Cristina Tortora

Increasing Crop Diversity Mitigates Weather Variations and Improves Yield Stability

Cropping sequence diversification provides a systems approach to reduce yield variations and improve resilience to multiple environmental stresses. Yield advantages of more diverse crop rotations and their synergistic effects with reduced tillage are well documented, but few studies have quantified the impact of these management practices on yields and their stability when soil moisture is limiting or in excess. Using yield and weather data obtained from a 31-year long term rotation and tillage trial in Ontario, we tested whether crop rotation diversity is associated with greater yield stability when abnormal weather conditions occur. We used parametric and non-parametric approaches to quantify the impact of rotation diversity (monocrop, 2-crops, 3-crops without or with one or two legume cover crops) and tillage (conventional or reduced tillage) on yield probabilities and the benefits of crop diversity under different soil moisture and temperature scenarios. Although the magnitude of rotation benefits varied with crops, weather patterns and tillage, yield stability significantly increased when corn and soybean were integrated into more diverse rotations. Introducing small grains into short corn-soybean rotation was enough to provide substantial benefits on long-term soybean yields and their stability while the effects on corn were mostly associated with the temporal niche provided by small grains for underseeded red clover or alfalfa. Crop diversification strategies increased the probability of harnessing favorable growing conditions while decreasing the risk of crop failure. In hot and dry years, diversification of corn-soybean rotations and reduced tillage increased yield by 7% and 22% for corn and soybean respectively. Given the additional advantages associated with cropping system diversification, such a strategy provides a more comprehensive approach to lowering yield variability and improving the resilience of cropping systems to multiple environmental stresses. This could help to sustain future yield levels in challenging production environments.

A mixture of generalized hyperbolic factor analyzers

The mixture of factor analyzers model, which has been used successfully for the model-based clustering of high-dimensional data, is extended to generalized hyperbolic mixtures. The development of a mixture of generalized hyperbolic factor analyzers is outlined, drawing upon the relationship with the generalized inverse Gaussian distribution. An alternating expectation-conditional maximization algorithm is used for parameter estimation, and the Bayesian information criterion is used to select the number of factors as well as the number of components. The performance of our generalized hyperbolic factor analyzers model is illustrated on real and simulated data, where it performs favourably compared to its Gaussian analogue and other approaches.

Unsupervised learning via mixtures of skewed distributions with hypercube contours

A multivariate generalization of the shifted asymmetric Laplace distribution is formulated.This distribution has convex upper level sets, making it excellent for cluster analysis.Finite mixtures of this generalization are developed for unsupervised learning.Parameter estimation is carried out via an EM algorithm.These mixtures give excellent results compared to the current state-of-the-art. Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace distributions. The component densities have a unique combination of features: they include a multivariate weight function and the marginal distributions are asymmetric Laplace. We use these mixtures of multiple scaled shifted asymmetric Laplace distributions for clustering applications, but they could be used in the supervised or semi-supervised paradigms. Parameter estimates are obtained via an expectation-maximization algorithm and the Bayesian information criterion is used for model selection. Simulated and real data sets are utilized to illustrate the approach and, in some cases, to visualize the skewed hypercube structure of the components.

Factor PD-Clustering

Probabilistic Distance (PD) Clustering is a non parametric probabilistic method to find homogeneous groups in multivariate datasets with J variables and n units. PD Clustering runs on an iterative algorithm and looks for a set of K group centers, maximising the empirical probabilities of belonging to a cluster of the n statistical units. As J becomes large the solution tends to become unstable. This paper extends the PD-Clustering to the context of Factorial clustering methods and shows that Tucker3 decomposition is a consistent transformation to project original data in a subspace defined according to the same PD-Clustering criterion. The method consists of a two step iterative procedure: a linear transformation of the initial data and PD-clustering on the transformed data. The integration of the PD Clustering and the Tucker3 factorial step makes the clustering more stable and lets us consider datasets with large J and let us use it in case of clusters not having elliptical form.

Factor PD-Co-clustering on Textual Data

In this paper we propose to extend factor probabilistic distance (FPD) clustering to FPDco-clustering for frequency data. FPD-clustering transforms the data using a factor decomposition and clusters the transformed data optimizing the same criterion. FPDco-clustering simultaneously finds clusters of rows and column basing on the PD-clustering criterion. The method is useful in case of large data sets. In this paper the new method is applied on large textual data sets with the aim of extracting interesting information.

Factor probabilistic distance clustering (FPDC): a new clustering method

Factor clustering methods have been developed in recent years thanks to improvements in computational power. These methods perform a linear transformation of data and a clustering of the transformed data, optimizing a common criterion. Probabilistic distance (PD)-clustering is an iterative, distribution free, probabilistic clustering method. Factor PD-clustering (FPDC) is based on PD-clustering and involves a linear transformation of the original variables into a reduced number of orthogonal ones using a common criterion with PD-clustering. This paper demonstrates that Tucker3 decomposition can be used to accomplish this transformation. Factor PD-clustering alternatingly exploits Tucker3 decomposition and PD-clustering on transformed data until convergence is achieved. This method can significantly improve the PD-clustering algorithm performance; large data sets can thus be partitioned into clusters with increasing stability and robustness of the results. Real and simulated data sets are used to compare FPDC with its main competitors, where it performs equally well when clusters are elliptically shaped but outperforms its competitors with non-Gaussian shaped clusters or noisy data.

Clustering in Feature Space for Interesting Pattern Identification of Categorical Data

Standard clustering methods fail when data are characterized by non-linear associations. A suitable solution consists in mapping data in a higher dimensional feature space where clusters are separable. The aim of the present contribution is to propose a new technique in this context to identify interesting patterns in large datasets.