Non-negative matrix factorization

Non-negative matrix factorization (NMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.

NMF finds applications in such fields as computer vision, document clustering,chemometrics, audio signal processing and recommender systems.

History

In chemometrics non-negative matrix factorization has a long history under the name "self modeling curve resolution". In this framework the vectors in the right matrix are continuous curves rather than discrete vectors. Also early work on non-negative matrix factorizations was performed by a Finnish group of researchers in the middle of the 1990s under the name positive matrix factorization. It became more widely known as non-negative matrix factorization after Lee and Seung investigated the properties of the algorithm and published some simple and useful algorithms for two types of factorizations.

New Music Festival 01

The first edition of New Music Festival took part in Stockholm, Sweden. Globen Arena was the venue chosen to host the contest and the hosts were Carina Berg and Kristian Luuk, two people very famous and program hosts in Sweden. The contest started with a lot of energy, since 37 countries participated. Most part of the edition was held in July 2009. There weren't big problems during the contest, but the most notable was that Russia withdraw in final. Final Top Five was constituted by Spain, United Kingdom, Moldova, USA and Sweden, 1st to 5th places, respectively.

Semifinals

3 semifinals supported the first part of this edition. The first semi had 13 countries participating, and the last 2 semis, took 12 contestants, each one. As this was the first edition, anybody was yet in final, so, the semifinals took all the participants that were trying to be qualifiers. A lot of kinds of music were taken by the players. From "House" to "RnB", the songs were played and the contest was very great, according to the most part of the players. The reason that made the manager took 3 semifinals, instead of 2, was that he wanted to take this contest attractive and original.