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In this paper, the authors introduce a lightweight dataset to interpret IoT (Internet of Things) activity in preparation to create decoys by replicating known data traffic patterns. The dataset comprises different scenarios in a real network setting. This paper also surveys information related to other IoT datasets along with the characteristics that make our data valuable. Many of the datasets available are synthesized (simulated) or often address industrial applications, while the IoT dataset we present is based on likely smart home scenarios. Further, there are only a limited number of IoT datasets that contain both normal operation and attack scenarios. A discussion of the network configuration and the steps taken to prepare this dataset are presented as we prepare to create replicative patterns for decoy purposes. The dataset, which we refer to as IoT Flex Data, consists of four categories, namely, IoT benign idle, IoT benign active, IoT setup, and malicious (attack) traffic associating the IoT devices with the scenarios under consideration., Comment: 13 pages, 4 figures, 4 tables

Cross-Encoder (CE) and Dual-Encoder (DE) models are two fundamental approaches for query-document relevance in information retrieval. To predict relevance, CE models use joint query-document embeddings, while DE models maintain factorized query and document embeddings; usually, the former has higher quality while the latter benefits from lower latency. Recently, late-interaction models have been proposed to realize more favorable latency-quality tradeoffs, by using a DE structure followed by a lightweight scorer based on query and document token embeddings. However, these lightweight scorers are often hand-crafted, and there is no understanding of their approximation power; further, such scorers require access to individual document token embeddings, which imposes an increased latency and storage burden. In this paper, we propose novel learnable late-interaction models (LITE) that resolve these issues. Theoretically, we prove that LITE is a universal approximator of continuous scoring functions, even for relatively small embedding dimension. Empirically, LITE outperforms previous late-interaction models such as ColBERT on both in-domain and zero-shot re-ranking tasks. For instance, experiments on MS MARCO passage re-ranking show that LITE not only yields a model with better generalization, but also lowers latency and requires 0.25x storage compared to ColBERT.

Graph-based data present unique challenges and opportunities for machine learning. Graph Neural Networks (GNNs), and especially those algorithms that capture graph topology through message passing for neighborhood aggregation, have been a leading solution. However, these networks often require substantial computational resources and may not optimally leverage the information contained in the graph's topology, particularly for large-scale or complex graphs. We propose Topology Coordinate Neural Network (TCNN) and Directional Virtual Coordinate Neural Network (DVCNN) as novel and efficient alternatives to message passing GNNs, that directly leverage the graph's topology, sidestepping the computational challenges presented by competing algorithms. Our proposed methods can be viewed as a reprise of classic techniques for graph embedding for neural network feature engineering, but they are novel in that our embedding techniques leverage ideas in Graph Coordinates (GC) that are lacking in current practice. Experimental results, benchmarked against the Open Graph Benchmark Leaderboard, demonstrate that TCNN and DVCNN achieve competitive or superior performance to message passing GNNs. For similar levels of accuracy and ROC-AUC, TCNN and DVCNN need far fewer trainable parameters than contenders of the OGBN Leaderboard. The proposed TCNN architecture requires fewer parameters than any neural network method currently listed in the OGBN Leaderboard for both OGBN-Proteins and OGBN-Products datasets. Conversely, our methods achieve higher performance for a similar number of trainable parameters. By providing an efficient and effective alternative to message passing GNNs, our work expands the toolbox of techniques for graph-based machine learning., Comment: This paper is submitted and will be published on Big Data Conference 2023, Data-driven Science for Graphs: Algorithms, Architectures, and Application workshop

As with many machine learning problems, the progress of image generation methods hinges on good evaluation metrics. One of the most popular is the Frechet Inception Distance (FID). FID estimates the distance between a distribution of Inception-v3 features of real images, and those of images generated by the algorithm. We highlight important drawbacks of FID: Inception's poor representation of the rich and varied content generated by modern text-to-image models, incorrect normality assumptions, and poor sample complexity. We call for a reevaluation of FID's use as the primary quality metric for generated images. We empirically demonstrate that FID contradicts human raters, it does not reflect gradual improvement of iterative text-to-image models, it does not capture distortion levels, and that it produces inconsistent results when varying the sample size. We also propose an alternative new metric, CMMD, based on richer CLIP embeddings and the maximum mean discrepancy distance with the Gaussian RBF kernel. It is an unbiased estimator that does not make any assumptions on the probability distribution of the embeddings and is sample efficient. Through extensive experiments and analysis, we demonstrate that FID-based evaluations of text-to-image models may be unreliable, and that CMMD offers a more robust and reliable assessment of image quality., Comment: Code is available at: https://github.com/google-research/google-research/tree/master/cmmd

Law-enforcement investigations aimed at preventing attacks by violent extremists have become increasingly important for public safety. The problem is exacerbated by the massive data volumes that need to be scanned to identify complex behaviors of extremists and groups. Automated tools are required to extract information to respond queries from analysts, continually scan new information, integrate them with past events, and then alert about emerging threats. We address challenges in investigative pattern detection and develop an Investigative Pattern Detection Framework for Counterterrorism (INSPECT). The framework integrates numerous computing tools that include machine learning techniques to identify behavioral indicators and graph pattern matching techniques to detect risk profiles/groups. INSPECT also automates multiple tasks for large-scale mining of detailed forensic biographies, forming knowledge networks, and querying for behavioral indicators and radicalization trajectories. INSPECT targets human-in-the-loop mode of investigative search and has been validated and evaluated using an evolving dataset on domestic jihadism., Comment: 9 pages, 4 figures

Network data analytics are now at the core of almost every networking solution. Nonetheless, limited access to networking data has been an enduring challenge due to many reasons including complexity of modern networks, commercial sensitivity, privacy and regulatory constraints. In this work, we explore how to leverage recent advancements in Diffusion Models (DM) to generate synthetic network traffic data. We develop an end-to-end framework - NetDiffus that first converts one-dimensional time-series network traffic into two-dimensional images, and then synthesizes representative images for the original data. We demonstrate that NetDiffus outperforms the state-of-the-art traffic generation methods based on Generative Adversarial Networks (GANs) by providing 66.4% increase in fidelity of the generated data and 18.1% increase in downstream machine learning tasks. We evaluate NetDiffus on seven diverse traffic traces and show that utilizing synthetic data significantly improves traffic fingerprinting, anomaly detection and traffic classification., Comment: 9 pages and 8 figures

Modern text-to-image generation models produce high-quality images that are both photorealistic and faithful to the text prompts. However, this quality comes at significant computational cost: nearly all of these models are iterative and require running sampling multiple times with large models. This iterative process is needed to ensure that different regions of the image are not only aligned with the text prompt, but also compatible with each other. In this work, we propose a light-weight approach to achieving this compatibility between different regions of an image, using a Markov Random Field (MRF) model. We demonstrate the effectiveness of this method on top of the latent token-based Muse text-to-image model. The MRF richly encodes the compatibility among image tokens at different spatial locations to improve quality and significantly reduce the required number of Muse sampling steps. Inference with the MRF is significantly cheaper, and its parameters can be quickly learned through back-propagation by modeling MRF inference as a differentiable neural-network layer. Our full model, MarkovGen, uses this proposed MRF model to both speed up Muse by 1.5X and produce higher quality images by decreasing undesirable image artifacts.

Large neural models (such as Transformers) achieve state-of-the-art performance for information retrieval (IR). In this paper, we aim to improve distillation methods that pave the way for the resource-efficient deployment of such models in practice. Inspired by our theoretical analysis of the teacher-student generalization gap for IR models, we propose a novel distillation approach that leverages the relative geometry among queries and documents learned by the large teacher model. Unlike existing teacher score-based distillation methods, our proposed approach employs embedding matching tasks to provide a stronger signal to align the representations of the teacher and student models. In addition, it utilizes query generation to explore the data manifold to reduce the discrepancies between the student and the teacher where training data is sparse. Furthermore, our analysis also motivates novel asymmetric architectures for student models which realizes better embedding alignment without increasing online inference cost. On standard benchmarks like MSMARCO, we show that our approach successfully distills from both dual-encoder (DE) and cross-encoder (CE) teacher models to 1/10th size asymmetric students that can retain 95-97% of the teacher performance.

Mixup is a regularization technique that artificially produces new samples using convex combinations of original training points. This simple technique has shown strong empirical performance, and has been heavily used as part of semi-supervised learning techniques such as mixmatch~\citep{berthelot2019mixmatch} and interpolation consistent training (ICT)~\citep{verma2019interpolation}. In this paper, we look at Mixup through a \emph{representation learning} lens in a semi-supervised learning setup. In particular, we study the role of Mixup in promoting linearity in the learned network representations. Towards this, we study two questions: (1) how does the Mixup loss that enforces linearity in the \emph{last} network layer propagate the linearity to the \emph{earlier} layers?; and (2) how does the enforcement of stronger Mixup loss on more than two data points affect the convergence of training? We empirically investigate these properties of Mixup on vision datasets such as CIFAR-10, CIFAR-100 and SVHN. Our results show that supervised Mixup training does not make \emph{all} the network layers linear; in fact the \emph{intermediate layers} become more non-linear during Mixup training compared to a network that is trained \emph{without} Mixup. However, when Mixup is used as an unsupervised loss, we observe that all the network layers become more linear resulting in faster training convergence.

Learning dynamics of collectively moving agents such as fish or humans is an active field in research. Due to natural phenomena such as occlusion and change of illumination, the multi-object methods tracking such dynamics might lose track of the agents where that might result fragmentation in the constructed trajectories. Here, we present an extended deep autoencoder (DA) that we train only on fully observed segments of the trajectories by defining its loss function as the Hadamard product of a binary indicator matrix with the absolute difference between the outputs and the labels. The trajectories of the agents practicing collective motion is low-rank due to mutual interactions and dependencies between the agents that we utilize as the underlying pattern that our Hadamard deep autoencoder (HDA) codes during its training. The performance of our HDA is compared with that of a low-rank matrix completion scheme in the context of fragmented trajectory reconstruction., Comment: 21 Pages, 5 figures, submitted into Pattern Recognition

In this paper, we propose a novel method to make distance predictions in real-world social networks. As predicting missing distances is a difficult problem, we take a two-stage approach. Structural parameters for families of synthetic networks are first estimated from a small set of measurements of a real-world network and these synthetic networks are then used to pre-train the predictive neural networks. Since our model first searches for the most suitable synthetic graph parameters which can be used as an "oracle" to create arbitrarily large training data sets, we call our approach "Oracle Search Pre-training" (OSP). For example, many real-world networks exhibit a Power law structure in their node degree distribution, so a Power law model can provide a foundation for the desired oracle to generate synthetic pre-training networks, if the appropriate Power law graph parameters can be estimated. Accordingly, we conduct experiments on real-world Facebook, Email, and Train Bombing networks and show that OSP outperforms models without pre-training, models pre-trained with inaccurate parameters, and other distance prediction schemes such as Low-rank Matrix Completion. In particular, we achieve a prediction error of less than one hop with only 1% of sampled distances from the social network. OSP can be easily extended to other domains such as random networks by choosing an appropriate model to generate synthetic training data, and therefore promises to impact many different network learning problems., Comment: KDD conference 2021

Negative sampling schemes enable efficient training given a large number of classes, by offering a means to approximate a computationally expensive loss function that takes all labels into account. In this paper, we present a new connection between these schemes and loss modification techniques for countering label imbalance. We show that different negative sampling schemes implicitly trade-off performance on dominant versus rare labels. Further, we provide a unified means to explicitly tackle both sampling bias, arising from working with a subset of all labels, and labeling bias, which is inherent to the data due to label imbalance. We empirically verify our findings on long-tail classification and retrieval benchmarks., Comment: To appear in ICML 2021

Deep learning has yielded extraordinary results in vision and natural language processing, but this achievement comes at a cost. Most models require enormous resources during training, both in terms of computation and in human labeling effort. We show that we can identify informative and diverse subsets of data that lead to deep learning models with similar performance as the ones trained with the original dataset. Prior methods have exploited diversity and uncertainty in submodular objective functions for choosing subsets. In addition to these measures, we show that balancing constraints on predicted class labels and decision boundaries are beneficial. We propose a novel formulation of these constraints using matroids, an algebraic structure that generalizes linear independence in vector spaces, and present an efficient greedy algorithm with constant approximation guarantees. We outperform competing baselines on standard classification datasets such as CIFAR-10, CIFAR-100, ImageNet, as well as long-tailed datasets such as CIFAR-100-LT., Comment: Added error bars to the experiments

We propose a kernelized classification layer for deep networks. Although conventional deep networks introduce an abundance of nonlinearity for representation (feature) learning, they almost universally use a linear classifier on the learned feature vectors. We advocate a nonlinear classification layer by using the kernel trick on the softmax cross-entropy loss function during training and the scorer function during testing. However, the choice of the kernel remains a challenge. To tackle this, we theoretically show the possibility of optimizing over all possible positive definite kernels applicable to our problem setting. This theory is then used to device a new kernelized classification layer that learns the optimal kernel function for a given problem automatically within the deep network itself. We show the usefulness of the proposed nonlinear classification layer on several datasets and tasks.

Real-world classification problems typically exhibit an imbalanced or long-tailed label distribution, wherein many labels are associated with only a few samples. This poses a challenge for generalisation on such labels, and also makes na\"ive learning biased towards dominant labels. In this paper, we present two simple modifications of standard softmax cross-entropy training to cope with these challenges. Our techniques revisit the classic idea of logit adjustment based on the label frequencies, either applied post-hoc to a trained model, or enforced in the loss during training. Such adjustment encourages a large relative margin between logits of rare versus dominant labels. These techniques unify and generalise several recent proposals in the literature, while possessing firmer statistical grounding and empirical performance., Comment: Published as a conference paper in ICLR 2021

We tackle the panoptic segmentation problem with a conditional random field (CRF) model. Panoptic segmentation involves assigning a semantic label and an instance label to each pixel of a given image. At each pixel, the semantic label and the instance label should be compatible. Furthermore, a good panoptic segmentation should have a number of other desirable properties such as the spatial and color consistency of the labeling (similar looking neighboring pixels should have the same semantic label and the instance label). To tackle this problem, we propose a CRF model, named Bipartite CRF or BCRF, with two types of random variables for semantic and instance labels. In this formulation, various energies are defined within and across the two types of random variables to encourage a consistent panoptic segmentation. We propose a mean-field-based efficient inference algorithm for solving the CRF and empirically show its convergence properties. This algorithm is fully differentiable, and therefore, BCRF inference can be included as a trainable module in a deep network. In the experimental evaluation, we quantitatively and qualitatively show that the BCRF yields superior panoptic segmentation results in practice.

Minimum resolution set and associated metric dimension provide the basis for unique and systematic labeling of nodes of a graph using distances to a set of landmarks. Such a distance vector set, however, may not be unique to the graph and does not allow for its exact construction. The concept of construction set is presented, which facilitates the unique representation of nodes and the graph as well as its exact construction. Link dimension is the minimum number of landmarks in a construction set. Results presented include necessary conditions for a set of landmarks to be a construction set, bounds for link dimension, and guidelines for transforming a resolution set to a construction set., Comment: 8pages, 1 figure, in review

For many important network types (e.g., sensor networks in complex harsh environments and social networks) physical coordinate systems (e.g., Cartesian), and physical distances (e.g., Euclidean), are either difficult to discern or inapplicable. Accordingly, coordinate systems and characterizations based on hop-distance measurements, such as Topology Preserving Maps (TPMs) and Virtual-Coordinate (VC) systems are attractive alternatives to Cartesian coordinates for many network algorithms. Herein, we present an approach to recover geometric and topological properties of a network with a small set of distance measurements. In particular, our approach is a combination of shortest path (often called geodesic) recovery concepts and low-rank matrix completion, generalized to the case of hop-distances in graphs. Results for sensor networks embedded in 2-D and 3-D spaces, as well as a social networks, indicates that the method can accurately capture the network connectivity with a small set of measurements. TPM generation can now also be based on various context appropriate measurements or VC systems, as long as they characterize different nodes by distances to small sets of random nodes (instead of a set of global anchors). The proposed method is a significant generalization that allows the topology to be extracted from a random set of graph shortest paths, making it applicable in contexts such as social networks where VC generation may not be possible., Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1712.10063

For many important network types (e.g., sensor networks in complex harsh environments and social networks) physical coordinate systems (e.g., Cartesian), and physical distances (e.g., Euclidean), are either difficult to discern or inappropriate. Accordingly, Topology Preserving Maps (TPMs) derived from a Virtual-Coordinate (VC) system representing the distance to a small set of anchors is an attractive alternative to physical coordinates for many network algorithms. Herein, we present an approach, based on the theory of low-rank matrix completion, to recover geometric properties of a network with only partial information about the VCs of nodes. In particular, our approach is a combination of geodesic recovery concepts and low-rank matrix completion, generalized to the case of hop-distances in graphs. Distortion evaluated using the change of distance among node pairs shows that even with up to 40% to 60% of random coordinates missing, accurate TPMs can be obtained. TPM generation can now also be based on different context appropriate VC systems or measurements as long as they characterize each node with distances to a small set of random nodes (instead of a global set of anchors). The proposed method is a significant generalization that allows the topology to be extracted from a random set of graph geodesics, making it applicable in contexts such as social networks where VC generation may not be possible., Comment: A more recent version uploaded

This paper proposes the use of graph pattern matching for investigative graph search, which is the process of searching for and prioritizing persons of interest who may exhibit part or all of a pattern of suspicious behaviors or connections. While there are a variety of applications, our principal motivation is to aid law enforcement in the detection of homegrown violent extremists. We introduce investigative simulation, which consists of several necessary extensions to the existing dual simulation graph pattern matching scheme in order to make it appropriate for intelligence analysts and law enforcement officials. Specifically, we impose a categorical label structure on nodes consistent with the nature of indicators in investigations, as well as prune or complete search results to ensure sensibility and usefulness of partial matches to analysts. Lastly, we introduce a natural top-k ranking scheme that can help analysts prioritize investigative efforts. We demonstrate performance of investigative simulation on a real-world large dataset., Comment: 8 pages, 6 figures. Paper to appear in the Fosint-SI 2016 conference proceedings in conjunction with the 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining ASONAM 2016

Recent works on zero-shot learning make use of side information such as visual attributes or natural language semantics to define the relations between output visual classes and then use these relationships to draw inference on new unseen classes at test time. In a novel extension to this idea, we propose the use of visual prototypical concepts as side information. For most real-world visual object categories, it may be difficult to establish a unique prototype. However, in cases such as traffic signs, brand logos, flags, and even natural language characters, these prototypical templates are available and can be leveraged for an improved recognition performance. The present work proposes a way to incorporate this prototypical information in a deep learning framework. Using prototypes as prior information, the deepnet pipeline learns the input image projections into the prototypical embedding space subject to minimization of the final classification loss. Based on our experiments with two different datasets of traffic signs and brand logos, prototypical embeddings incorporated in a conventional convolutional neural network improve the recognition performance. Recognition accuracy on the Belga logo dataset is especially noteworthy and establishes a new state-of-the-art. In zero-shot learning scenarios, the same system can be directly deployed to draw inference on unseen classes by simply adding the prototypical information for these new classes at test time. Thus, unlike earlier approaches, testing on seen and unseen classes is handled using the same pipeline, and the system can be tuned for a trade-off of seen and unseen class performance as per task requirement. Comparison with one of the latest works in the zero-shot learning domain yields top results on the two datasets mentioned above., Comment: 12 Pages, 6 Figures, 2 Tables, in British Machine Vision Conference (BMVC), 2015

We address the problem of semantic segmentation using deep learning. Most segmentation systems include a Conditional Random Field (CRF) to produce a structured output that is consistent with the image's visual features. Recent deep learning approaches have incorporated CRFs into Convolutional Neural Networks (CNNs), with some even training the CRF end-to-end with the rest of the network. However, these approaches have not employed higher order potentials, which have previously been shown to significantly improve segmentation performance. In this paper, we demonstrate that two types of higher order potential, based on object detections and superpixels, can be included in a CRF embedded within a deep network. We design these higher order potentials to allow inference with the differentiable mean field algorithm. As a result, all the parameters of our richer CRF model can be learned end-to-end with our pixelwise CNN classifier. We achieve state-of-the-art segmentation performance on the PASCAL VOC benchmark with these trainable higher order potentials., Comment: ECCV 2016

Pixel-level labelling tasks, such as semantic segmentation, play a central role in image understanding. Recent approaches have attempted to harness the capabilities of deep learning techniques for image recognition to tackle pixel-level labelling tasks. One central issue in this methodology is the limited capacity of deep learning techniques to delineate visual objects. To solve this problem, we introduce a new form of convolutional neural network that combines the strengths of Convolutional Neural Networks (CNNs) and Conditional Random Fields (CRFs)-based probabilistic graphical modelling. To this end, we formulate mean-field approximate inference for the Conditional Random Fields with Gaussian pairwise potentials as Recurrent Neural Networks. This network, called CRF-RNN, is then plugged in as a part of a CNN to obtain a deep network that has desirable properties of both CNNs and CRFs. Importantly, our system fully integrates CRF modelling with CNNs, making it possible to train the whole deep network end-to-end with the usual back-propagation algorithm, avoiding offline post-processing methods for object delineation. We apply the proposed method to the problem of semantic image segmentation, obtaining top results on the challenging Pascal VOC 2012 segmentation benchmark., Comment: This paper is published in IEEE ICCV 2015

Symmetric Positive Definite (SPD) matrices have become popular to encode image information. Accounting for the geometry of the Riemannian manifold of SPD matrices has proven key to the success of many algorithms. However, most existing methods only approximate the true shape of the manifold locally by its tangent plane. In this paper, inspired by kernel methods, we propose to map SPD matrices to a high dimensional Hilbert space where Euclidean geometry applies. To encode the geometry of the manifold in the mapping, we introduce a family of provably positive definite kernels on the Riemannian manifold of SPD matrices. These kernels are derived from the Gaussian ker- nel, but exploit different metrics on the manifold. This lets us extend kernel-based algorithms developed for Euclidean spaces, such as SVM and kernel PCA, to the Riemannian manifold of SPD matrices. We demonstrate the benefits of our approach on the problems of pedestrian detection, ob- ject categorization, texture analysis, 2D motion segmentation and Diffusion Tensor Imaging (DTI) segmentation., Comment: Published in CVPR 2013. arXiv admin note: substantial text overlap with arXiv:1412.0265

We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these spaces, most existing shape classification algorithms resort to nearest neighbor methods and to learning distances on shape spaces. Here, we propose to map shapes on Kendall's shape manifold to a high dimensional Hilbert space where Euclidean geometry applies. To this end, we introduce a kernel on this manifold that permits such a mapping, and prove its positive definiteness. This kernel lets us extend kernel-based algorithms developed for Euclidean spaces, such as SVM, MKL and kernel PCA, to the shape manifold. We demonstrate the benefits of our approach over the state-of-the-art methods on shape classification, clustering and retrieval., Comment: Published in ICCV 2013

We tackle the problem of optimizing over all possible positive definite radial kernels on Riemannian manifolds for classification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However, the number of known positive definite kernels on manifolds remain very limited. Furthermore, most kernels typically depend on at least one parameter that needs to be tuned for the problem at hand. A poor choice of kernel, or of parameter value, may yield significant performance drop-off. Here, we show that positive definite radial kernels on the unit n-sphere, the Grassmann manifold and Kendall's shape manifold can be expressed in a simple form whose parameters can be automatically optimized within a support vector machine framework. We demonstrate the benefits of our kernel learning algorithm on object, face, action and shape recognition., Comment: Published in CVPR 2014

In this paper, we develop an approach to exploiting kernel methods with manifold-valued data. In many computer vision problems, the data can be naturally represented as points on a Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, usual Euclidean computer vision and machine learning algorithms yield inferior results on such data. In this paper, we define Gaussian radial basis function (RBF)-based positive definite kernels on manifolds that permit us to embed a given manifold with a corresponding metric in a high dimensional reproducing kernel Hilbert space. These kernels make it possible to utilize algorithms developed for linear spaces on nonlinear manifold-valued data. Since the Gaussian RBF defined with any given metric is not always positive definite, we present a unified framework for analyzing the positive definiteness of the Gaussian RBF on a generic metric space. We then use the proposed framework to identify positive definite kernels on two specific manifolds commonly encountered in computer vision: the Riemannian manifold of symmetric positive definite matrices and the Grassmann manifold, i.e., the Riemannian manifold of linear subspaces of a Euclidean space. We show that many popular algorithms designed for Euclidean spaces, such as support vector machines, discriminant analysis and principal component analysis can be generalized to Riemannian manifolds with the help of such positive definite Gaussian kernels.

Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g, support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as we will show- is universal, which limits their ability to approximate a target function arbitrarily well. Here, we introduce several positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing.

Emerging collaborative Peer-to-Peer (P2P) systems require discovery and utilization of diverse, multi-attribute, distributed, and dynamic groups of resources to achieve greater tasks beyond conventional file and processor cycle sharing. Collaborations involving application specific resources and dynamic quality of service goals are stressing current P2P architectures. Salient features and desirable characteristics of collaborative P2P systems are highlighted. Resource advertising, selecting, matching, and binding, the critical phases in these systems, and their associated challenges are reviewed using examples from distributed collaborative adaptive sensing systems, cloud computing, and mobile social networks. State-of-the-art resource discovery/aggregation solutions are compared with respect to their architecture, lookup overhead, load balancing, etc., to determine their ability to meet the goals and challenges of each critical phase. Incentives, trust, privacy, and security issues are also discussed, as they will ultimately determine the success of a collaborative P2P system. Open issues and research opportunities that are essential to achieve the true potential of collaborative P2P systems are discussed., Comment: Keywords - Collaborative applications, multi-attribute resources, peer-to-peer, resource discovery; H. M. N. D. Bandara and A. P. Jayasumana, "Collaborative applications over peer-to-peer systems - Challenges and solutions," Peer-to-Peer Networking and Applications, Springer, 2012