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Principal component analysis

Principal component analysis is a statistical procedure that uses an orthogonal transformation to convert a set of observations of correlated variables into a set of values of linearly uncorrelated variables called principal components. This transformation is defined in such a way that the first principal component has the largest possible variance, each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components; the resulting vectors are an uncorrelated orthogonal basis set. PCA is sensitive to the relative scaling of the original variables. PCA was invented in 1901 as an analogue of the principal axis theorem in mechanics. Depending on the field of application, it is named the discrete Karhunen–Loève transform in signal processing, the Hotelling transform in multivariate quality control, proper orthogonal decomposition in mechanical engineering, singular value decomposition of X, eigenvalue decomposition of XTX in linear algebra, factor analysis, Eckart–Young theorem, or empirical orthogonal functions in meteorological science, empirical eigenfunction decomposition, empirical component analysis, quasiharmonic modes, spectral decomposition in noise and vibration, empirical modal analysis in structural dynamics.

PCA is used as a tool in exploratory data analysis and for making predictive models. It is used to visualize genetic distance and relatedness between populations. PCA can be done by eigenvalue decomposition of a data covariance matrix or singular value decomposition of a data matrix after a normalization step of the initial data; the normalization of each attribute consists of mean centering – subtracting each data value from its variable's measured mean so that its empirical mean is zero – and normalizing each variable's variance to make it equal to 1. The results of a PCA are discussed in terms of component scores, sometimes called factor scores, loadings. If component scores are standardized to unit variance, loadings must contain the data variance in them. If component scores are not standardized loadings must be unit-scaled, these weights are called eigenvectors. PCA is the simplest of the true eigenvector-based multivariate analyses, its operation can be thought of as revealing the internal structure of the data in a way that best explains the variance in the data.

If a multivariate dataset is visualised as a set of coordinates in a high-dimensional data space, PCA can supply the user with a lower-dimensional picture, a projection of this object when viewed from its most informative viewpoint. This is done by using only the first few principal components so that the dimensionality of the transformed data is reduced. PCA is related to factor analysis. Factor analysis incorporates more domain specific assumptions about the underlying structure and solves eigenvectors of a different matrix. PCA is related to canonical correlation analysis. CCA defines coordinate systems that optimally describe the cross-covariance between two datasets while PCA defines a new orthogonal coordinate system that optimally describes variance in a single dataset. Robust and L1-norm-based variants of standard PCA have been proposed. PCA can be thought of as fitting a p-dimensional ellipsoid to the data, where each axis of the ellipsoid represents a principal component. If some axis of the ellipsoid is small the variance along that axis is small, by omitting that axis and its corresponding principal component from our representation of the dataset, we lose only an small amount of information.

To find the axes of the ellipsoid, we must first subtract the mean of each variable from the dataset to center the data around the origin. We compute the covariance matrix of the data and calculate the eigenvalues and corresponding eigenvectors of this covariance matrix. We must normalize each of the orthogonal eigenvectors to become unit vectors. Once this is done, each of the mutually orthogonal, unit eigenvectors can be interpreted as an axis of the ellipsoid fitted to the data; this choice of basis will transform our covariance matrix into a diagonalised form with the diagonal elements representing the variance of each axis. The proportion of the variance that each eigenvector represents can be calculated by dividing the eigenvalue corresponding to that eigenvector by the sum of all eigenvalues; this procedure is sensitive to the scaling of the data, there is no consensus as to how to best scale the data to obtain optimal results. PCA is mathematically defined as an orthogonal linear transformation that transforms the data to a new coordinate system such that the greatest variance by some scalar projection of the data comes to lie on the first coordinate, the second greatest variance on the second coordinate

Narrow Stairs

Narrow Stairs is the sixth studio album by indie rock band Death Cab for Cutie, released on May 12, 2008 in the United Kingdom and on May 13, 2008, in the United States, on Atlantic and Barsuk Records. Four singles were released for the album: "I Will Possess Your Heart", "Cath...", "No Sunlight", "Grapevine Fires". "I Will Possess Your Heart" reached number six on the U. S. Alternative Songs chart, was named iTunes UK song of the year 2008, was nominated for the 2009 Grammy Award for Best Rock Song. "Cath..." and "Grapevine Fires" reached number ten and number twenty-one on the U. S. Alternative Songs chart, respectively. Narrow Stairs reached number one on the Billboard 200, making it Death Cab for Cutie's highest charting album to-date. In October 2007, producer and guitarist Chris Walla said that Death Cab for Cutie's new album "is in full swing, he went on to say, "thus far it's pretty spectacular. It's creepy and heavy... we've got a ten minute long Can jam, had you suggested that possibility to me in 1998, I'd have eaten your puppy's brain with a spoon."

In a Billboard piece, Walla described the album: "It's weird. It's really good, I think, but it's a curve ball, I think it's gonna be a polarizing record, but I'm excited about it. It's got some teeth; the landscape of the thing is way, way more lunar than the urban meadow sort of thing, happening for the last couple of records." Walla went on to say," louder and more dissonant and I think abrasive. Heavy, slow metal synth-punk band Brainiac." Ben Gibbard, lead singer and writer, commented, "I just don't feel like we have anything to prove of it other than to ourselves and to making a record we enjoy."In 2011 Walla stated, "the master plan for Narrow Stairs was to be as invisible and hands-off as a producer as I could. I was interested in seeing what would happen; when we started that record, we had been on tour for the better part of two years. All we could remember was being on playing. So the whole idea was: what happens if we’re just on stage and we play, except we’re in the studio and we’re recording?"

Walla added "Narrow Stairs was much a commitment to just crashing through the songs as we recorded them, like four people in a room." While promoting the band's subsequent album and Keys, Benjamin Gibbard reflected upon Narrow Stairs' lyrical content, stating, "That record is kind of a fulcrum in my life. So much of the negativity in my life got funneled into it. I realized. I wanted it to be my own emotional spectrum in terms of writing. I had no grandiose plans to turn my life around." Several of the songs have literary or cultural themes, for example "Grapevine Fires" appears to be centered on the wildfires that raged in California during the summer and fall of 2007. "Bixby Canyon Bridge" features many references to writer Jack Kerouac, whom Ben Gibbard notes as a favorite author in interviews, the song was written during a trip to Big Sur, the location of Bixby Creek Bridge. Gibbard has written lyrics referencing Kerouac before, including the songs "Lowell, MA" and "Title Track" from Death Cab for Cutie's 2000 album, We Have the Facts and We're Voting Yes, his contribution of lyrics and vocals to a song by Styrofoam titled "Couches in Alleys".

"Pity and Fear" features an abrupt ending where the song finishes without warning during an instrumental. In an interview, the band stated that the tape machine they were using broke toward the end, however the band liked so much that they included it in the final version of the song; the final track on the album, "The Ice Is Getting Thinner", is used in the first-season finale of the television series Gossip Girl, as well as in the fourth season of reality series The Hills. The song "No Sunlight" is included in the soundtrack for Choke. "Pity and Fear" was included in the ending of an episode of CSI: Crime Scene Investigation. The first track, "Bixby Canyon Bridge", was used at the end of the Friday Night Lights episode, "How the Other Side Lives"; the cover art was created by the art director for Tegan and Sara. The album holds a score of 73 out of 100 from Metacritic based on "generally favorable reviews". MTV's James Montgomery referred to Narrow Stairs as "unquestionably the best thing done".

Rolling Stone called the album "a dark, strangely compelling record that trades the group's bright melancholy for something nearer to despair." In his Consumer Guide, Robert Christgau gave it a two-star honorable mention, while picking out two songs from the album and stating that the album has "Unfailingly melodic dynamic, somewhat overextended love problems, if so smart why doesn't he shelve music and solve them?"The album has been rated by critics and fans, having been awarded 4 stars out of 5 by publications such as Rolling Stone, Blender Kerrang!, Alternative Press, The Times, The Observer, The Independent and The Guardian, as well as by the websites AllMusic and Consequence of Sound, Tiny Mix Tapes. TIME magazine awarded the album a "B+" rating, with The A. V. Club giving it an "A" rating. Boston radio station WERS ranked Narrow Stairs as the No.8 album of 2008 based on a listener poll. More favorable reviews come from such publishers as Under the Radar, The Boston Globe, Hartford Courant and Filter.

Other reviews that are given three stars out of five are Mojo, Q, Prefix Magazine, as well as the

Johnny Maestro & the Brooklyn Bridge

Johnny Maestro & the Brooklyn Bridge is an American musical group, best known for their million-selling rendition of Jimmy Webb's "Worst That Could Happen". New York City-born Johnny Maestro began his career in 1957 as the original lead singer of The Crests, one of the first interracial groups of the recording industry. Patricia Van Dross, older sister to famed R&B singer Luther Vandross, sang with Johnny Maestro while The Crests were signed to the Joyce Record label. Before The Crests signed with Coed Records, Patricia left the group because her mother didn't want her 15-year-old daughter touring with the older guys. After a regional hit with "My Juanita"/"Sweetest One" on the Joyce label, he had three years of chart success with The Crests on Coed Records with "16 Candles", "Six Nights A Week", "Step by Step", "The Angels Listened In", "Trouble in Paradise". Between "Step by Step" and "Trouble in Paradise", Coed released a single "The Great Physician"/"Say It Isn't So" under the name Johnny Masters.

Late in 1960, Maestro would leave The Crests for a solo career. Maestro was unable to reach his former chart heights with The Crests, but did have Top 40 hits with "What A Surprise" and "Model Girl" in 1961 as solo artist Johnny Mastro, "The Voice of the Crests" for Coed Records. For his next three singles with the label, he was known as Johnny Maestro, the third spelling change for the label. None of those records charted and Maestro recorded for three different labels before recording with new backup singers as Johnny Maestro & The Crests in 1965 and 1966, which produced four singles on two more labels. By 1967, another New York vocal group called The Del-Satins—who had become well known in the New York area as weekly performers on the local dance party program The Clay Cole Show, had made several non-charting recordings between 1959 and 1967 under their own name, were noted for backing up Dion on his post-Belmonts recordings—were looking for a new lead singer to replace original lead Stan Zizka.

Other members were Les Cauchi and Bobby Faila. According to Cauchi, members of the group ran into Maestro at a local gym, playing his guitar, approached him with the offer to join the group. After turning them down, Maestro's manager, Betty Sperber, called Cauchi and told him Maestro had changed his mind. In 1968, Sperber and founder of the talent management and booking agency Action Talents in New York City, was hosting her once a month Battle of the Bands talent search at the Cloud Nine nightclub in Long Island and brought Maestro along as the evening's special guest star. Action Talents' Vice President and General Manager Alan White suggested that Maestro be backed up that night by a seven-piece brass-filled group of youngsters called The Rhythm Method; that night's performance was such a success that the next day Sperber decided to combine the talents of Maestro, the four Del-Satins, The Rhythm Method. The new group's name came about after White made the off-handed comment that "it would be easier to sell the Brooklyn Bridge" than book the proposed 11-piece act.

Johnny and the Bridge rehearsed their unusual combination of smooth vocal harmonies and full horns, signed a recording contract with Buddah records. Their first release, a version of the Jimmy Webb song "Worst That Could Happen", reached No. 3 on the Billboard pop chart. It sold over one and a quarter million copies, was awarded a gold disc by the R. I. A. A.. The follow-up, "Welcome Me Love", its flip side, "Blessed is the Rain" — both by Tony Romeo — each reached the Top 50. A dramatic version of "You'll Never Walk Alone" and the controversial "Your Husband, My Wife" reached the middle ranges of the charts; the group sold over 10 million records by 1972, including LP sales produced by Wes Farrell. Appearances on The Ed Sullivan Show, The Della Reese Show, other programs helped to bring the group to the national stage. After its heyday, the Brooklyn Bridge downsized to a five-man group, with the vocalists playing their own instruments. For example, Maestro could be seen on stage playing rhythm guitar, while former Rhythm Method bassist Jim Rosica picked up a vocal part.

In the 1970s, as the Rock and Roll Revival evolved from a nostalgic fad to a respected genre, the group began to add members, retaining its core vocalists. By 1985, the group had solidified into an eight piece group, including original Del Satins, Fred Ferrara, original Bridge member Rosica, augmented by a horn section for special occasions; the drummer for the current line up, Lou Agiesta, was the drummer for the Original American Touring Company of Jesus Christ Superstar. Today he is sub drummer for Little Anthony and The Imperials; the version of the Brooklyn Bridge released a Christmas EP in 1989 and a greatest hits compilation in 1993, re-recording Maestro's hits with The Crests. In the early 1990s, Maestro moonlighted as the background tenor on Joel Katz's studio project CD Joel & the Dymensions. In 1994, The Brooklyn Bridge recorded the 10-song CD Acappella. On December 5, 1999, the Brooklyn Bridge was featured in one of PBS's biggest fundraising events "Doo Wop 50", performing both "16 Candles" and "The Worst That Could Happen".

In 2005, the Brooklyn Bridge released a full concert-length DVD as part of the Pops Legends Live serie

Don Quickshot of the Rio Grande

Don Quickshot of the Rio Grande is a 1923 American silent western film directed by George E. Marshall and written by George Hively; the film stars Jack Hoxie, Emmett King, Elinor Field, Fred C. Jones, William Steele, Bob McKenzie, it is based on a 1921 short story of the same name by Stephen Chalmer. The film was released on June 1923, by Universal Pictures. Jack Hoxie as'Pep' Pepper Emmett King as Jim Hellier Elinor Field as Tulip Hellier Fred C. Jones as George Vivian William Steele as Bill Barton Bob McKenzie as Sheriff Littlejohn Harry Woods as a Knight Hank Bell and Ben Corbett as Henchman Skeeter Bill Robbins as Barfly A copy of Don Quickshot of the Rio Grande is housed at the UCLA Film and Television Archive. Don Quickshot of the Rio Grande at the American Film Institute Catalog Don Quickshot of the Rio Grande on IMDb Synopsis at AllMovie

John Whitley

John Whitley was a Louisiana corrections officer who served as the warden of Louisiana State Penitentiary, the largest maximum-security in the United States, from 1990 to 1995. Time magazine credited Warden Whitley with turning around hopelessness and violence at Angola with "little more than his sense of decency and fairness." John Whitley attended Southeastern Louisiana University in Hammond and graduated in 1968. He enlisted in the United States Army that year, served during the Vietnam War before his discharge in 1970. Shortly after, he began his career in corrections. Whitley started his career as a corrections officer at Angola in 1970, he rose through the ranks during the prison's most violent years. He was promoted to warden of another Louisiana prison, Hunt Correctional Center, left the state to run a private prison in Texas. In 1990 Louisiana recruited him to return to Angola to restore order. At a time of frequent stabbings and escapes, a United States Federal Judge declared a state of emergency at the prison in response to an ACLU suit against the state for the horrendous conditions.

Within two years, Whitley had stemmed the violence. He established incentives for good behavior, such as extra visits, increased educational opportunities with literacy tutoring, computer and paralegal courses, he enabled some trustworthy and deserving inmates to travel outside the prison as part of athletic teams and inmate bands that provided entertainment for churches, nursing homes, other charitable organizations. Whitley launched an outreach program to all criminal justice programs in the State of Louisiana, he offered to send both prison officials and inmates to college classrooms to help both students and faculty better understand the realities of prison management and prison life. Like several Louisiana wardens before him, Whitley was committed to an open door policy with the media, he told editors of the inmate-produced newsmagazine, The Angolite, that he would continue the decades-long policy of lack of censorship. This had enabled the inmates to produce reporting on difficult issues and to win major national journalism awards for investigating problems at the prison.

He said that he would continue to welcome outside media and cooperate with them: "We're not going to have anything to hide in Angola," he said. "And, if there's something that's wrong in the prison, I want to know about it, my staff better correct it—because I intend to be proud of this prison and the way we operate it." Under Whitley, The Angolite began to produce material for uncensored radio and television journalism. Whitley believed these efforts were related to the prison's other outreach programs designed to educate the public about prison life and issues; as he explained to National Public Radio's Fresh Air host, Terry Gross, about his philosophy that lay behind the lack of censorship: "We want … different views of prison. Some of the views, I don't like, it upsets me sometimes. We're looking for the truth." In July 1991, inmate welders were ordered by a corrections department employee to build a "hospital examining table". They soon learned; this took place hours. One of the welders had a brother, executed at the prison.

Learning of these plans, hundreds of fellow inmates staged a work strike. When Whitley learned what was happening, he locked up the strikers, he brought in SWAT teams to prepare for the strike. But he told the media that deceiving the inmate workers was wrong and the work order should never have been issued, he understood that it put the inmates in a bad position, he was not going to subject them to building the lethal injection gurney. With that statement, he ended the strike without violence and gained the respect of both the inmate population and his security force; the conservative Baton Rouge Morning Advocate commended him in two editorials for admitting the prison had erred and correcting the mistake. "It's refreshing to see a high-ranking government official admit mistakes and attempt to rectify them. It's a sign of integrity and responsibility." Time magazine invited Whitley to New York City to share his management philosophy with its corporate officers and editors, profiled him in a three-page feature.

He is the only American prison warden to be so profiled. The Russian language magazine, followed suit with a six-page profile of Whitley. Angola first earned accreditation from the American Correctional Association during Whitley's tenure; this was a concrete measure of the success of reforms he had enacted to increase the safety under which both inmates and employees live and work on the prison farm. Having accomplished his goal of turning Angola into the safest maximum security in America, Whitley retired as warden in 1995. In what "may have been a first in the history of U. S. prisons," more than 100 inmate leaders pooled their money to throw Whitley a farewell party. It was attended by prison employees and officials, covered by news media throughout Louisiana. After leaving Angola, Whitley ran a private prison in Florida, he was called back to Louisiana to serve as the Court Expert for the U. S. Middle District Court of Louisiana, it continued to oversee the state's prisons compliance with a 1975 federal court order about conditions.

He served in that position until 2003. Whitley received numerous honors during his tenure as Warden. Several of those were: Profile in "Time" Magazine, December 1992.

Pop Smith

Charles Marv "Pop" Smith was a Canadian Major League Baseball player from Digby, Nova Scotia, Canada. Pop played as an infielder for ten different teams over his 12-year career, spanning from 1880 to 1891. On April 17, 1890, Smith became the first player to come up to the plate 6 times and not have an official-at-bat, he received 5 was a hit by the pitcher in the remaining at-bat. Smith died in Boston, Massachusetts at the age of 70, was buried in Evergreen Cemetery in Brighton, Massachusetts. In 2005, Charles "Pop" Smith was inducted into the Canadian Baseball Hall of Fame. List of Major League Baseball annual triples leaders List of Major League Baseball career stolen bases leaders Career statistics and player information from Baseball-Reference, or Baseball-Reference SABR Biographical Project