Music intelligence universe server2010-03-04/>[0096] It is based on a transformation from two input variables [0, 1]脳[0, 1] to three variables. The output 3D vector is normalized using a cylindrical transformation. From a geographical point of view, the kernel maps a 2D quadrant into the surface of a quadrant of a sphere. This is depicted in FIG. 16.
[0097] The first step of the kernelization adds a margin to the data in order to avoid null border values in order to maintain nulls out of the transformation chain. gx=0.005 0.99sx gy=0.005 0.99sy
[0098] In classic EVE, only the angle between the two variables was significant. In the current algorithm, the non-linearity comes from also using the module of the vector. This makes it possible to learn in which part of the Music Universe the user taste resides. r= {square root over (gx2 gy2)},r>1鈫抮=1 胃=atan2(gy,gx)
[0099] The 2D to 3D transformation is performed mapping input variables into spherical coordinates: k r = 1 k 胃 = 蟺 2 脳 r k 桅 = 胃
[0100] The operational space for classic EVE is Cartesian and kernelized variables are finally obtained by the Spherical-to-Cartesian transformation: kx=k.sub.r cos k蠁 sin k胃k.sub.y=k.sub.r sin k蠁 sin k胃k.sub.z=k.sub.r cos k胃
[0101] In summary, the Kernelized Eva is a classic EVE that operates within a universe that has one more dimension. This makes possible to learn non-linear music tastes in a controlled manner as the convergence of classic EVE is assured because it is a linear algorithm. The estimated vector has, therefore, three dimensions. Accordingly, the recommendation of songs also must be performed in the kernelized universe. 3D classic EVE is a bit more complicated because there is one more dimension and the region update strategy is not so straightforward. Furthermore, in the selection of pairs of songs an extra degree of freedom has to be taken into consideration.
[0102] Imagine that the database consisted of less than a thousand songs. Then the total number of pair of songs is given by the following expression: N(N-1)/2
[0103] With less than 1000 songs, it is possible to compute all the possible pairs (0.5 Mpairs) and select and store those more adequate for learning. The MIU Server, however, supports music databases of several millions of songs. FIG. 17 shows the number of pairs to evaluate as a function of the total number of songs.
[0104] Looking to the rapidly growing function, it is clear that it is not possible to sweep all pairs to determine the preferable pair of songs for learning. This is the key of the music learning process, defining what a good question means. Intuitively, two songs very similar (with a small Euclidean distance in the Music Universe) cannot form a learning pair because it should be difficult for the user to select the preferred one. This is one of the three criteria: Euclidean distance has to be maximized in song pair selection for the learning process. The second criterion is quite obvious but it has a significant impact in the design. Sometimes, a song has some properties (resides near the border of the music universe for example) that makes it very useful for music taste learning. However, it is very poor for a music interface point of view to repeat songs in consecutive questions so the algorithm needs to have memory. Finally, the last and most important idea: the pair that maximizes music taste learning convergence, besides the song distance, depends on the current state of the algorithm; in other words, it depends on the answers given by the user to previous questions. To summarize these facts, the conditions for song pair selection are: [0105] Maximum Euclidean distance between the songs to help the user selecting the preferred one. [0106] Non-repeatability of songs during learning and from previous learning (algorithm song black list and diversity generation) [0107] Maximum orthogonality to the current Music Universe region to help the learning algorithm converge.
[0108] With only a few thousands of songs, all the possible pairs can be evaluated to see if they accomplish all the previous criteria to be included in the learning song pair database. Nevertheless, with millions of songs, this is very inefficient. Let us re
member that songs are kernelized from the bidimensional PCA universe to an extended universe with three variables. Songs are therefore projected into the first quadrant of a sphere. Every point has norm equal to one and therefore it can be referenced with two spherical coordinate angles (latitude and longitude for a geographical system).
[0109] In a preferred embodiment, the approach followed in order to sweep all the possible pairs of songs is to divide and conquer. The sphere surface is divided with the use of meridians and parallels as seen in FIG. 18.
[0110] Instead of looking for the longest distances between the songs, the examination is done only between the crossing of the parallels and meridians and songs are grouped in these crossings. The surface is therefore divided in a grid and every song belongs to one cell of the grid. Only the longest cell distances are computed and the total number of possible pairs is reduced dramatically without losing any high distance pair.
[0111] To increase performance dramatically and control algorithm behavior during runtime all the possible states of the learning progress are calculated in the encoding of the database. For example, for 10 questions (by default), t...
