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Representing the 10th District of Pennsylvania
\begin{array}{@{}[email protected]{}} J(W^{(t+1)}) \leq J(W^{(t)}), \end{array}
(32)
\begin{array}{@{}[email protected]{}} J(W) = tr\left(A-XWH^{T}Y^{T}\right)^{T}D\left(A-XWH^{T}Y^{T}\right)\\ +\lambda_{1} tr\left(W^{T}PW\right) +\lambda_{2} tr\left(H^{T}QH\right) \end{array}
(33)

And, according to the statement of Lemma 6, under the W update rule in Algorithm 3, J ( W ) monotonically decreases. In order to prove the statement, we follow the approaches utilizing auxiliary functions [ 13 , ONeill Mens Phluff Daddy 2 Sandal Tan Suede QmbWRwVnzr
]. □

Definition 2

(, ) is an auxiliary function for the function () if (, )≥() for all and (,)=().

\begin{array}{@{}[email protected]{}} W^{(t+1)} = \underset{W}{\text{argmin}} \quad G\left(W,W^{(t)}\right) \end{array}
\begin{array}{@{}[email protected]{}} J\left(W^{(t+1)}\right) = G\left(W^{(t+1)},W^{(t+1)}\right) \leq G\left(W^{(t+1)},W^{(t)}\right)\\ \leq G\left(W^{(t)},W^{(t)}\right) = J\left(W^{(t)}\right) \end{array}

This proves that J ( W ( t ) ) is monotonically decreasing.

Lemma 9
\begin{array}{*{20}l} G(W,W^{\prime}) = tr\left(A^{T}DA\right) - 2tr\left(YHW^{T}X^{T}DA\right)\\ \quad +\lambda_{1} tr\left(W^{T}PW\right)+ \lambda_{2} tr\left(H^{T}QH\right) \\ \quad + \sum_{i=1}^{m}\sum_{j=1}^{r} \frac{\left(X^{T}DXW^{\prime}H^{T}Y^{T}YH\right)_{{ij}}W^{2}_{{ij}}}{{W^{\prime}}_{{ij}}} \end{array}
(34)
\begin{array}{*{20}l} J(W) = tr\left(A^{T}DA\right) - 2tr\left(YHW^{T}X^{T}DA\right)\\ \quad + \lambda_{1} tr\left(W^{T}PW\right)+ \lambda_{2} tr\left(H^{T}QH\right)\\ \quad + tr\left(W^{T}X^{T}DXWH^{T}Y^{T}YH\right) \end{array}
(35)
\begin{array}{@{}[email protected]{}} tr\left(W^{T}\Lambda WB\right) \leq \sum_{i}\sum_{j}\left(\Lambda W^{\prime} B\right)_{{ji}}\frac{W^{2}_{{ij}}}{W^{\prime}_{{ij}}}, \end{array}
(36)

where, Λ , B , W are non-negative matrices, and Λ , B are symmetric matrices. And obviously the equality holds in Eq. KENDALL KYLIE Womens Shoes Tyler Mesh Glitter Sneaker Spring Summer 2018 Silver G90M30Yt
when W = W .

In Eq. Badgley Mischka Womens Karter II Ballet Flat Rose Gold vXg97Aw
, if we do the substitutions: Λ = X T D X , B = H T Y T Y H , W = W , W = W , we see that the fifth term of Eq. InterestPrint Womens Casual Soft Sports Road Running Walking Shoes Merry Christmas Funny Cartoon Santa Claus Multi 1 bR2f2
is smaller than the fifth term of Eq. AllhqFashion Womens Pu Solid LaceUp Open Toe High Heels Sandals Black NnYNr
. However, the equality holds when W = W . Thus G ( W , W ) in Eq. 34 is an auxiliary function of J ( W ). □

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IndieFlix brings independent films to the masses

What would you do if I sang out of tune? Would you stand up and walk out on me?

Joe Cocker’s broken, downbeat version of the Beatles’ song resounded through American living rooms in the late ’80s, a signal to gather around the TV and watch The Wonder Years, an offbeat show that championed the outsider.

“I pretty much dressed Winnie Cooper as I had dressed as a kid,” Andreen recalled. “Of course, I always checked the dates in my research that consisted of yearbooks and Sears catalogs that were piled high on my desk.”

She was nominated for an Emmy, and the show gave her the financial freedom to start participating in the indie film circuit. Such is the backstory for IndieFlix, Andreen’s streaming service for independent films which challenges traditional distribution models by directly connecting artists with their audience and paying the filmmakers according to a unique revenue-per-minute model. It’s an artist-centered forum which can potentially change the game for indie filmmakers, allowing them to use their work to directly generate revenue for their next project.

Streaming technology finally keeps pace with Andreen’s vision
The IndieFlix crew at a festival

Andreen is a CEO and an artist, and she pushes the boundaries of both roles. Her current project is called Angst: Breaking the Stigma Around Anxiety. It tells stories of anxiety and how it impacts individuals as well as society at large. The project will be released as a multimedia experience: a movie, a documentary series, app and virtual reality experience designed to simulate a panic attack. She wants to use art to break through the isolation of anxiety disorder and tell the larger story.

Andreen’s love of independent films goes back to her days on The Wonder Years. “During my hiatus, I would produce or direct a movie and travel with that film through the film festival circuit,” Andreen said. ”It was during that time I learned about how many thousands upon thousands of incredible films are made every year and yet less than 1 percent find any kind of meaningful distribution.”

It was a critical insight. The prospect of distribution was a slim all-or-nothing experience. Filmmakers dreamed of getting noticed and having their projects picked up by the artistic branch of a big studio. Artists were at the mercy of the Hollywood studios and only potentially profitable projects really had a shot. There were breakout hits where indie movies crossed into the mainstream, but for the most part the big distribution model left an endless number of unwatched independent films in limbo. Why not help people see them?

Andreen’s idea was the true beginning of IndieFlix, although the state of technology at the time couldn’t support the concept.