François-Xavier Jollois

Clustering Large Categorical Data

Clustering methods often come down to the optimization of a numeric criterion defined from a distance or from a dissimilarity measure. It is possible to show that this problem is often equivalent to the estimation of the parameters of a probabilistic model under the classification likelihood approach. For instance, we know that the inertia criterion optimized under the k-means algorithm corresponds to the hypothesis of a population arising from a Gaussian mixture. In this paper, we propose an adapted mixture model for categorical data. Using the classification likelihood approach, we develop the Classification EM algorithm (CEM) to estimate the parameters of the mixture model. With our probabilistic model, the data are not denatured and the estimated parameters readily indicate the characteristics of the clusters. This probabilistic approach gives an interpretation of the criterion optimized by the k-modes algorithm which is an extension of k-means to categorical attributes and allows us to study the behavior of this algorithm.

Speed-up for the expectation-maximization algorithm for clustering categorical data

In model-based cluster analysis, the expectation-maximization (EM) algorithm has a number of desirable properties, but in some situations, this algorithm can be slow to converge. Some variants are proposed to speed-up EM in reducing the time spent in the E-step, in the case of Gaussian mixture. The main aims of such methods is first to speed-up convergence of EM, and second to yield same results (or not so far) than EM itself. In this paper, we compare these methods from categorical data, with the latent class model, and we propose a new variant that sustains better results on synthetic and real data sets, in terms of convergence speed-up and number of misclassified objects.

Unsupervised anomaly detection for Aircraft Condition Monitoring System

Anomaly detection is an important field for the anticipation of aircraft maintenance operations, working as an enabler of diagnostic and prognostic functions. A method has been implemented to detect abnormal data in Aircraft Condition Monitoring System (ACMS) records. Rather than using already known and usual detection triggers which are partial detectors and insensitive to new flight and system conditions, this method automatically extracts abnormal data points without requiring any a priori information about the system and its conditions. To accomplish this objective, we propose to combine a segmentation based and density clustering approaches for detecting and filtering anomalies. This method was applied on A340 ACMS data recordings. The detection logics associated with the new anomalies can be used as new detection conditions to be potentially implemented onboard, further extending legacy detection capabilities.

Adaptive Threshold for Anomaly Detection Using Time Series Segmentation

Time series data are generated from almost every domain and anomaly detection becomes extremely important in the last decade. It consists in detecting anomalous patterns through identifying some new and unknown behaviors that are abnormal or inconsistent relative to most of the data. An efficient anomaly detection algorithm has to adapt the detection process for each system condition and each time series behavior. In this paper, we propose an adaptive threshold able to detect anomalies in univariate time series. Our algorithm is based on segmentation and local means and standard deviations. It allows us to simplify time series visualization and to detect new abnormal data as time series jumps within different time series behavior. On synthetic and real datasets the proposed approach shows good ability in detecting abnormalities.

Pixel-based visualization and density-based tabular model

Visualization of the massive datasets needs new methods which are able to quickly and easily reveal their contents. The projection of the data cloud is an interesting paradigm in spite of its difficulty to be explored when data plots are too numerous. So we study a new way to show a bidimensional projection from a multidimensional data cloud: our generative model constructs a tabular view of the projected cloud. We are able to show the high densities areas by their non equidistributed discretization. This approach is an alternative to the self-organizing map when a projection does already exist. The resulting pixel views of a dataset are illustrated by projecting a data sample of real images: it becomes possible to observe how are laid out the class labels or the frequencies of a group of modalities without being lost because of a zoom enlarging change for instance. The conclusion gives perspectives to this original promising point of view to get a readable projection for a statistical data analysis of large data samples.

Assessing the Number of Clusters of the Latent Class Model

When partitioning the data is the main concern, it is implicitly assumed that each cluster can be approximately regarded as a sample from one component of a mixture model. Thus, the clustering problem can be viewed as an estimation problem of the parameters of the mixture. Setting this problem under the Maximum likelihood and Classification likelihood approaches, we first study the clustering of objects described by categorical attributes using the latent class model and we concentrate our attention on the problem of the number of components. To this end, we use three criteria derived within a Bayesian framework to tackle this problem. These criteria based on approximations of integrated likelihood and of integrated classification likelihood have been recently compared in Gaussian mixture. In this work, we propose to extend these comparisons to the latent class model.