Contribution to Graph-based Manifold Learning with Application to Image Categorization.

122 pLos algoritmos de aprendizaje de variedades basados en grafos (Graph,based manifold) son técnicas que han demostrado ser potentes herramientas para la extracción de características y la reducción de la dimensionalidad en los campos de reconomiento de patrones, visión por computador y aprendizaje automático. Estos algoritmos utilizan información basada en las similitudes de pares de muestras y del grafo ponderado resultante para revelar la estructura geométrica intrínseca de la variedad

Contribution to Graph-based Manifold Learning with Application to Image Categorization.

122 pLos algoritmos de aprendizaje de variedades basados en grafos (Graph,based manifold) son técnicas que han demostrado ser potentes herramientas para la extracción de características y la reducción de la dimensionalidad en los campos de reconomiento de patrones, visión por computador y aprendizaje automático. Estos algoritmos utilizan información basada en las similitudes de pares de muestras y del grafo ponderado resultante para revelar la estructura geométrica intrínseca de la variedad

On the use of high-order feature propagation in Graph Convolution Networks with Manifold Regularization

Graph Convolutional Networks (GCNs) have received a lot of attention in pattern recognition and machine learning. In this paper, we present a revisited scheme for the new method called "GCNs with Manifold Regularization" (GCNMR). While manifold regularization can add additional information, the GCN-based semi-supervised classification process cannot consider the full layer-wise structured information. Inspired by graph-based label propagation approaches, we will integrate high-order feature propagation into each GCN layer. High-order feature propagation over the graph can fully exploit the structured information provided by the latter at all the GCN's layers. It fully exploits the clustering assumption, which is valid for structured data but not well exploited in GCNs. Our proposed scheme would lead to more informative GCNs. Using the revisited model, we will conduct several semi-supervised classification experiments on public image datasets containing objects, faces and digits: Extended Yale, PF01, Caltech101 and MNIST. We will also consider three citation networks. The proposed scheme performs well compared to several semi-supervised methods. With respect to the recent GCNMR approach, the average improvements were 2.2%, 4.5%, 1.0% and 10.6% on Extended Yale, PF01, Caltech101 and MNIST, respectively.This work is supported in part by the University of the Basque Country UPV/EHU grant GIU19/027

Building Deep Networks on Grassmann Manifolds

Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean network paradigm to Grassmann manifolds. In particular, we design full rank mapping layers to transform input Grassmannian data to more desirable ones, exploit re-orthonormalization layers to normalize the resulting matrices, study projection pooling layers to reduce the model complexity in the Grassmannian context, and devise projection mapping layers to respect Grassmannian geometry and meanwhile achieve Euclidean forms for regular output layers. To train the Grassmann networks, we exploit a stochastic gradient descent setting on manifolds of the connection weights, and study a matrix generalization of backpropagation to update the structured data. The evaluations on three visual recognition tasks show that our Grassmann networks have clear advantages over existing Grassmann learning methods, and achieve results comparable with state-of-the-art approaches.Comment: AAAI'18 pape

Generative Model with Coordinate Metric Learning for Object Recognition Based on 3D Models

Given large amount of real photos for training, Convolutional neural network shows excellent performance on object recognition tasks. However, the process of collecting data is so tedious and the background are also limited which makes it hard to establish a perfect database. In this paper, our generative model trained with synthetic images rendered from 3D models reduces the workload of data collection and limitation of conditions. Our structure is composed of two sub-networks: semantic foreground object reconstruction network based on Bayesian inference and classification network based on multi-triplet cost function for avoiding over-fitting problem on monotone surface and fully utilizing pose information by establishing sphere-like distribution of descriptors in each category which is helpful for recognition on regular photos according to poses, lighting condition, background and category information of rendered images. Firstly, our conjugate structure called generative model with metric learning utilizing additional foreground object channels generated from Bayesian rendering as the joint of two sub-networks. Multi-triplet cost function based on poses for object recognition are used for metric learning which makes it possible training a category classifier purely based on synthetic data. Secondly, we design a coordinate training strategy with the help of adaptive noises acting as corruption on input images to help both sub-networks benefit from each other and avoid inharmonious parameter tuning due to different convergence speed of two sub-networks. Our structure achieves the state of the art accuracy of over 50\% on ShapeNet database with data migration obstacle from synthetic images to real photos. This pipeline makes it applicable to do recognition on real images only based on 3D models.Comment: 14 page