Samuel Rota Bulò

Structured class-labels in random forests for semantic image labelling

In this paper we propose a simple and effective way to integrate structural information in random forests for semantic image labelling. By structural information we refer to the inherently available, topological distribution of object classes in a given image. Different object class labels will not be randomly distributed over an image but usually form coherently labelled regions. In this work we provide a way to incorporate this topological information in the popular random forest framework for performing low-level, unary classification. Our paper has several contributions: First, we show how random forests can be augmented with structured label information. In the second part, we introduce a novel data splitting function that exploits the joint distributions observed in the structured label space for learning typical label transitions between object classes. Finally, we provide two possibilities for integrating the structured output predictions into concise, semantic labellings. In our experiments on the challenging MSRC and CamVid databases, we compare our method to standard random forest and conditional random field classification results.

Dense Non-rigid Shape Correspondence Using Random Forests

We propose a shape matching method that produces dense correspondences tuned to a specific class of shapes and deformations. In a scenario where this class is represented by a small set of example shapes, the proposed method learns a shape descriptor capturing the variability of the deformations in the given class. The approach enables the wave kernel signature to extend the class of recognized deformations from near isometries to the deformations appearing in the example set by means of a random forest classifier. With the help of the introduced spatial regularization, the proposed method achieves significant improvements over the baseline approach and obtains state-of-the-art results while keeping short computation times.

Grouping with Asymmetric Affinities: A Game-Theoretic Perspective

Pairwise grouping and clustering approaches have traditionally worked under the assumption that the similarities or compatibilities between the elements to be grouped are symmetric. However, asymmetric compatibilities arise naturally in many areas of computer vision and pattern recognition. Hence, there is a need for a new generic approach to clustering and grouping that can deal with asymmetries in the compatibilities. In this paper, we present a generic framework for grouping and clustering derived from a game-theoretic formalization of the competition between the hypotheses of group membership, and apply it to perceptual grouping. In the proposed approach groups correspond to evolutionary stable strategies, a classic notion in evolutionary game theory. We also provide a combinatorial characterization of the stable strategies, and, hence, of the elements that belong to a group. Experiments show that our approach outperforms both state-of-the-art clustering-based perceptual grouping approacheswith symmetric compatibilities, and other approaches explicitly designed to make use of asymmetric compatibilities.

Matching as a non-cooperative game

With this paper we offer a game-theoretic perspective for the all-pervasive matching problem in computer vision. Specifically, we formulate the matching problem as a (population) non-cooperative game where the potential associations between the items to be matched correspond to (pure) strategies, while payoffs reflect the degree of compatibility between competing hypotheses. Within this formulation, the solutions of the matching problem correspond to evolutionary stable states (ESSs), a robust population-based generalization of the notion of a Nash equilibrium. In order to find ESSs of our matching game, we propose using a novel, fast evolutionary game dynamics motivated by Darwinian selection processes, which let the pure strategies play against each other until an equilibrium is reached. A distinguishing feature of the proposed framework is that it allows one to naturally deal with general many-to-many matching problems even in the presence of asymmetric compatibilities. The potential of the proposed approach is demonstrated via two sets of image matching experiments, both of which show that our results outperform those obtained using well-known domain-specific algorithms.

Deep Neural Decision Forests

We present Deep Neural Decision Forests - a novel approach that unifies classification trees with the representation learning functionality known from deep convolutional networks, by training them in an end-to-end manner. To combine these two worlds, we introduce a stochastic and differentiable decision tree model, which steers the representation learning usually conducted in the initial layers of a (deep) convolutional network. Our model differs from conventional deep networks because a decision forest provides the final predictions and it differs from conventional decision forests since we propose a principled, joint and global optimization of split and leaf node parameters. We show experimental results on benchmark machine learning datasets like MNIST and ImageNet and find on-par or superior results when compared to state-of-the-art deep models. Most remarkably, we obtain Top5-Errors of only 7.84%/6.38% on ImageNet validation data when integrating our forests in a single-crop, single/seven model GoogLeNet architecture, respectively. Thus, even without any form of training data set augmentation we are improving on the 6.67% error obtained by the best GoogLeNet architecture (7 models, 144 crops).

A generalization of the Motzkin–Straus theorem to hypergraphs

In 1965, Motzkin and Straus established a remarkable connection between the global maxima of the Lagrangian of a graph G over the standard simplex and the clique number of G. In this paper, we provide a generalization of the Motzkin–Straus theorem to k-uniform hypergraphs (k-graphs). Specifically, given a k-graph G, we exhibit a family of (parameterized) homogeneous polynomials whose local (global) minimizers are shown to be in one-to-one correspondence with maximal (maximum) cliques of G.

Neural Decision Forests for Semantic Image Labelling

In this work we present Neural Decision Forests, a novel approach to jointly tackle data representation- and discriminative learning within randomized decision trees. Recent advances of deep learning architectures demonstrate the power of embedding representation learning within the classifier -- An idea that is intuitively supported by the hierarchical nature of the decision forest model where the input space is typically left unchanged during training and testing. We bridge this gap by introducing randomized Multi- Layer Perceptrons (rMLP) as new split nodes which are capable of learning non-linear, data-specific representations and taking advantage of them by finding optimal predictions for the emerging child nodes. To prevent overfitting, we i) randomly select the image data fed to the input layer, ii) automatically adapt the rMLP topology to meet the complexity of the data arriving at the node and iii) introduce an l1-norm based regularization that additionally sparsifies the network. The key findings in our experiments on three different semantic image labelling datasets are consistently improved results and significantly compressed trees compared to conventional classification trees.

Beyond partitions: Allowing overlapping groups in pairwise clustering

The field of pairwise clustering is currently dominated by the idea of dividing a set of objects into disjoints classes, thereby giving rise to (hard) partitions of the input data. However, in many computer vision and pattern recognition problems this approach is too restrictive as objects might reasonably belong to more than one class. In this paper, we adopt a game-theoretic perspective to the iterative extraction of possibly overlapping clusters: Game dynamics are used to locate individual groups, and after each extraction the similarity matrix is transformed in such a way as to make the located cluster unstable under the dynamics, without affecting the remaining groups.

Is data clustering in adversarial settings secure

Clustering algorithms have been increasingly adopted in security applications to spot dangerous or illicit activities. However, they have not been originally devised to deal with deliberate attack attempts that may aim to subvert the clustering process itself. Whether clustering can be safely adopted in such settings remains thus questionable. In this work we propose a general framework that allows one to identify potential attacks against clustering algorithms, and to evaluate their impact, by making specific assumptions on the adversarys goal, knowledge of the attacked system, and capabilities of manipulating the input data. We show that an attacker may significantly poison the whole clustering process by adding a relatively small percentage of attack samples to the input data, and that some attack samples may be obfuscated to be hidden within some existing clusters. We present a case study on single-linkage hierarchical clustering, and report experiments on clustering of malware samples and handwritten digits.

New Bounds on the Clique Number of Graphs Based on Spectral Hypergraph Theory

This work introduces new bounds on the clique number of graphs derived from a result due to Sos and Straus, which generalizes the Motzkin-Straus Theorem to a specific class of hypergraphs. In particular, we generalize and improve the spectral bounds introduced by Wilf in 1967 and 1986 establishing an interesting link between the clique number and the emerging spectral hypergraph theory field. In order to compute the bounds we face the problem of extracting the leading H-eigenpair of supersymmetric tensors, which is still uncovered in the literature. To this end, we provide two approaches to serve the purpose. Finally, we present some preliminary experimental results.