Graphical Model approaches for Biclustering

In many scientific areas, it is crucial to group (cluster) a set of objects, based on a set of observed features. Such operation is widely known as Clustering and it has been exploited in the most different scenarios ranging from Economics to Biology passing through Psychology. Making a step forward, there exist contexts where it is crucial to group objects and simultaneously identify the features that allow to recognize such objects from the others. In gene expression analysis, for instance, the identification of subsets of genes showing a coherent pattern of expression in subsets of objects/samples can provide crucial information about active biological processes. Such information, which cannot be retrieved by classical clustering approaches, can be extracted with the so called Biclustering, a class of approaches which aim at simultaneously clustering both rows and columns of a given data matrix (where each row corresponds to a different object/sample and each column to a different feature). The problem of biclustering, also known as co-clustering, has been recently exploited in a wide range of scenarios such as Bioinformatics, market segmentation, data mining, text analysis and recommender systems. Many approaches have been proposed to address the biclustering problem, each one characterized by different properties such as interpretability, effectiveness or computational complexity. A recent trend involves the exploitation of sophisticated computational models (Graphical Models) to face the intrinsic complexity of biclustering, and to retrieve very accurate solutions. Graphical Models represent the decomposition of a global objective function to analyse in a set of smaller/local functions defined over a subset of variables. The advantages in using Graphical Models relies in the fact that the graphical representation can highlight useful hidden properties of the considered objective function, plus, the analysis of smaller local problems can be dealt with less computational effort. Due to the difficulties in obtaining a representative and solvable model, and since biclustering is a complex and challenging problem, there exist few promising approaches in literature based on Graphical models facing biclustering. 3 This thesis is inserted in the above mentioned scenario and it investigates the exploitation of Graphical Models to face the biclustering problem. We explored different type of Graphical Models, in particular: Factor Graphs and Bayesian Networks. We present three novel algorithms (with extensions) and evaluate such techniques using available benchmark datasets. All the models have been compared with the state-of-the-art competitors and the results show that Factor Graph approaches lead to solid and efficient solutions for dataset of contained dimensions, whereas Bayesian Networks can manage huge datasets, with the overcome that setting the parameters can be not trivial. As another contribution of the thesis, we widen the range of biclustering applications by studying the suitability of these approaches in some Computer Vision problems where biclustering has been never adopted before. Summarizing, with this thesis we provide evidence that Graphical Model techniques can have a significant impact in the biclustering scenario. Moreover, we demonstrate that biclustering techniques are ductile and can produce effective solutions in the most different fields of applications

On the use of learning-based forecasting methods for ameliorating fashion business processes: A position paper

The fashion industry is one of the most active and competitive markets in the world, manufacturing millions of products and reaching large audiences every year. A plethora of business processes are involved in this large-scale industry, but due to the generally short life-cycle of clothing items, supply-chain management and retailing strategies are crucial for good market performance. Correctly understanding the wants and needs of clients, managing logistic issues and marketing the correct products are high-level problems with a lot of uncertainty associated to them given the number of influencing factors, but most importantly due to the unpredictability often associated with the future. It is therefore straightforward that forecasting methods, which generate predictions of the future, are indispensable in order to ameliorate all the various business processes that deal with the true purpose and meaning of fashion: having a lot of people wear a particular product or style, rendering these items, people and consequently brands fashionable. In this paper, we provide an overview of three concrete forecasting tasks that any fashion company can apply in order to improve their industrial and market impact. We underline advances and issues in all three tasks and argue about their importance and the impact they can have at an industrial level. Finally, we highlight issues and directions of future work, reflecting on how learning-based forecasting methods can further aid the fashion industry.Comment: 2nd International Workshop on Industrial Machine Learning @ ICPR 202

The Multi-Modal Universe of Fast-Fashion: The Visuelle 2.0 Benchmark

We present Visuelle 2.0, the first dataset useful for facing diverse prediction problems that a fast-fashion company has to manage routinely. Furthermore, we demonstrate how the use of computer vision is substantial in this scenario. Visuelle 2.0 contains data for 6 seasons / 5355 clothing products of Nuna Lie, a famous Italian company with hundreds of shops located in different areas within the country. In particular, we focus on a specific prediction problem, namely short-observation new product sale forecasting (SO-fore). SO-fore assumes that the season has started and a set of new products is on the shelves of the different stores. The goal is to forecast the sales for a particular horizon, given a short, available past (few weeks), since no earlier statistics are available. To be successful, SO-fore approaches should capture this short past and exploit other modalities or exogenous data. To these aims, Visuelle 2.0 is equipped with disaggregated data at the item-shop level and multi-modal information for each clothing item, allowing computer vision approaches to come into play. The main message that we deliver is that the use of image data with deep networks boosts performances obtained when using only the time series in long-term forecasting scenarios, ameliorating the WAPE by 8.2% and the MAE by 7.7%

Disentangled Latent Spaces Facilitate Data-Driven Auxiliary Learning

In deep learning, auxiliary objectives are often used to facilitate learning in situations where data is scarce, or the principal task is extremely complex. This idea is primarily inspired by the improved generalization capability induced by solving multiple tasks simultaneously, which leads to a more robust shared representation. Nevertheless, finding optimal auxiliary tasks that give rise to the desired improvement is a crucial problem that often requires hand-crafted solutions or expensive meta-learning approaches. In this paper, we propose a novel framework, dubbed Detaux, whereby a weakly supervised disentanglement procedure is used to discover new unrelated classification tasks and the associated labels that can be exploited with the principal task in any Multi-Task Learning (MTL) model. The disentanglement procedure works at a representation level, isolating a subspace related to the principal task, plus an arbitrary number of orthogonal subspaces. In the most disentangled subspaces, through a clustering procedure, we generate the additional classification tasks, and the associated labels become their representatives. Subsequently, the original data, the labels associated with the principal task, and the newly discovered ones can be fed into any MTL framework. Extensive validation on both synthetic and real data, along with various ablation studies, demonstrate promising results, revealing the potential in what has been, so far, an unexplored connection between learning disentangled representations and MTL. The code will be made publicly available upon acceptance.Comment: Under review in Pattern Recognition Letter

Biclustering gene expressions using factor graphs and the max-sum algorithm

Biclustering is an intrinsically challenging andhighly complex problem, particularly studied in thebiology field, where the goal is to simultaneouslycluster genes and samples of an expression data matrix.In this paper we present a novel approach togene expression biclustering by providing a binaryFactor Graph formulation to such problem. In moredetail, we reformulate biclustering as a sequentialsearch for single biclusters and use an efficient optimizationprocedure based on the Max Sum algorithm.Such approach, drastically alleviates thescaling issues of previous approaches for biclusteringbased on Factor Graphs obtaining significantlymore accurate results on synthetic datasets. A furtheranalysis on two real-world datasets confirmsthe potentials of the proposed methodology whencompared to alternative state of the art methods

Biclustering of time series data using factor graphs

Biclustering regards the simultaneous clustering of both rows and columns of a given data matrix. A specific applica- tion scenario for biclustering techniques concerns the anal- ysis of gene expression time-series data, wherein columns dataset are temporally related. In this context, bicluster- ing solutions should involve subset of genes sharing \u2018simi- lar\u2019 behaviours among consecutive experimental conditions. Due to the intrinsic spatial constraint required by time-series dataset, current Factor Graph (FG) based approaches can- not be applied. In this paper we introduce Time-Series constraints forcing biclustering solution to have contiguous columns. We optimize the model by using the Max-Sum algorithm, whose message update rules have been derived exploiting The Higher Order Potentials (THOP). The pro- posed method has been assessed on a real world dataset and the retrieved biclusters show that it can provide accurate and biologically relevant solutions

A Quantum Annealing Approach to Biclustering

Several problem in Artificial Intelligence and Pattern Recognition are computationally intractable due to their inherent complexity and the exponential size of the solution space. One example of such problems is biclustering, a specific clustering problem where rows and columns of a data-matrix must be clustered simultaneously. Quantum information processing could provide a viable alternative to combat such a complexity. A notable work in this direction is the recent development of the D-Wave computer, whose processor is able to exploit quantum mechanical effects in order to perform quantum annealing. The question motivating this work is whether the use of this special hardware is a viable approach to efficiently solve the biclustering problem. As a first step towards the solution of this problem, we show a feasible encoding of biclustering into the D-Wave quantum annealing hardware, and provide a theoretical analysis of its correctness

A biclustering approach based on factor graphs and the max-sum algorithm

Biclustering represents an intrinsically complex problem, where the aim is to perform a simultaneous row- and column-clustering of a given data matrix. Some recent approaches model this problem using factor graphs, so to exploit their ability to open the door to efficient optimization approaches for well designed function decompositions. However, while such models provide promising results, they do not scale to data matrices of reasonable size. In this paper, we take a step towards addressing this issue, by proposing a novel approach to biclustering based on factor graphs, which yields high quality solutions and scales more favorably than previous methods. Specifically, we cast biclustering as the sequential search for a single bicluster, and propose a binary and compact factor graph that can be solved efficiently using the max-sum algorithm. The proposed approach has been tested and compared with state-of-the-art methods on four datasets (two synthetic and two real world data), providing encouraging results with respect both to previous approaches based on factor graphs and to other state-of-the-art method

Biclustering with a quantum annealer

Several problem in Artificial Intelligence and Pattern Recognition are computationally intractable due to their inherent complexity and the exponential size of the solution space. One example of such problems is biclustering, a specific clustering problem where rows and columns of a data-matrix must be clustered simultaneously. Quantum information processing could provide a viable alternative to combat such a complexity. A notable work in this direction is the recent development of the D-Wave computer, whose processor has been designed to the purpose of solving Quadratic Unconstrained Binary Optimization (QUBO) problems. In this paper, we investigate the use of quantum annealing by providing the first QUBO model for biclustering and a theoretical analysis of its properties (correctness and complexity). We empirically evaluated the accuracy of the model on a synthetic data-set and then performed experiments on a D-Wave machine discussing its practical applicability and embedding propertie

Region-based Correspondence Between 3D Shapes via Spatially Smooth Biclustering

International audienceRegion-based correspondence (RBC) is a highly relevant and non-trivial computer vision problem. Given two 3D shapes, RBC seeks segments/regions on these shapes that can be reliably put in correspondence. The problem thus consists both in finding the regions and determining the correspondences between them. This problem statement is similar to that of " biclustering " , implying that RBC can be cast as a biclustering problem. Here, we exploit this implication by tackling RBC via a novel biclustering approach, called S 4 B (spatially smooth spike and slab biclustering), which: (i) casts the problem in a probabilistic low-rank matrix fac-torization perspective; (ii) uses a spike and slab prior to induce sparsity; (iii) is enriched with a spatial smoothness prior, based on geodesic distances, encouraging nearby vertices to belong to the same bicluster. This type of spatial prior cannot be used in classical biclustering techniques. We test the proposed approach on the FAUST dataset, out-performing both state-of-the-art RBC techniques and classical biclustering methods