# Relevant publications

## Large Scale Data Analysis

## Noise estimation using density estimation for self-supervised multimodal learning

One of the key factors of enabling machine learning models to comprehend and solve real-world tasks is to leverage multimodal data. Unfortunately, the annotation of multimodal data is challenging and expensive. Recently, self-supervised multimodal methods that combine vision and language were proposed to learn multimodal representations without annotation. However, these methods choose to ignore the presence of high levels of noise and thus yield sub-optimal results. In this work, we show that the problem of noise estimation for multimodal data can be reduced to a multimodal density estimation task. Using multimodal density estimation, we propose a noise estimation building block for multimodal representation learning that is based strictly on the inherent correlation between different modalities. We demonstrate how our noise estimation can be broadly integrated and achieves comparable results to state-of-the-art performance on five different benchmark datasets for two challenging multimodal tasks: Video Question Answering and Text-To-Video Retrieval.

## Spectral geometric matrix completion

Deep Matrix Factorization (DMF) is an emerging approach to the problem of reconstructing a matrix from a subset of its entries. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix. Despite these promising theoretical results, empirical evaluation of vanilla DMF on real benchmarks exhibits poor reconstructions which we attribute to the extremely low number of samples available. We propose an explicit spectral regularization scheme that is able to make DMF models competitive on real benchmarks, while still maintaining the implicit regularization induced by gradient descent, thus enjoying the best of both worlds.

## Single-node attack for fooling graph neural networks

Graph neural networks (GNNs) have shown broad applicability in a variety of domains. Some of these domains, such as social networks and product recommendations, are fertile ground for malicious users and behavior. In this paper, we show that GNNs are vulnerable to the extremely limited scenario of a single-node adversarial example, where the node cannot be picked by the attacker. That is, an attacker can force the GNN to classify any target node to a chosen label by only slightly perturbing another single arbitrary node in the graph, even when not being able to pick that specific attacker node. When the adversary is allowed to pick a specific attacker node, the attack is even more effective. We show that this attack is effective across various GNN types, such as GraphSAGE, GCN, GAT, and GIN, across a variety of real-world datasets, and as a targeted and a non-targeted attack.

## Self-Supervised Object Detection and Retrieval Using Unlabeled Videos

Unlabeled video in the wild presents a valuable, yet so far unharnessed, source of information for learning vision tasks. We present the first attempt of fully self-supervised learning of object detection from subtitled videos without any manual object annotation. To this end, we use the How2 multi-modal collection of instructional videos with English subtitles. We pose the problem as learning with a weakly- and noisily-labeled data, and propose a novel training model that can confront high noise levels, and yet train a classifier to localize the object of interest in the video frames, without any manual labeling involved. We evaluate our approach on a set of 11 manually annotated objects in over 5000 frames and compare it to an existing weakly-supervised approach as baseline. Benchmark data and code will be released upon acceptance of the paper.

## Intrinsic multi-scale evaluation of generative models

Generative models are often used to sample high-dimensional data points from a manifold with small intrinsic dimension. Existing techniques for comparing generative models focus on global data properties such as mean and covariance; in that sense, they are extrinsic and uni-scale. We develop the first, to our knowledge, intrinsic and multi-scale method for characterizing and comparing underlying data manifolds, based on comparing all data moments by lower-bounding the spectral notion of the Gromov-Wasserstein distance between manifolds. In a thorough experimental study, we demonstrate that our method effectively evaluates the quality of generative models; further, we showcase its efficacy in discerning the disentanglement process in neural networks.

## Deep matrix factorization with spectral geometric regularization

We address the problem of reconstructing a matrix from a subset of its entries. Current methods, branded as geometric matrix completion, augment classical rank regularization techniques by incorporating geometric information into the solution. This information is usually provided as graphs encoding relations between rows/columns. In this work, we propose a simple spectral approach for solving the matrix completion problem, via the framework of functional maps. We introduce the zoomout loss, a multiresolution spectral geometric loss inspired by recent advances in shape correspondence, whose minimization leads to state-of-the-art results on various recommender systems datasets. Surprisingly, for some datasets, we were able to achieve comparable results even without incorporating geometric information. This puts into question both the quality of such information and current methods’ ability to use it in a meaningful and efficient way.

Code is available either as Google Colab notebook, or via https://github.com/amitboy/SGMC

## DIMAL: Deep isometric manifold learning using sparse geodesic sampling

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to solve the problem of least squares multidimensional scaling for generating maps that approximately preserve geodesic distances. By training with only a few landmarks, we show a significantly improved local and nonlocal generalization of the isometric mapping as compared to analogous non-parametric counterparts. Importantly, the combination of a deep-learning framework with a multidimensional scaling objective enables a numerical analysis of network architectures to aid in understanding their representation power. This provides a geometric perspective to the generalizability of deep learning.

## Multidimensional scaling

The various multidimensional scaling models can be broadly classified into metric vs. non-metric, and strain (classical scaling) vs. stress (distance scaling) based MDS models. In metric MDS the goal is to maintain the distances in the embedding space as close as possible to the given dissimilarities, while in nonmetric MDS only the order relations between the dissimilarities are important. Strain-based MDS is an algebraic version of the problem that can be solved by eigenvalue decomposition. Stress-based MDS uses a geometric distortion criterion which results in a non-linear and non-convex optimization problem. Each of these models has its own merits and drawbacks, both numerically and application-wise. On top of these basic models, there exist numerous generalizations, including embedding into non-Euclidean domains, working with different stress models, working in different subspaces, and incorporating machine learning approaches to obtain faster, more accurate and more robust embeddings. This chapter reviews these models, with emphasis on their role in computer vision applications.

## ForestHash: Semantic hashing with shallow random forests and tiny convolutional networks

Hash codes are efficient data representations for coping with the ever growing amounts of data. In this paper, we introduce a random forest semantic hashing scheme that embeds tiny convolutional neural networks (CNN) into shallow random forests, with near-optimal information-theoretic code aggregation among trees. We start with a simple hashing scheme, where random trees in a forest act as hashing functions by setting `1′ for the visited tree leaf, and `0′ for the rest. We show that traditional random forests fail to generate hashes that preserve the underlying similarity between the trees, rendering the random forests approach to hashing challenging. To address this, we propose to first randomly group arriving classes at each tee split node into two groups, obtaining a significantly simplified two-class classification problem, which can be handled using a light-weight CNN weak learner. Such random class grouping scheme enables code uniqueness by enforcing each class to share its code with different classes in different trees. A non-conventional low-rank loss is further adopted for the CNN weak learners to encourage code consistency by minimizing intra-class variations and maximizing inter-class distance for the two random class groups. Finally, we introduce an information-theoretic approach for aggregating codes of individual trees into a single hash code, producing a near-optimal unique hash for each class. The proposed approach significantly outperforms state-of-the-art hashing methods for image retrieval tasks on large-scale public datasets, while performing at the level of other state-of-the-art image classification techniques while utilizing a more compact and efficient scalable representation. This work proposes a principled and robust procedure to train and deploy in parallel an ensemble of light-weight CNNs, instead of simply going deeper.

## NetLSD: Hearing the shape of a graph

Comparison among graphs is ubiquitous in graph analytics. However, it is a hard task in terms of the expressiveness of the employed similarity measure and the efficiency of its computation. Ideally, graph comparison should be invariant to the order of nodes and the sizes of compared graphs, adaptive to the scale of graph patterns, and scalable. Unfortunately, these properties have not been addressed together. Graph comparisons still rely on direct approaches, graph kernels, or representation-based methods, which are all inefficient and impractical for large graph collections. In this paper, we propose the Network Laplacian Spectral Descriptor (NetLSD): the first, to our knowledge, permutation- and size-invariant, scale-adaptive, and efficiently computable graph representation method that allows for straightforward comparisons of large graphs. NetLSD extracts a compact signature that inherits the formal properties of the Laplacian spectrum, specifically its heat or wave kernel; thus, it hears the shape of a graph. Our evaluation on a variety of real-world graphs demonstrates that it outperforms previous works in both expressiveness and efficiency.

## SGR: Self-supervised spectral graph representation learning

Representing a graph as a vector is a challenging task; ideally, the representation should be easily computable and conducive to efficient comparisons among graphs, tailored to the particular data and an analytical task at hand. Unfortunately, a “one-size-fits-all” solution is unattainable, as different analytical tasks may require different attention to global or local graph features. We develop SGR, the first, to our knowledge, method for learning graph representations in a self-supervised manner. Grounded on spectral graph analysis, SGR seamlessly combines all aforementioned desirable properties. In extensive experiments, we show how our approach works on large graph collections, facilitates self-supervised representation learning across a variety of application domains, and performs competitively to state-of-the-art methods without re-training.

## Subspace least squares multidimensional scaling

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the analysis and reconstruction of non-rigid shapes. In this regard, MDS can be thought of as a shape from metric algorithm, consisting of finding a configuration of points in the Euclidean space that realize, as isometrically as possible, some given distance structure. In the present work we cast the least squares variant of MDS (LS-MDS) in the spectral domain. This uncovers a multiresolution property of distance scaling which speeds up the optimization by a significant amount, while producing comparable, and sometimes even better, embeddings.

## Multimodal manifold analysis using simultaneous diagonalization of Laplacians

We construct an extension of spectral and diffusion geometry to multiple modalities through simultaneous diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, retrieval, and clustering demonstrating that the joint spectral geometry frequently better captures the inherent structure of multi-modal data. We also show the relation of many previous approaches to multimodal manifold analysis to our framework, of which the can be seen as particular cases.

## Random forests can hash

Hash codes are a very efficient data representation needed to be able to cope with the ever growing amounts of data. We introduce a random forest semantic hashing scheme with information-theoretic code aggregation, showing for the first time how random forest, a technique that together with deep learning have shown spectacular results in classification, can also be extended to large-scale retrieval. Traditional random forest fails to enforce the consistency of hashes generated from each tree for the same class data, i.e., to preserve the underlying similarity, and it also lacks a principled way for code aggregation across trees. We start with a simple hashing scheme, where independently trained random trees in a forest are acting as hashing functions. We the propose a subspace model as the splitting function, and show that it enforces the hash consistency in a tree for data from the same class. We also introduce an information-theoretic approach for aggregating codes of individual trees into a single hash code, producing a near-optimal unique hash for each class. Experiments on large-scale public datasets are presented, showing that the proposed approach significantly outperforms state-of-the-art hashing methods for retrieval tasks.

## Multimodal similarity-preserving hashing

We introduce an efficient computational framework for hashing data belonging to multiple modalities into a single representation space where they become mutually comparable. The proposed approach is based on a novel coupled siamese neural network architecture and allows unified treatment of intra- and inter-modality similarity learning. Unlike existing cross-modality similarity learning approaches, our hashing functions are not limited to binarized linear projections and can assume arbitrarily complex forms. We show experimentally that our method significantly outperforms state-of-the-art hashing approaches on multimedia retrieval tasks.

## Sparse similarity-preserving hashing

In recent years, a lot of attention has been devoted to efficient nearest neighbor search by means of similarity-preserving hashing. One of the plights of existing hashing techniques is the intrinsic trade-off between performance and computational complexity: while longer hash codes allow for lower false positive rates, it is very difficult to increase the embedding dimensionality without incurring in very high false negatives rates or prohibiting computational costs. In this paper, we propose a way to overcome this limitation by enforcing the hash codes to be sparse. Sparse high-dimensional codes enjoy from the low false positive rates typical of long hashes, while keeping the false negative rates similar to those of a shorter dense hashing scheme with equal number of degrees of freedom. We use a tailored feed-forward neural network for the hashing function. Extensive experimental evaluation involving visual and multi-modal data shows the benefits of the proposed method.

## LDAHash: improved matching with smaller descriptors

SIFT-like local feature descriptors are ubiquitously employed in such computer vision applications as content-based retrieval, video analysis, copy detection, object recognition, photo-tourism, and 3D reconstruction from multiple views. Feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations, in particular, affine and intensity scale transformations. However, real transformations that an image can undergo can only be approximately modeled in this way, and thus most descriptors are only approximately invariant in practice. Secondly, descriptors are usually high-dimensional (e.g. SIFT is represented as a 128-dimensional vector). In large-scale retrieval and matching problems, this can pose challenges in storing and retrieving descriptor data. We propose mapping the descriptor vectors into the Hamming space, in which the Hamming metric is used to compare the resulting representations. This way, we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples. We show extensive experimental validation, demonstrating the advantage of the proposed approach.

## Data fusion through cross-modality metric learning using similarity-sensitive hashing

Visual understanding is often based on measuring similarity between observations. Learning similarities specific to a certain perception task from a set of examples has been shown advantageous in various computer vision and pattern recognition problems. In many important applications, the data that one needs to compare come from different representations or modalities, and the similarity between such data operates on objects that may have different and often incommensurable structure and dimensionality. In this paper, we propose a framework for supervised similarity learning based on embedding the input data from two arbitrary spaces into the Hamming space. The mapping is expressed as a binary classification problem with positive and negative examples, and can be efficiently learned using boosting algorithms. The utility and efficiency of such a generic approach is demonstrated on several challenging applications including cross-representation shape retrieval and alignment of multi-modal medical images.

## Nonlinear dimensionality reduction by topologically constrained isometric embedding

Many manifold learning procedures try to embed a given feature data into a flat space of low dimensionality while preserving as much as possible the metric in the natural feature space. The embedding process usually relies on distances between neighboring features, mainly since distances between features that are far apart from each other often provide an unreliable estimation of the true distance on the feature manifold due to its non-convexity. Distortions resulting from using long geodesics indiscriminately lead to a known limitation of the Isomap algorithm when used to map nonconvex manifolds. Presented is a framework for nonlinear dimensionality reduction that uses both local and global distances in order to learn the intrinsic geometry of flat manifolds with boundaries. The resulting algorithm filters out potentially problematic distances between distant feature points based on the properties of the geodesics connecting those points and their relative distance to the boundary of the feature manifold, thus avoiding an inherent limitation of the Isomap algorithm. Since the proposed algorithm matches non-local structures, it is robust to strong noise. We show experimental results demonstrating the advantages of the proposed approach over conventional dimensionality reduction techniques, both global and local in nature.

## Multigrid multidimensional scaling

Multidimensional scaling (MDS) is a generic name for a family of algorithms that construct a configuration of points in a target metric space from information about inter-point distances measured in some other metric space. Large-scale MDS problems often occur in data analysis, representation, and visualization. Solving such problems efficiently is of key importance in many applications. In this paper, we present a multigrid framework for MDS problems. We demonstrate the performance of our algorithm on dimensionality reduction and isometric embedding problems, two classical problems requiring efficient large-scale MDS. Simulation results show that the proposed approach significantly outperforms conventional MDS algorithms.

## A multigrid approach for multi-dimensional scaling

A multigrid approach for the efficient solution of large-scale multidimensional scaling (MDS) problems is presented. The main motivation is a recent application of MDS to isometry-invariant representation of surfaces, in particular, for expression-invariant recognition of human faces. Simulation results show that the proposed approach significantly outperforms conventional MDS algorithms.