media Studio suite on Twitter.[456] As of February 24, 2018, the ten Twitter accounts with the most followers were:[457] The oldest Twitter accounts are 14 accounts that became active on March 21, 2006, all belonging to Twitter employees at the time and including @jack (Jack Dorsey), @biz (Biz Stone), and @noah (Noah Glass).[458] A

How to use login verification

To set up login verification on Twitter for Android: Now, when you log in to your account on, Twitter for iOS, Twitter for Android, or, a six-digit login code will be sent via text message to your phone.

To choose between login verification type on Twitter for Android: You can choose to use a separate third-party app to generate a login code.  To set up using a separate third-party app for verification on Twitter for Android: You can use a third-party authenticator app, such as Google Authenticator, Duo Mobile, Authy, or similar, installed on your mobile device.

Singular Value Decomposition (SVD) Tutorial: Applications, Examples, Exercises

This singular value decomposition tutorial assumes you have a good working knowledge of both matrix algebra and vector calculus.

Because of this, they hypothesized that there was a general measure of intelligence in common, which they called “g,” for “general intelligence,” now more commonly known as “I.Q.” So they set about teasing out the different factors that made up intelligence so as to pull out the most important one.

In the early days, as the above passage implies, it was called, “factor analysis.” Other terms include principal component (PC) decomposition and empirical orthogonal function (EOF) analysis.

The variables, {sᵢ}, are called singular values and are normally arranged from largest to smallest: The columns of U are called left singular vectors, while those of V are called right singular vectors.

Using the orthogonality property, we can rearrange (1) into the following pair of eigenvalue equations: Since Transpose(A)A is the same size or smaller than A Transpose(A), a typical procedure is to plug Equation (3) into an eigenvalue calculator to find V and S² and then find U by projecting A onto V: Note that the method is completely symmetric;

Let x’=(x’, y’) be the transformed coordinates: where R is a rotation matrix: and M is a diagonal matrix containing the major and minor axes: Lets write this out term-by-term, both for the general case: where mᵢ is the ith diagonal of the matrix, M, and for the two-dimension case: Note that the rotation is clockwise, opposite the usual sense because we are going from the untransformed to the transformed coordinate system rather than the other way around.

The equation for a unit circle is as follows: We wish to fit a set of x’s, which we collect as the rows of a matrix, X: The resulting matrix equation is given: This is just a rearrangement of equation (3).

Some more rearrangement of (1) shows that SVD can be used for solving systems of linear equations: or, in summation notation: If this was all there was to it, there would be little to recommend SVD over simpler matrix solvers, such as QR decomposition or even Gaussian elimination.

For non-square matrices, matrix inversion using singular value decomposition is equivalent to solving the normal equation: and produces the solution for x that is closest to the origin, that is, of minimal length.

Suppose that the m × n matrix, A, stores a set of training data with each training vector taking up one row as in (5) and that n, the dimension of each vector, is very large.

We are using a canned singular value decomposition routine that is contained in the header file, svd.h: SVD routines are often more complicated than this, particularly in regards to the matrix and vector types used, but it would be straightforward to encapsulate the whole thing in a “wrapper” function.

i ∈ [1, c]}: In the third part of the program, continuing from above, we generate the cluster centers: Because the clustering algorithm used the transformed training data, cluster centers will be in the transformed system: or: Writing it out component-by-component: where p is the number of coordinates in the reduced system.

Machine Learning for Humans, Part 3: Unsupervised Learning

The two unsupervised learning tasks we will explore are clustering the data into groups by similarity and reducing dimensionality to compress the data while maintaining its structure and usefulness.

This service segments U.S. households into 70 distinct clusters within 21 life stage groups that are used by advertisers when targeting Facebook ads, display ads, direct mail campaigns, etc.

You can imagine how having access to these clusters is extremely useful for advertisers who want to (1) understand their existing customer base and (2) use their ad spend effectively by targeting potential new customers with relevant demographics, interests, and lifestyles.

“And k rings were given to the race of Centroids, who above all else, desire power.” The goal of clustering is to create groups of data points such that points in different clusters are dissimilar while points within a cluster are similar.

You’ll notice that the centroids (the larger blue, red, and green circles) start randomly and then quickly adjust to capture their respective clusters.

In this 4,096-dimensional world, k-means clustering allows us to group the images that are close together and assume they represent the same digit, which can achieve pretty good results for digit recognition.

On the homepage you’d want a few broad categories of items for simple navigation, but as you go into more specific shopping categories you’d want increasing levels of granularity, i.e.

If you take a simple 128 x 128 x 3 pixels image (length x width x RGB value), that’s 49,152 dimensions of data.

If you’re able to reduce the dimensionality of the space in which these images live without destroying too much of the meaningful content in the images, then you’ve done a good job at dimensionality reduction.

If you have the patience for it, you’ll convince yourself that the point labeled (2,2) in the i’, j’ coordinate system is labeled (6, 6) in the i, j system.

These basis vectors are called principal components, and the subset you select constitute a new space that is smaller in dimensionality than the original space but maintains as much of the complexity of the data as possible.

SVD is a computation that allows us to decompose that big matrix into a product of 3 smaller matrices (U=m x r, diagonal matrix Σ=r x r, and V=r x n where r is a small number).

If you drop the smallest 20% of singular values and the associated columns in matrices U and V, you save quite a bit of space and still get a decent representation of the underlying matrix.

First, we show that if we rank the singular values (the values of the matrix Σ) by magnitude, the first 50 singular values contain 85% of the magnitude of the whole matrix Σ.

We can use this fact to discard the next 250 values of sigma (i.e., set them to 0) and just keep a “rank 50” version of the image of the dog.

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