Hierarchical Label Partitioning for Large Scale Classification

International audienceExtreme classification task where the number of classes is very large has received important focus over the last decade. Usual efficient multi-class classification approaches have not been designed to deal with such large number of classes. A particular issue in the context of large scale problems concerns the computational classification complexity : best multi-class approaches have generally a linear complexity with respect to the number of classes which does not allow these approaches to scale up. Recent works have put their focus on using hierarchical classification process in order to speed-up the classification of new instances. A priori information on labels is not always available nor useful to build hierarchical models. Finding a suitable hierarchical organization of the labels is thus a crucial issue as the accuracy of the model depends highly on the label assignment through the label tree. We propose in this work a new algorithm to build iteratively a hierarchical label structure by proposing a partitioning algorithm which optimizes simultaneously the structure in terms of classification complexity and the label partitioning problem in order to achieve high classification performances. Beginning from a flat tree structure, our algorithm selects iteratively a node to expand by adding a new level of nodes between the considered node and its children. This operation increases the speed-up of the classification process. Once the node is selected, best partitioning of the classes has to be computed. We propose to consider a measure based on the maximization of the expected loss of the sub-levels in order to minimize the global error of the structure. This choice enforces hardly separable classes to be group together in same partitions at the first levels of the tree structure and it delays errors at a deep level of the structure where there is no incidence on the accuracy of other classes

Topological structures in the equities market network

We present a new method for articulating scale-dependent topological descriptions of the network structure inherent in many complex systems. The technique is based on "Partition Decoupled Null Models,'' a new class of null models that incorporate the interaction of clustered partitions into a random model and generalize the Gaussian ensemble. As an application we analyze a correlation matrix derived from four years of close prices of equities in the NYSE and NASDAQ. In this example we expose (1) a natural structure composed of two interacting partitions of the market that both agrees with and generalizes standard notions of scale (eg., sector and industry) and (2) structure in the first partition that is a topological manifestation of a well-known pattern of capital flow called "sector rotation.'' Our approach gives rise to a natural form of multiresolution analysis of the underlying time series that naturally decomposes the basic data in terms of the effects of the different scales at which it clusters. The equities market is a prototypical complex system and we expect that our approach will be of use in understanding a broad class of complex systems in which correlation structures are resident.Comment: 17 pages, 4 figures, 3 table