Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric scattering transform on manifolds. Similar to the Euclidean scattering transform, the geometric scattering transform is based on a cascade of wavelet filters and pointwise nonlinearities. It is invariant to local isometries and stable to certain types of diffeomorphisms. Empirical results demonstrate its utility on several geometric learning tasks. Our results generalize the deformation stability and local translation invariance of Euclidean scattering, and demonstrate the importance of linking the used filter structures to the underlying geometry of the data.Comment: 35 pages; 3 figures; 2 tables; v3: Revisions based on reviewer comment

Product innovation as a static game of incomplete information in a non-Bayesian environment

Includes bibliographical references.The apparent failure of incumbent firms to produce radical innovations is one that continues to provoke significant debate in the economic literature. This phenomenon, termed the "Incumbent's Curse" by Chandy and Tellis (2000, p.2) receives significant support. Rosenbloom and Christensen (1994, p.655) go as far as to say that this is one of the "stylised facts" in the innovation literature. The concept of incumbent failure to innovate receives support both in theoretic modelling (e.g. Ghemawat 1991, Reinganum, 1983) and in empirical case studies (e.g. Christensen 1993, Henderson and Clark 1990). Chandy and Tellis (2000) rightly point out however that such literature has focused on industries in which there is such incumbent inertia. There are well documented examples of leadership in a high profile industry changing with new product innovations, e.g. typewriters, computer disks

Fisher Vectors Derived from Hybrid Gaussian-Laplacian Mixture Models for Image Annotation

In the traditional object recognition pipeline, descriptors are densely sampled over an image, pooled into a high dimensional non-linear representation and then passed to a classifier. In recent years, Fisher Vectors have proven empirically to be the leading representation for a large variety of applications. The Fisher Vector is typically taken as the gradients of the log-likelihood of descriptors, with respect to the parameters of a Gaussian Mixture Model (GMM). Motivated by the assumption that different distributions should be applied for different datasets, we present two other Mixture Models and derive their Expectation-Maximization and Fisher Vector expressions. The first is a Laplacian Mixture Model (LMM), which is based on the Laplacian distribution. The second Mixture Model presented is a Hybrid Gaussian-Laplacian Mixture Model (HGLMM) which is based on a weighted geometric mean of the Gaussian and Laplacian distribution. An interesting property of the Expectation-Maximization algorithm for the latter is that in the maximization step, each dimension in each component is chosen to be either a Gaussian or a Laplacian. Finally, by using the new Fisher Vectors derived from HGLMMs, we achieve state-of-the-art results for both the image annotation and the image search by a sentence tasks.Comment: new version includes text synthesis by an RNN and experiments with the COCO benchmar

COMMUNITY COLLEGE CAMPUSES AND SEXUAL MINORITIES: THE EXPERIENCE OF LGBTQ STUDENTS AT COMMUNITY COLLEGES

The purpose of this study was to examine national survey data from across the United States for respondents from two-year community colleges. Historically little empirical evidence exists in the literature about this population of students who identity as sexual minorities. The study begins with a historical overview of the LGBTQ rights movement. This provides a baseline for why studies including this invisible minority group are important and especially timely for two-year college campuses. Literature is barrowed from four-year college and university studies. Data were analyzed using the Rasch Partial Credit model. This analysis included testing for data-fit to the model, evaluation of items which did not fit the model, item mapping, differential functioning based on sexual identity, and standard descriptive statistics. The aim of this analysis was to determine if harassment, discrimination, and violence on campus towards sexual minority students occur and attempt to assess the prevalence of such activities. Results indicate that there doesn’t exist differences in responses between male and female participants. However, differences exist related to campus perceptions for sexual minority students and their non-minority (heterosexual) peers