Parametric Local Metric Learning for Nearest Neighbor Classification

We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility its downside is the considerable risk of overfitting. We present a new parametric local metric learning method in which we learn a smooth metric matrix function over the data manifold. Using an approximation error bound of the metric matrix function we learn local metrics as linear combinations of basis metrics defined on anchor points over different regions of the instance space. We constrain the metric matrix function by imposing on the linear combinations manifold regularization which makes the learned metric matrix function vary smoothly along the geodesics of the data manifold. Our metric learning method has excellent performance both in terms of predictive power and scalability. We experimented with several large-scale classification problems, tens of thousands of instances, and compared it with several state of the art metric learning methods, both global and local, as well as to SVM with automatic kernel selection, all of which it outperforms in a significant manner

Person Re-Identification by Deep Joint Learning of Multi-Loss Classification

Existing person re-identification (re-id) methods rely mostly on either localised or global feature representation alone. This ignores their joint benefit and mutual complementary effects. In this work, we show the advantages of jointly learning local and global features in a Convolutional Neural Network (CNN) by aiming to discover correlated local and global features in different context. Specifically, we formulate a method for joint learning of local and global feature selection losses designed to optimise person re-id when using only generic matching metrics such as the L2 distance. We design a novel CNN architecture for Jointly Learning Multi-Loss (JLML) of local and global discriminative feature optimisation subject concurrently to the same re-id labelled information. Extensive comparative evaluations demonstrate the advantages of this new JLML model for person re-id over a wide range of state-of-the-art re-id methods on five benchmarks (VIPeR, GRID, CUHK01, CUHK03, Market-1501).Comment: Accepted by IJCAI 201

Universal expressions of population change by the Price equation: natural selection, information, and maximum entropy production

The Price equation shows the unity between the fundamental expressions of change in biology, in information and entropy descriptions of populations, and in aspects of thermodynamics. The Price equation partitions the change in the average value of a metric between two populations. A population may be composed of organisms or particles or any members of a set to which we can assign probabilities. A metric may be biological fitness or physical energy or the output of an arbitrarily complicated function that assigns quantitative values to members of the population. The first part of the Price equation describes how directly applied forces change the probabilities assigned to members of the population when holding constant the metrical values of the members---a fixed metrical frame of reference. The second part describes how the metrical values change, altering the metrical frame of reference. In canonical examples, the direct forces balance the changing metrical frame of reference, leaving the average or total metrical values unchanged. In biology, relative reproductive success (fitness) remains invariant as a simple consequence of the conservation of total probability. In physics, systems often conserve total energy. Nonconservative metrics can be described by starting with conserved metrics, and then studying how coordinate transformations between conserved and nonconserved metrics alter the geometry of the dynamics and the aggregate values of populations. From this abstract perspective, key results from different subjects appear more simply as universal geometric principles for the dynamics of populations subject to the constraints of particular conserved quantitiesComment: v2: Complete rewrite, new title and abstract. Changed focus to Price equation as basis for universal expression of changes in populations. v3: Cleaned up usage of terms virtual and reversible displacements and virtual work and usage of d'Alembert's principle. v4: minor editing and correction