Laura Anderlucci

Roberta Falcone, Angela Montanari, Laura Anderlucci

Matrix sketching is a recently developed data compression technique. An input matrix A is efficiently approximated with a smaller matrix B, so that B preserves most of the properties of A up to some guaranteed approximation ratio. In so doing numerical operations on big data sets become faster. Sketching algorithms generally use random projections to compress the original dataset and this stochastic generation process makes them amenable to statistical analysis. The statistical properties of sketching algorithms have been widely studied in the context of multiple linear regression. In this paper we propose matrix sketching as a tool for rebalancing class sizes in supervised classification with imbalanced classes. It is well-known in fact that class imbalance may lead to poor classification performances especially as far as the minority class is concerned.

Laura Anderlucci, Lucia Guastadisegni, Cinzia Viroli

This paper focuses on a comparative evaluation of the most common and modern methods for text classification, including the recent deep learning strategies and ensemble methods. The study is motivated by a challenging real data problem, characterized by high-dimensional and extremely sparse data, deriving from incoming calls to the customer care of an Italian phone company. We will show that deep learning outperforms many classical (shallow) strategies but the combination of shallow and deep learning methods in a unique ensemble classifier may improve the robustness and the accuracy of "single" classification methods.

Cinzia Viroli, Laura Anderlucci

Mixtures of Unigrams are one of the simplest and most efficient tools for clustering textual data, as they assume that documents related to the same topic have similar distributions of terms, naturally described by Multinomials. When the classification task is particularly challenging, such as when the document-term matrix is high-dimensional and extremely sparse, a more composite representation can provide better insight on the grouping structure. In this work, we developed a deep version of mixtures of Unigrams for the unsupervised classification of very short documents with a large number of terms, by allowing for models with further deeper latent layers; the proposal is derived in a Bayesian framework. The behaviour of the Deep Mixtures of Unigrams is empirically compared with that of other traditional and state-of-the-art methods, namely $k$-means with cosine distance, $k$-means with Euclidean distance on data transformed according to Semantic Analysis, Partition Around Medoids, Mixture of Gaussians on semantic-based transformed data, hierarchical clustering according to Ward's method with cosine dissimilarity, Latent Dirichlet Allocation, Mixtures of Unigrams estimated via the EM algorithm, Spectral Clustering and Affinity Propagation clustering. The performance is evaluated in terms of both correct classification rate and Adjusted Rand Index. Simulation studies and real data analysis prove that going deep in clustering such data highly improves the classification accuracy.