196,091 research outputs found
Detecting Public Social Spending Patterns in Italy Using a Three-Way Relative Variation Approach
No full textStudies on public social spending often fail to address the issues connected with budgetary constraints. Budget lines require public entities to partition resources among sectors of spending on the basis of preferred combinations and trade-offs. Standard exploratory tools do not allow to unveil this preference structure as they are hindered by the differences in budget scales and by the bounded nature of sector variability, i.e. an increase in one sector means a missed increase or a decrease in other sectors. In this work Italian public social spending is modeled with an alternative log-ratio methodology which allows to study relative variation patterns among sectors. It is also important to note that since the data is collected across time a three-way approach is recommended so that the variability of each mode is kept separate
A procedure for the three-mode analysis of compositions
No full textThe Tucker3 model is one of the most widely used tools for factorial analysis of three-way data arrays. When orthogonal factors are extracted this model can be seen as a three-way PCA (principal component analysis). The Tucker3 model is characterized by extreme flexibility as it allows for the use of a different number of factors in each mode and it yields non-unique results. This adaptability makes the Tucker3 model extremely effective for decomposition and compression of data in many applications and fields. When this model is applied to vectors of non-negative values with a sum constraint all problems connected with the statistical analysis of compositions must be taken into consideration. Like other standard statistical techniques, this model cannot be directly applied. The aim of this paper is to present the theory behind the correct application of the Tucker3 model on compositional data and to describe the TUCKALS3 algorithm
Statistical tools for student evaluation of academic educational quality
No full textMeasuring academic educational quality presents three major difficulties, typical
of all customer satisfaction and service quality studies: the use of subjective scales; the
ordinal nature of the data; and the multifold structure of satisfaction. In order to solve these
problems, principal component analysis (PCA) of compositional data is proposed in this
work. The core idea behind this methodology is to analyze by PCA the relative information
within the data rather than focusing on absolute scores. This approach is discussed in
comparison with a widely used Item Response Theory method (the Partial Credit Model) in
order to assess its merits, e.g. always identifying a coherent preference structure. Both
procedures were, thus, carried out on a real dataset collected with the 2013/14 ANVUR
questionnaire by L’Universita´ di Napoli-L’Orientale
An ATLD–ALS method for the trilinear decomposition of large third-order tensors
No full textCP decomposition of large third-order tensors can be computationally challenging. Parameters are typically estimated by means of the ALS procedure because it yields least-squares solutions and provides consistent outcomes. Nevertheless, ALS presents two major flaws which are particularly problematic for large-scale problems: slow convergence and sensitiveness to degeneracy conditions such as over-factoring, collinearity, bad initialization and local minima. More efficient algorithms have been proposed in the literature. They are, however, much less dependable than ALS in delivering stable results because the increased speed often comes at the expense of accuracy. In particular, the ATLD procedure is one of the fastest alternatives, but it is hardly employed because of the unreliable nature of its convergence. As a solution, multi-optimization is proposed. ATLD and ALS steps are concatenated in an integrated procedure with the purpose of increasing efficiency without a significant loss in precision. This methodology has been implemented and tested under realistic conditions on simulated data sets
Improving PARAFAC-ALS performance by initialization
No full textThe CANDECOMP/PARAFAC (CP) model (Carroll and Chang, 1970; Harshman, 1970)
is a trilinear decomposition which provides a low rank approximation of a three-way array in
a manner that preserves the multi-mode structure of the data. This is achieved by estimating
three sets of parameters, one for each dimension of the array, namely observation units, variables
and occasions. The CP model, however, due to an elevated number of degrees of freedom, can
be quite challenging to estimate. The most commonly used algorithm to t this model to the
data is PARAFAC-ALS. Comparative studies (Tomasi and Bro, 2006) have shown that this
procedure is, in general, more reliable and accurate than other algorithms proposed in the
literature. Nonetheless, it presents some non-trivial issues: it can be slow at converging and
may run into over-factoring and bad initialization degeneracies.
With respect to these setbacks, some of the alternative estimating procedures are able to perform
better than ALS, specically the Alternating Trilinear Decomposition (ATLD) and Self-weighted
Alternating Trilin-ear Decomposition (SWATLD) proposed by Wu et al. (1998) and Chen et al.
(2000) respectively. These algorithms are faster and less likely to be aected by over-factoring
and bad initial values. They present, however, diculties connected to their non-least squares
objective functions and for this reason they are seldom used in practice. In this work it is
suggested that a successful way to improve on ALS performance with respect to the presented
drawbacks is to initialize it with either ATLD or SWATLD steps, obtaining two integrated ALS
procedures. The eectiveness of this methodology is demonstrated by comparing the results of
standard ALS with the ones of the proposed integrated ALS variants in an extensive simulation
design
Improving PARAFAC-ALS estimates with a double optimization procedure
No full textAn adaptation of the PARAFAC-ALS algorithm is implemented with the purpose of providing accurate and efficient estimates of CANDECOMP/PARAFAC parameters without being influenced by data characteristics and model specifications. This is a dual-optimization procedure in which values are first estimated by SWATLD and then refined through standard ALS steps. The use of an additional optimization phase is suggested with the purpose of canceling out specific ALS inefficiencies such as slow convergence and occurrence of over-factoring degeneracies. A complex simulation study is then implemented in order to identify the most adequate transition point between the stages of the proposed methodology and to show its advantages with respect to standard ALS
CP model estimation with incorrect rank of factorization on large data sets
No full textThe accuracy of the ALS procedure for fitting the CP decomposition is
affected by incorrect model selection due to the properties of its objective function.
A study on ALS performance is presented in order to show that for large data sets
this occasional shortcoming becomes prevalent. This deficiency should warn off
researchers from employing ALS unless the rank of the underlying trilinear structure
can be established in advance. Multi-optimization provides a possible solution: ALS
can be initialized with procedures insensitive to over-factoring such as SWATLD
and ATLD. In this manner it is possible to overcome factorization issues and provide
a gain in efficiency without relying on computationally expensive model selection
procedures
How to improve the Quality Assurance System of the Universities: a study based on compositional analysis
No full texthe National Agency for the Evaluation of Universities and Research (ANVUR) has for some decades defined the criteria for systematically evaluating student satisfaction. The analysis of these data presents various difficulties both in terms of data collection and analysis. The aim of this work is to propose Cande- comp/Parafac for a compositional analysis, which is able to capture the multidi- mensional aspects of the phenomenon taking into account its ordinal nature and the temporal characteristics of data collection
A PARAFAC-ALS variant for fitting large datasets
No full textThe PARAFAC-ALS algorithm is the most widely used procedure for
approximating arrays with a trilinear structure because it provides least squares
solutions and delivers consistent outputs. Nonetheless, it is particularly slow at
converging especially under challenging conditions, i.e. data multicollinearity, high
factors’ congruence and over-factoring. This shortcoming can be quite problematic
when dealing with three-way arrays of large dimensions.
More efficient procedures can be employed, such as ATLD, however they are far less
reliable. As an alternative, ATLD and ALS can be combined in a multi-optimization
procedure in order to increase efficiency without reducing accuracy. This novel
approach has been carried out and tested on artificial and real data
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