CLC-Conference-Proceeding-2018

Figura 5: On the left the matrix associated with
the image and on the right the image with
missing pixels and the corresponding absent data
matrix (taken from xlix ).
To compute the NMF Garza de la Luna explain
in l how a modification of the ALS method can be
used to deal with the missing data. In section 1.2,
the vector formulation of ALS is presented as a
Least Squared Problem with inequality
restrictions (LSI). The idea is to eliminate from
the sum the elements that depend on values of
the data that are not known. For them, values pij
(weights) are introduced such that
The weighted version of the cost function is
obtained
subject to x ≥ 0, the algorithm with the modified
cost function is known as weighted ALS.
Once the matrices A and X are calculated, even if
the matrix Y has missing data, the coefficients of
A and X are all known and if the product is
computed an approximation of the data matrix Y
is obtained.
1.2 Study of the Cuban public Spanish
NMF have been widely used in Text Mining. In
this example will be presented the main ideas of
another application of the NMF.
.
At the University of Havana, the
Faculties of Mathematics and Computer Science
and the Faculty of Arts and Letters work together
in a project for the study of the Public Spanish of
Cuba. To do this, a corpus with representative
texts is created and studied. The corpus has been
called CORESPUC and has 4 large groups of
texts. The detection of main topics is one of the
studies that are in develop right now. This
application is the one most frequently reported in
the literature.
Although the NMF became well known
with the works of Lee and Seung li , especially by
its application to the Database of face images,
the applications in Text Mining lii . In the same
work, Lee and Seung reported an application to
the semantic analysis of documents with the
same multiplicative rules presented as an
algorithm for the images and applied it to a
Database of 30,991 articles of the Grolier
Encyclopedia. In this application, the count of
occurrences of each of the words (15,276) that
appeared in the vocabulary to form the matrix
Y30,991x15,276 was performed.
The experiment in development has as its
first objective to obtain semantically related
documents. For this, several sets of texts formed
by letters to the Juventud Rebelde newspaper
among others.
As a second objective, the Biber
Methodology liii is applied to study the registry
variation in this set of texts. A register is
characterized by a set of linguistic features. Once
the linguists define the features to be taken into
account, the aforementioned methodology is
applied. In the literature, a factorial analysis of
the covariance matrix is applied. In this research
an NMF of this matrix is looked for and its
effectiveness on the proposal of the literature is
studied. ■