arXiv subjects

Hanane Azzag

Publications and source records attributed to Hanane Azzag.

23 records · Page 2Linked to original sources

arXiv2020

A Survey and Implementation of Performance Metrics for Self-Organized Maps

Self-Organizing Map algorithms have been used for almost 40 years across various application domains such as biology, geology, healthcare, industry and humanities as an interpretable tool to explore, cluster and visualize high-dimensional data sets. In every application, practitioners need to know whether they can \textit{trust} the resulting mapping, and perform model selection to tune algorithm parameters (e.g. the map size). Quantitative evaluation of self-organizing maps (SOM) is a subset of clustering validation, which is a challenging problem as such. Clustering model selection is typically achieved by using clustering validity indices. While they also apply to self-organized clustering models, they ignore the topology of the map, only answering the question: do the SOM code vectors approximate well the data distribution? Evaluating SOM models brings in the additional challenge of assessing their topology: does the mapping preserve neighborhood relationships between the map and the original data? The problem of assessing the performance of SOM models has already been tackled quite thoroughly in literature, giving birth to a family of quality indices incorporating neighborhood constraints, called \textit{topographic} indices. Commonly used examples of such metrics are the topographic error, neighborhood preservation or the topographic product. However, open-source implementations are almost impossible to find. This is the issue we try to solve in this work: after a survey of existing SOM performance metrics, we implemented them in Python and widely used numerical libraries, and provide them as an open-source library, SOMperf. This paper introduces each metric available in our module along with usage examples.

cs.NE↗

arXiv2020

Conditional Latent Block Model: a Multivariate Time Series Clustering Approach for Autonomous Driving Validation

Autonomous driving systems validation remains one of the biggest challenges car manufacturers must tackle in order to provide safe driverless cars. The high complexity stems from several factors: the multiplicity of vehicles, embedded systems, use cases, and the very high required level of reliability for the driving system to be at least as safe as a human driver. In order to circumvent these issues, large scale simulations reproducing this huge variety of physical conditions are intensively used to test driverless cars. Therefore, the validation step produces a massive amount of data, including many time-indexed ones, to be processed. In this context, building a structure in the feature space is mandatory to interpret the various scenarios. In this work, we propose a new co-clustering approach adapted to high-dimensional time series analysis, that extends the standard model-based co-clustering. The FunCLBM model extends the recently proposed Functional Latent Block Model and allows to create a dependency structure between row and column clusters. This structured partition acts as a feature selection method, that provides several clustering views of a dataset, while discriminating irrelevant features. In this workflow, times series are projected onto a common interpolated low-dimensional frequency space, which allows to optimize the projection basis. In addition, FunCLBM refines the definition of each latent block by performing block-wise dimension reduction and feature selection. We propose a SEM-Gibbs algorithm to infer this model, as well as a dedicated criterion to select the optimal nested partition. Experiments on both simulated and real-case Renault datasets shows the effectiveness of the proposed tools and the adequacy to our use case.

cs.LG↗

arXiv2019

Algorithms for an Efficient Tensor Biclustering

Consider a data set collected by (individuals-features) pairs in different times. It can be represented as a tensor of three dimensions (Individuals, features and times). The tensor biclustering problem computes a subset of individuals and a subset of features whose signal trajectories over time lie in a low-dimensional subspace, modeling similarity among the signal trajectories while allowing different scalings across different individuals or different features. This approach are based on spectral decomposition in order to build the desired biclusters. We evaluate the quality of the results from each algorithms with both synthetic and real data set.

cs.LG↗

arXiv2019

Nearest Neighbor Median Shift Clustering for Binary Data

We describe in this paper the theory and practice behind a new modal clustering method for binary data. Our approach (BinNNMS) is based on the nearest neighbor median shift. The median shift is an extension of the well-known mean shift, which was designed for continuous data, to handle binary data. We demonstrate that BinNNMS can discover accurately the location of clusters in binary data with theoretical and experimental analyses.

cs.LG↗

arXiv2019

A Distributed and Approximated Nearest Neighbors Algorithm for an Efficient Large Scale Mean Shift Clustering

In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means clustering. Mean Shift clustering is a generalization of the k-means clustering which computes arbitrarily shaped clusters as defined as the basins of attraction to the local modes created by the density gradient ascent paths. Despite its potential, the Mean Shift approach is a computationally expensive method for unsupervised learning. Thus, we introduce two contributions aiming to provide clustering algorithms with a linear time complexity, as opposed to the quadratic time complexity for the exact Mean Shift clustering. Firstly we propose a scalable procedure to approximate the density gradient ascent. Second, our proposed scalable cluster labeling technique is presented. Both propositions are based on Locality Sensitive Hashing (LSH) to approximate nearest neighbors. These two techniques may be used for moderate sized datasets. Furthermore, we show that using our proposed approximations of the density gradient ascent as a pre-processing step in other clustering methods can also improve dedicated classification metrics. For the latter, a distributed implementation, written for the Spark/Scala ecosystem is proposed. For all these considered clustering methods, we present experimental results illustrating their labeling accuracy and their potential to solve concrete problems.

cs.LG↗