The optimization of functions to find the best solution according to one or several objectives has a central role in many engineering and research fields. Recently, a new family of optimization algorithms, named Quality-Diversity optimization, has been introduced, and contrasts with classic algorithms. Instead of searching for a single solution, Quality-Diversity algorithms are searching for a large collection of both diverse and high-performing solutions. The role of this collection is to cover the range of possible solution types as much as possible, and to contain the best solution for each type. The contribution of this paper is threefold. Firstly, we present a unifying framework of Quality-Diversity optimization algorithms that covers the two main algorithms of this family (Multi-dimensional Archive of Phenotypic Elites and the Novelty Search with Local Competition), and that highlights the large variety of variants that can be investigated within this family. Secondly, we propose algorithms with a new selection mechanism for Quality-Diversity algorithms that outperforms all the algorithms tested in this paper. Lastly, we present a new collection management that overcomes the erosion issues observed when using unstructured collections. These three contributions are supported by extensive experimental comparisons of Quality-Diversity algorithms on three different experimental scenarios.
However, the obligation to discretize the descriptor space may be limiting for some applications, and the uniform random selection may not be suitable for particularly large collections, as it dilutes the selection pressure. Indeed, the uniform random selection of individuals among the collection makes the selection pressure inversely proportional to the number of solutions actually contained in the collection. A simple way to mitigate this limitation is to use a biased selection according to the solution performance or according to its novelty score (like introduced by @cite_19 @cite_50 ). Another direction consists in having a number of cells irrespective of the dimensionality descriptor space, for example by using computational geometry to uniformly partition the high-dimensional descriptor space into a pre-defined number of regions @cite_27 , or by using Hierarchical Spatial Partitioning @cite_59 .
@cite_19 @cite_27 @cite_59 @cite_50
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The effective large-scale properties of materials with random heterogeneities on a small scale are typically determined by the method of representative volumes: A sample of the random material is chosen - the representative volume - and its effective properties are computed by the cell formula. Intuitively, for a fixed sample size it should be possible to increase the accuracy of the method by choosing a material sample which captures the statistical properties of the material particularly well: For example, for a composite material consisting of two constituents, one would select a representative volume in which the volume fraction of the constituents matches closely with their volume fraction in the overall material. Inspired by similar attempts in material science, Le Bris, Legoll, and Minvielle have designed a selection approach for representative volumes which performs remarkably well in numerical examples of linear materials with moderate contrast. In the present work, we provide a rigorous analysis of this selection approach for representative volumes in the context of stochastic homogenization of linear elliptic equations. In particular, we prove that the method essentially never performs worse than a random selection of the material sample and may perform much better if the selection criterion for the material samples is chosen suitably. Current work in object categorization discriminates among objects that typically possess gross differences which are readily apparent. However, many applications require making much finer distinctions. We address an insect categorization problem that is so challenging that even trained human experts cannot readily categorize images of insects considered in this paper. The state of the art that uses visual dictionaries, when applied to this problem, yields mediocre results (16.1 error). Three possible explanations for this are (a) the dictionaries are unsupervised, (b) the dictionaries lose the detailed information contained in each keypoint, and (c) these methods rely on hand-engineered decisions about dictionary size. This paper presents a novel, dictionary-free methodology. A random forest of trees is first trained to predict the class of an image based on individual keypoint descriptors. A unique aspect of these trees is that they do not make decisions but instead merely record evidence-i.e., the number of descriptors from training examples of each category that reached each leaf of the tree. We provide a mathematical model showing that voting evidence is better than voting decisions. To categorize a new image, descriptors for all detected keypoints are “dropped” through the trees, and the evidence at each leaf is summed to obtain an overall evidence vector. This is then sent to a second-level classifier to make the categorization decision. We achieve excellent performance (6.4 error) on the 9-class STONEFLY9 data set. Also, our method achieves an average AUC of 0.921 on the PASCAL06 VOC, which places it fifth out of 21 methods reported in the literature and demonstrates that the method also works well for generic object categorization. This paper explores the power and the limitations of weakly supervised categorization. We present a complete framework that starts with the extraction of various local regions of either discontinuity or homogeneity. A variety of local descriptors can be applied to form a set of feature vectors for each local region. Boosting is used to learn a subset of such feature vectors (weak hypotheses) and to combine them into one final hypothesis for each visual category. This combination of individual extractors and descriptors leads to recognition rates that are superior to other approaches which use only one specific extractor descriptor setting. To explore the limitation of our system, we had to set up new, highly complex image databases that show the objects of interest at varying scales and poses, in cluttered background, and under considerable occlusion. We obtain classification results up to 81 percent ROC-equal error rate on the most complex of our databases. Our approach outperforms all comparable solutions on common databases. Hierarchical conditional random fields have been successfully applied to object segmentation. One reason is their ability to incorporate contextual information at different scales. However, these models do not allow multiple labels to be assigned to a single node. At higher scales in the image, this yields an oversimplified model, since multiple classes can be reasonable expected to appear within one region. This simplified model especially limits the impact that observations at larger scales may have on the CRF model. Neglecting the information at larger scales is undesirable since class-label estimates based on these scales are more reliable than at smaller, noisier scales. To address this problem, we propose a new potential, called harmony potential, which can encode any possible combination of class labels. We propose an effective sampling strategy that renders tractable the underlying optimization problem. Results show that our approach obtains state-of-the-art results on two challenging datasets: Pascal VOC 2009 and MSRC-21. High-dimensional binary classification tasks, e.g. the classification of microarray samples into normal and cancer tissues, usually involve a tuning parameter adjusting the complexity of the applied method to the examined data set. By reporting the performance of the best tuning parameter value only, over-optimistic prediction errors are published. The contribution of this paper is two-fold. Firstly, we develop a new method for tuning bias correction which can be motivated by decision theoretic considerations. The method is based on the decomposition of the unconditional error rate involving the tuning procedure. Our corrected error estimator can be written as a weighted mean of the errors obtained using the different tuning parameter values. It can be interpreted as a smooth version of nested cross-validation (NCV) which is the standard approach for avoiding tuning bias. In contrast to NCV, the weighting scheme of our method guarantees intuitive bounds for the corrected error. Secondly, we suggest to use bias correction methods also to address the bias resulting from the optimal choice of the classification method among several competitors. This method selection bias is particularly relevant to prediction problems in high-dimensional data. In the absence of standards, it is common practice to try several methods successively, which can lead to an optimistic bias similar to the tuning bias. We demonstrate the performance of our method to address both types of bias based on microarray data sets and compare it to existing methods. This study confirms that our approach yields estimates competitive to NCV at a much lower computational price. This paper introduces dynamic object colocation, an optimization to reduce copying costs in generational and other incremental garbage collectors by allocating connected objects together in the same space. Previous work indicates that connected objects belong together because they often have similar lifetimes. Generational collectors, however, allocate all new objects in a nursery space. If these objects are connected to data structures residing in the mature space, the collector must copy them. Our solution is a cooperative optimization that exploits compiler analysis to make runtime allocation decisions. The compiler analysis discovers potential object connectivity for newly allocated objects. It then replaces these allocations with calls to coalloc, which takes an extra parameter called the colocator object. At runtime, coalloc determines the location of the colocator and allocates the new object together with it in either the nursery or mature space. Unlike pretenuring, colocation makes precise per-object allocation decisions and does not require lifetime analysis or allocation site homogeneity. Experimental results for SPEC Java benchmarks using Jikes RVM show colocation can reduce garbage collection time by 50 to 75 , and total performance by up to 1 . This paper provides a novel technique for the analysis of randomized algorithms for optimization problems on metric spaces, by relating the randomized performance ratio for any, metric space to the randomized performance ratio for a set of "simple" metric spaces. We define a notion of a set of metric spaces that probabilistically-approximates another metric space. We prove that any metric space can be probabilistically-approximated by hierarchically well-separated trees (HST) with a polylogarithmic distortion. These metric spaces are "simple" as being: (1) tree metrics; (2) natural for applying a divide-and-conquer algorithmic approach. The technique presented is of particular interest in the context of on-line computation. A large number of on-line algorithmic problems, including metrical task systems, server problems, distributed paging, and dynamic storage rearrangement are defined in terms of some metric space. Typically for these problems, there are linear lower bounds on the competitive ratio of deterministic algorithms. Although randomization against an oblivious adversary has the potential of overcoming these high ratios, very little progress has been made in the analysis. We demonstrate the use of our technique by obtaining substantially improved results for two different on-line problems. We propose using five data-driven community detection approaches from social networks to partition the label space in the task of multi-label classification as an alternative to random partitioning into equal subsets as performed by RAkELd. We evaluate modularity-maximizing using fast greedy and leading eigenvector approximations, infomap, walktrap and label propagation algorithms. For this purpose, we propose to construct a label co-occurrence graph (both weighted and unweighted versions) based on training data and perform community detection to partition the label set. Then, each partition constitutes a label space for separate multi-label classification sub-problems. As a result, we obtain an ensemble of multi-label classifiers that jointly covers the whole label space. Based on the binary relevance and label powerset classification methods, we compare community detection methods to label space divisions against random baselines on 12 benchmark datasets over five evaluation measures. We discover that data-driven approaches are more efficient and more likely to outperform RAkELd than binary relevance or label powerset is, in every evaluated measure. For all measures, apart from Hamming loss, data-driven approaches are significantly better than RAkELd ( α = 0 . 05 ), and at least one data-driven approach is more likely to outperform RAkELd than a priori methods in the case of RAkELd’s best performance. This is the largest RAkELd evaluation published to date with 250 samplings per value for 10 values of RAkELd parameter k on 12 datasets published to date. This paper considers the effect of stochasticity on the quality of convergence of genetic algorithms (GAs). In many problems, the variance of building-block fitness or so-called collateral noise is the major source of variance, and a population-sizing equation is derived to ensure that average signal-to-collateral-noise ratios are favorable to the discrimination of the best building blocks required to solve a problem of bounded deception. The sizing relation is modified to permit the inclusion of other sources of stochasticity, such as the noise of selection, the noise of genetic operators, and the explicit noise or nondeterminism of the objective function. In a test suite of five functions, the sizing relation proves to be a conservative predictor of average correct convergence, as long as all major sources of noise are considered in the sizing calculation. These results suggest how the sizing equation may be viewed as a coarse delineation of a boundary between what a physicist might call two distinct phases of GA behavior. At low population sizes the GA makes many errors of decision, and the quality of convergence is largely left to the vagaries of chance or the serial fixup of flawed results through mutation or other serial injection of diversity. At large population sizes, GAs can reliably discriminate between good and bad building blocks, and parallel processing and recombination of building blocks lead to quick solution of even difficult deceptive problems. Additionally, the paper outlines a number of extensions to this work, including the development of more refined models of the relation between generational average error and ultimate convergence quality, the development of online methods for sizing populations via the estimation of populations via the estimation of population-sizing parameters, and the investigation of populationsizing in the context of niching and other schemes designed for use in problems with high cardinality solution sets. The paper also discusses how these results may one day lead to rigorous proofs of convergence for recombinative G As operating on problems of bounded description. Many state-of-the-art garbage collectors are generational, collecting the young nursery objects more frequently than old objects. These collectors perform well because young objects tend to die at a higher rate than old ones. However, these collectors do not examine object lifetimes with respect to any particular program or allocation site. This paper introduces low-cost object sampling to dynamically determine lifetimes. The sampler marks an object and records its allocation site every n bytes of allocation. The collector then computes per-site nursery survival rates. Sampling degrades total performance by only 3 on average for sample rates of 256 bytes in jikes, a rate at which overall lifetime accuracy compares well with sampling every object. An adaptive collector can use this information to tune itself. For example, pretenuring decreases nursery collection work by allocating new, but long-lived, objects directly into the mature space. We introduce a dynamic pretenuring mechanism that detects long lived allocation sites and pretenures them, given sufficient samples. To react to phase changes, it occasionally backsamples. As with previous online pretenuring, consistent performance improvements on SPECjvm98 benchmarks are difficult to attain since only two combine sufficient allocation load with high nursery survival. Our pretenuring system consistently improves one of these, javac, by 2 to 9 of total time by decreasing collection time by over a factor of two. Sampling and pretenuring overheads slow down all the others. This paper thus provides an efficient sampling mechanism that accurately predicts lifetimes, but leaves open optimization policies that can exploit this information. We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. In this paper we introduce a method for person re-identification based on discriminative, sparse basis expansions of targets in terms of a labeled gallery of known individuals. We propose an iterative extension to sparse discriminative classifiers capable of ranking many candidate targets. The approach makes use of soft- and hard- re-weighting to redistribute energy among the most relevant contributing elements and to ensure that the best candidates are ranked at each iteration. Our approach also leverages a novel visual descriptor which we show to be discriminative while remaining robust to pose and illumination variations. An extensive comparative evaluation is given demonstrating that our approach achieves state-of-the-art performance on single- and multi-shot person re-identification scenarios on the VIPeR, i-LIDS, ETHZ, and CAVIAR4REID datasets. The combination of our descriptor and iterative sparse basis expansion improves state-of-the-art rank-1 performance by six percentage points on VIPeR and by 20 on CAVIAR4REID compared to other methods with a single gallery image per person. With multiple gallery and probe images per person our approach improves by 17 percentage points the state-of-the-art on i-LIDS and by 72 on CAVIAR4REID at rank-1. The approach is also quite efficient, capable of single-shot person re-identification over galleries containing hundreds of individuals at about 30 re-identifications per second. Semantic parts have shown a powerful discriminative capacity for action recognition. However, many existing methods select parts according to predefined heuristic rules, which may cause the correlation among parts to be lost, or do not appropriately consider the cluttered candidate part space, which may result in weak generalizability of the resulting action labels. Therefore, better consideration of the correlation among parts and refinement of the candidate space will lead to a more discriminative action representation. This paper achieves improved performance by more elegantly addressing these two factors. First, considering the cluttered nature of the candidate space, we propose a recursive part elimination strategy for iterative refinement of the candidate parts. In each iteration, we eliminate the parts with the lowest weights, which are deemed to be noise. Second, we measure the discriminative capabilities of the candidates and select the top-ranked parts by applying a maximum margin model, which can alleviate overfitting while simultaneously improving generalizability and correlation extraction. Finally, using the selected parts, we extract mid-level features. We report experiments conducted on four datasets (KTH, Olympic Sports, UCF50, and HMDB51). The proposed method can achieve significant improvements compared with other recent methods, including a lower computational cost, a faster speed, and higher accuracy. By working with high-dimensional representations of covers, modern steganographic methods are capable of preserving a large number of complex dependencies among individual cover elements and thus avoid detection using current best steganalyzers. Inevitably, steganalysis needs to start using high-dimensional feature sets as well. This brings two key problems - construction of good high-dimensional features and machine learning that scales well with respect to dimensionality. Depending on the classifier, high dimensionality may lead to problems with the lack of training data, infeasibly high complexity of training, degradation of generalization abilities, lack of robustness to cover source, and saturation of performance below its potential. To address these problems collectively known as the curse of dimensionality, we propose ensemble classifiers as an alternative to the much more complex support vector machines. Based on the character of the media being analyzed, the steganalyst first puts together a high-dimensional set of diverse "prefeatures" selected to capture dependencies among individual cover elements. Then, a family of weak classifiers is built on random subspaces of the prefeature space. The final classifier is constructed by fusing the decisions of individual classifiers. The advantage of this approach is its universality, low complexity, simplicity, and improved performance when compared to classifiers trained on the entire prefeature set. Experiments with the steganographic algorithms nsF5 and HUGO demonstrate the usefulness of this approach over current state of the art. We report on a novel technique called spatial coupling and its application in the analysis of random constraint satisfaction problems (CSP). Spatial coupling was invented as an engineering construction in the area of error correcting codes where it has resulted in efficient capacity-achieving codes for a wide range of channels. However, this technique is not limited to problems in communications, and can be applied in the much broader context of graphical models. We describe here a general methodology for applying spatial coupling to random constraint satisfaction problems and obtain lower bounds for their (rough) satisfiability threshold. The main idea is to construct a distribution of geometrically structured random K-SAT instances - namely the spatially coupled ensemble - which has the same (rough) satisfiability threshold, and is at the same time algorithmically easier to solve. Then by running well-known algorithms on the spatially coupled ensemble we obtain a lower bound on the (rough) satisfiability threshold of the original ensemble. The method is versatile because one can choose the CSP, there is a certain amount of freedom in the construction of the spatially coupled ensemble, and also in the choice of the algorithm. In this work we focus on random K-SAT but we have also checked that the method is successful for Coloring, NAE-SAT and XOR-SAT. We choose Unit Clause propagation for the algorithm which is analyzed over the spatially coupled instances. For K = 3, for instance, our lower bound is equal to 3.67 which is better than the current bounds in the literature. Similarly, for graph 3-colorability we get a bound of 2.22 which is also better than the current bounds in the literature. Visual search and image retrieval underpin numerous applications, however the task is still challenging predominantly due to the variability of object appearance and ever increasing size of the databases, often exceeding billions of images. Prior art methods rely on aggregation of local scale-invariant descriptors, such as SIFT, via mechanisms including Bag of Visual Words (BoW), Vector of Locally Aggregated Descriptors (VLAD) and Fisher Vectors (FV). However, their performance is still short of what is required. This paper presents a novel method for deriving a compact and distinctive representation of image content called Robust Visual Descriptor with Whitening (RVD-W). It significantly advances the state of the art and delivers world-class performance. In our approach local descriptors are rank-assigned to multiple clusters. Residual vectors are then computed in each cluster, normalized using a direction-preserving normalization function and aggregated based on the neighborhood rank. Importantly, the residual vectors are de-correlated and whitened in each cluster before aggregation, leading to a balanced energy distribution in each dimension and significantly improved performance. We also propose a new post-PCA normalization approach which improves separability between the matching and non-matching global descriptors. This new normalization benefits not only our RVD-W descriptor but also improves existing approaches based on FV and VLAD aggregation. Furthermore, we show that the aggregation framework developed using hand-crafted SIFT features also performs exceptionally well with Convolutional Neural Network (CNN) based features. The RVD-W pipeline outperforms state-of-the-art global descriptors on both the Holidays and Oxford datasets. On the large scale datasets, Holidays1M and Oxford1M, SIFT-based RVD-W representation obtains a mAP of 45.1 and 35.1 percent, while CNN-based RVD-W achieve a mAP of 63.5 and 44.8 percent, all yielding superior performance to the state-of-the-art. Bag of features (BoF) representation has attracted an increasing amount of attention in large scale image processing systems. BoF representation treats images as loose collections of local invariant descriptors extracted from them. The visual codebook is generally constructed by using an unsupervised algorithm such as K-means to quantize the local descriptors into clusters. Images are then represented by the frequency histograms of the codewords contained in them. To build a compact and discriminative codebook, codeword selection has become an indispensable tool. However, most of the existing codeword selection algorithms are supervised and the human labeling may be very expensive. In this paper, we consider the problem of unsupervised codeword selection, and propose a novel algorithm called Discriminative Codeword Selection (DCS). Motivated from recent studies on discriminative clustering, the central idea of our proposed algorithm is to select those codewords so that the cluster structure of the image database can be best respected. Specifically, a multi-output linear function is fitted to model the relationship between the data matrix after codeword selection and the indicator matrix. The most discriminative codewords are thus defined as those leading to minimal fitting error. Experiments on image retrieval and clustering have demonstrated the effectiveness of the proposed method. A major challenge for collaborative filtering (CF) techniques in recommender systems is the data sparsity that is caused by missing and noisy ratings. This problem is even more serious for CF domains where the ratings are expressed numerically, e.g. as 5-star grades. We assume the 5-star ratings are unordered bins instead of ordinal relative preferences. We observe that, while we may lack the information in numerical ratings, we sometimes have additional auxiliary data in the form of binary ratings. This is especially true given that users can easily express themselves with their preferences expressed as likes or dislikes for items. In this paper, we explore how to use these binary auxiliary preference data to help reduce the impact of data sparsity for CF domains expressed in numerical ratings. We solve this problem by transferring the rating knowledge from some auxiliary data source in binary form (that is, likes or dislikes), to a target numerical rating matrix. In particular, our solution is to model both the numerical ratings and ratings expressed as like or dislike in a principled way. We present a novel framework of Transfer by Collective Factorization (TCF), in which we construct a shared latent space collectively and learn the data-dependent effect separately. A major advantage of the TCF approach over the previous bilinear method of collective matrix factorization is that we are able to capture the data-dependent effect when sharing the data-independent knowledge. This allows us to increase the overall quality of knowledge transfer. We present extensive experimental results to demonstrate the effectiveness of TCF at various sparsity levels, and show improvements of our approach as compared to several state-of-the-art methods. Local feature descriptor is an important module for face recognition and those like Gabor and local binary patterns (LBP) have proven effective face descriptors. Traditionally, the form of such local descriptors is predefined in a handcrafted way. In this paper, we propose a method to learn a discriminant face descriptor (DFD) in a data-driven way. The idea is to learn the most discriminant local features that minimize the difference of the features between images of the same person and maximize that between images from different people. In particular, we propose to enhance the discriminative ability of face representation in three aspects. First, the discriminant image filters are learned. Second, the optimal neighborhood sampling strategy is soft determined. Third, the dominant patterns are statistically constructed. Discriminative learning is incorporated to extract effective and robust features. We further apply the proposed method to the heterogeneous (cross-modality) face recognition problem and learn DFD in a coupled way (coupled DFD or C-DFD) to reduce the gap between features of heterogeneous face images to improve the performance of this challenging problem. Extensive experiments on FERET, CAS-PEAL-R1, LFW, and HFB face databases validate the effectiveness of the proposed DFD learning on both homogeneous and heterogeneous face recognition problems. The DFD improves POEM and LQP by about 4.5 percent on LFW database and the C-DFD enhances the heterogeneous face recognition performance of LBP by over 25 percent. We investigate a principle way to progressively mine discriminative object regions using classification networks to address the weakly-supervised semantic segmentation problems. Classification networks are only responsive to small and sparse discriminative regions from the object of interest, which deviates from the requirement of the segmentation task that needs to localize dense, interior and integral regions for pixel-wise inference. To mitigate this gap, we propose a new adversarial erasing approach for localizing and expanding object regions progressively. Starting with a single small object region, our proposed approach drives the classification network to sequentially discover new and complement object regions by erasing the current mined regions in an adversarial manner. These localized regions eventually constitute a dense and complete object region for learning semantic segmentation. To further enhance the quality of the discovered regions by adversarial erasing, an online prohibitive segmentation learning approach is developed to collaborate with adversarial erasing by providing auxiliary segmentation supervision modulated by the more reliable classification scores. Despite its apparent simplicity, the proposed approach achieves 55.0 and 55.7 mean Intersection-over-Union (mIoU) scores on PASCAL VOC 2012 val and test sets, which are the new state-of-the-arts.