Nested dictionary learning for hierarchical organization of imagery and text

A tree-based dictionary learning model is developed for joint analysis of imagery and associated text. The dictionary learning may be applied directly to the imagery from patches, or to general feature vectors extracted from patches or superpixels (using any existing method for image feature extraction). Each image is associated with a path through the tree (from root to a leaf), and each of the multiple patches in a given image is associated with one node in that path. Nodes near the tree root are shared between multiple paths, representing image characteristics that are common among different types of images. Moving toward the leaves, nodes become specialized, representing details in image classes. If available, words (text) are also jointly modeled, with a path-dependent probability over words. The tree structure is inferred via a nested Dirichlet process, and a retrospective stick-breaking sampler is used to infer the tree depth and width.

Biogeography in deep time - What do phylogenetics, geology, and paleoclimate tell us about early platyrrhine evolution?

Molecular data have converged on a consensus about the genus-level phylogeny of extant platyrrhine monkeys, but for most extinct taxa and certainly for those older than the Pleistocene we must rely upon morphological evidence from fossils. This raises the question as to how well anatomical data mirror molecular phylogenies and how best to deal with discrepancies between the molecular and morphological data as we seek to extend our phylogenies to the placement of fossil taxa. Here I present parsimony-based phylogenetic analyses of extant and fossil platyrrhines based on an anatomical dataset of 399 dental characters and osteological features of the cranium and postcranium. I sample 16 extant taxa (one from each platyrrhine genus) and 20 extinct taxa of platyrrhines. The tree structure is constrained with a "molecular scaffold" of extant species as implemented in maximum parsimony using PAUP with the molecular-based 'backbone' approach. The data set encompasses most of the known extinct species of platyrrhines, ranging in age from latest Oligocene (∼26 Ma) to the Recent. The tree is rooted with extant catarrhines, and Late Eocene and Early Oligocene African anthropoids. Among the more interesting patterns to emerge are: (1) known early platyrrhines from the Late Oligocene through Early Miocene (26-16.5Ma) represent only stem platyrrhine taxa; (2) representatives of the three living platyrrhine families first occur between 15.7 Ma and 13.5 Ma; and (3) recently extinct primates from the Greater Antilles (Cuba, Jamaica, Hispaniola) are sister to the clade of extant platyrrhines and may have diverged in the Early Miocene. It is probable that the crown platyrrhine clade did not originate before about 20-24 Ma, a conclusion consistent with the phylogenetic analysis of fossil taxa presented here and with recent molecular clock estimates. The following biogeographic scenario is consistent with the phylogenetic findings and climatic and geologic evidence: Tropical South America has been a center for platyrrhine diversification since platyrrhines arrived on the continent in the middle Cenozoic. Platyrrhines dispersed from tropical South America to Patagonia at ∼25-24 Ma via a "Paraná Portal" through eastern South America across a retreating Paranense Sea. Phylogenetic bracketing suggests Antillean primates arrived via a sweepstakes route or island chain from northern South America in the Early Miocene, not via a proposed land bridge or island chain (GAARlandia) in the Early Oligocene (∼34 Ma). Patagonian and Antillean platyrrhines went extinct without leaving living descendants, the former at the end of the Early Miocene and the latter within the past six thousand years. Molecular evidence suggests crown platyrrhines arrived in Central America by crossing an intermittent connection through the Isthmus of Panama at or after 3.5Ma. Any more ancient Central American primates, should they be discovered, are unlikely to have given rise to the extant Central American taxa in situ.

Learning from Geometry

Subspaces and manifolds are two powerful models for high dimensional signals. Subspaces model linear correlation and are a good fit to signals generated by physical systems, such as frontal images of human faces and multiple sources impinging at an antenna array. Manifolds model sources that are not linearly correlated, but where signals are determined by a small number of parameters. Examples are images of human faces under different poses or expressions, and handwritten digits with varying styles. However, there will always be some degree of model mismatch between the subspace or manifold model and the true statistics of the source. This dissertation exploits subspace and manifold models as prior information in various signal processing and machine learning tasks.

A near-low-rank Gaussian mixture model measures proximity to a union of linear or affine subspaces. This simple model can effectively capture the signal distribution when each class is near a subspace. This dissertation studies how the pairwise geometry between these subspaces affects classification performance. When model mismatch is vanishingly small, the probability of misclassification is determined by the product of the sines of the principal angles between subspaces. When the model mismatch is more significant, the probability of misclassification is determined by the sum of the squares of the sines of the principal angles. Reliability of classification is derived in terms of the distribution of signal energy across principal vectors. Larger principal angles lead to smaller classification error, motivating a linear transform that optimizes principal angles. This linear transformation, termed TRAIT, also preserves some specific features in each class, being complementary to a recently developed Low Rank Transform (LRT). Moreover, when the model mismatch is more significant, TRAIT shows superior performance compared to LRT.

The manifold model enforces a constraint on the freedom of data variation. Learning features that are robust to data variation is very important, especially when the size of the training set is small. A learning machine with large numbers of parameters, e.g., deep neural network, can well describe a very complicated data distribution. However, it is also more likely to be sensitive to small perturbations of the data, and to suffer from suffer from degraded performance when generalizing to unseen (test) data.

From the perspective of complexity of function classes, such a learning machine has a huge capacity (complexity), which tends to overfit. The manifold model provides us with a way of regularizing the learning machine, so as to reduce the generalization error, therefore mitigate overfiting. Two different overfiting-preventing approaches are proposed, one from the perspective of data variation, the other from capacity/complexity control. In the first approach, the learning machine is encouraged to make decisions that vary smoothly for data points in local neighborhoods on the manifold. In the second approach, a graph adjacency matrix is derived for the manifold, and the learned features are encouraged to be aligned with the principal components of this adjacency matrix. Experimental results on benchmark datasets are demonstrated, showing an obvious advantage of the proposed approaches when the training set is small.

Stochastic optimization makes it possible to track a slowly varying subspace underlying streaming data. By approximating local neighborhoods using affine subspaces, a slowly varying manifold can be efficiently tracked as well, even with corrupted and noisy data. The more the local neighborhoods, the better the approximation, but the higher the computational complexity. A multiscale approximation scheme is proposed, where the local approximating subspaces are organized in a tree structure. Splitting and merging of the tree nodes then allows efficient control of the number of neighbourhoods. Deviation (of each datum) from the learned model is estimated, yielding a series of statistics for anomaly detection. This framework extends the classical {\em changepoint detection} technique, which only works for one dimensional signals. Simulations and experiments highlight the robustness and efficacy of the proposed approach in detecting an abrupt change in an otherwise slowly varying low-dimensional manifold.

Design of Latent Thermal Energy Storage Systems

This dissertation documents the results of a theoretical and numerical study of time dependent storage of energy by melting a phase change material. The heating is provided along invading lines, which change from single-line invasion to tree-shaped invasion. Chapter 2 identifies the special design feature of distributing energy storage in time-dependent fashion on a territory, when the energy flows by fluid flow from a concentrated source to points (users) distributed equidistantly on the area. The challenge in this chapter is to determine the architecture of distributed energy storage. The chief conclusion is that the finite amount of storage material should be distributed proportionally with the distribution of the flow rate of heating agent arriving on the area. The total time needed by the source stream to ‘invade’ the area is cumulative (the sum of the storage times required at each storage site), and depends on the energy distribution paths and the sequence in which the users are served by the source stream. Chapter 3 shows theoretically that the melting process consists of two phases: “invasion” thermal diffusion along the invading line, which is followed by “consolidation” as heat diffuses perpendicularly to the invading line. This chapter also reports the duration of both phases and the evolution of the melt layer around the invading line during the two-dimensional and three-dimensional invasion. It also shows that the amount of melted material increases in time according to a curve shaped as an S. These theoretical predictions are validated by means of numerical simulations in chapter 4. This chapter also shows that the heat transfer rate density increases (i.e., the S curve becomes steeper) as the complexity and number of degrees of freedom of the structure are increased, in accord with the constructal law. The optimal geometric features of the tree structure are detailed in this chapter. Chapter 5 documents a numerical study of time-dependent melting where the heat transfer is convection dominated, unlike in chapter 3 and 4 where the melting is ruled by pure conduction. In accord with constructal design, the search is for effective heat-flow architectures. The volume-constrained improvement of the designs for heat flow begins with assuming the simplest structure, where a single line serves as heat source. Next, the heat source is endowed with freedom to change its shape as it grows. The objective of the numerical simulations is to discover the geometric features that lead to the fastest melting process. The results show that the heat transfer rate density increases as the complexity and number of degrees of freedom of the structure are increased. Furthermore, the angles between heat invasion lines have a minor effect on the global performance compared to other degrees of freedom: number of branching levels, stem length, and branch lengths. The effect of natural convection in the melt zone is documented.

The receptor kinase family: primary structure of rhodopsin kinase reveals similarities to the beta-adrenergic receptor kinase.

Light-dependent deactivation of rhodopsin as well as homologous desensitization of beta-adrenergic receptors involves receptor phosphorylation that is mediated by the highly specific protein kinases rhodopsin kinase (RK) and beta-adrenergic receptor kinase (beta ARK), respectively. We report here the cloning of a complementary DNA for RK. The deduced amino acid sequence shows a high degree of homology to beta ARK. In a phylogenetic tree constructed by comparing the catalytic domains of several protein kinases, RK and beta ARK are located on a branch close to, but separate from the cyclic nucleotide-dependent protein kinase and protein kinase C subfamilies. From the common structural features we conclude that both RK and beta ARK are members of a newly delineated gene family of guanine nucleotide-binding protein (G protein)-coupled receptor kinases that may function in diverse pathways to regulate the function of such receptors.