Preprint

# Learning to Separate Domains in Generalized Zero-Shot and Open Set Learning: a probabilistic perspective

Authors:
Preprints and early-stage research may not have been peer reviewed yet.
To read the file of this research, you can request a copy directly from the authors.

## Abstract

This paper studies the problem of domain division problem which aims to segment instances drawn from different probabilistic distributions. Such a problem exists in many previous recognition tasks, such as Open Set Learning (OSL) and Generalized Zero-Shot Learning (G-ZSL), where the testing instances come from either seen or novel/unseen classes of different probabilistic distributions. Previous works focused on either only calibrating the confident prediction of classifiers of seen classes (W-SVM), or taking unseen classes as outliers. In contrast, this paper proposes a probabilistic way of directly estimating and fine-tuning the decision boundary between seen and novel/unseen classes. In particular, we propose a domain division algorithm of learning to split the testing instances into known, unknown and uncertain domains, and then conduct recognize tasks in each domain. Two statistical tools, namely, bootstrapping and Kolmogorov-Smirnov (K-S) Test, for the first time, are introduced to discover and fine-tune the decision boundary of each domain. Critically, the uncertain domain is newly introduced in our framework to adopt those instances whose domain cannot be predicted confidently. Extensive experiments demonstrate that our approach achieved the state-of-the-art performance on OSL and G-ZSL benchmarks.

## No file available

ResearchGate has not been able to resolve any citations for this publication.
Conference Paper
Full-text available
Article
Full-text available
The number of categories for action recognition is growing rapidly and it has become increasingly hard to label sufficient training data for learning conventional models for all categories. Instead of collecting ever more data and labelling them exhaustively for all categories, an attractive alternative approach is "zeroshot learning" (ZSL). To that end, in this study we construct a mapping between visual features and a semantic descriptor of each action category, allowing new categories to be recognised in the absence of any visual training data. Existing ZSL studies focus primarily on still images, and attribute-based semantic representations. In this work, we explore word-vectors as the shared semantic space to embed videos and category labels for ZSL action recognition. This is a more challenging problem than existing ZSL of still images and/or attributes, because the mapping between the semantic space and video space-time features of actions is more complex and harder to learn for the purpose of generalising over any cross-category domain shift. To solve this generalisation problem in ZSL action recognition, we investigate a series of synergistic improvements to the standard ZSL pipeline. First, we enhance significantly the semantic space mapping by proposing manifold-regularised regression and data augmentation strategies. Second, we evaluate two existing post processing strategies (transductive self-training and hubness correction), and show that they are complementary. We evaluate extensively our model on a wide range of human action datasets including HMDB51, UCF101, OlympicSports, CCV and TRECVID MED 13. The results demonstrate that our approach achieves the state-of-the-art zero-shot action recognition performance with a simple and efficient pipeline, and without supervised annotation of attributes.
Conference Paper
Full-text available
Image classification has advanced significantly in recent years with the availability of large-scale image sets. However, fine-grained classification remains a major challenge due to the annotation cost of large numbers of fine-grained categories. This project shows that compelling classification performance can be achieved on such categories even without labeled training data. Given image and class embeddings, we learn a compatibility function such that matching embeddings are assigned a higher score than mismatching ones; zero-shot classification of an image proceeds by finding the label yielding the highest joint compatibility score. We use state-of-the-art image features and focus on different supervised attributes and unsuper-vised output embeddings either derived from hierarchies or learned from unlabeled text corpora. We establish a substantially improved state-of-the-art on the Animals with Attributes and Caltech-UCSD Birds datasets. Most encourag-ingly, we demonstrate that purely unsupervised output em-beddings (learned from Wikipedia and improved with fine-grained text) achieve compelling results, even outperform-ing the previous supervised state-of-the-art. By combining different output embeddings, we further improve results.
Article
Full-text available
Attributes act as intermediate representations that enable parameter sharing between classes, a must when training data is scarce. We propose to view attribute-based image classification as a label-embedding problem: each class is embedded in the space of attribute vectors. We introduce a function that measures the compatibility between an image and a label embedding. The parameters of this function are learned on a training set of labeled samples to ensure that, given an image, the correct classes rank higher than the incorrect ones. Results on the Animals With Attributes and Caltech-UCSD-Birds datasets show that the proposed framework outperforms the standard Direct Attribute Prediction baseline in a zero-shot learning scenario. Label embedding enjoys a built-in ability to leverage alternative sources of information instead of or in addition to attributes, such as e.g. class hierarchies or textual descriptions. Moreover, label embedding encompasses the whole range of learning settings from zero-shot learning to regular learning with a large number of labeled examples.
Article
Full-text available
Most existing zero-shot learning approaches exploit transfer learning via an intermediate-level semantic representation shared between an annotated auxiliary dataset and a target dataset with different classes and no annotation. A projection from a low-level feature space to the semantic representation space is learned from the auxiliary dataset and is applied without adaptation to the target dataset. In this paper we identify two inherent limitations with these approaches. First, due to having disjoint and potentially unrelated classes, the projection functions learned from the auxiliary dataset/domain are biased when applied directly to the target dataset/domain. We call this problem the projection domain shift problem and propose a novel framework, transductive multi-view embedding, to solve it. The second limitation is the prototype sparsity problem which refers to the fact that for each target class, only a single prototype is available for zero-shot learning given a semantic representation. To overcome this problem, a novel heterogeneous multi-view hypergraph label propagation method is formulated for zero-shot learning in the transductive embedding space. It effectively exploits the complementary information offered by different semantic representations and takes advantage of the manifold structures of multiple representation spaces in a coherent manner. We demonstrate through extensive experiments that the proposed approach (1) rectifies the projection shift between the auxiliary and target domains, (2) exploits the complementarity of multiple semantic representations, (3) significantly outperforms existing methods for both zero-shot and N-shot recognition on three image and video benchmark datasets, and (4) enables novel cross-view annotation tasks.
Article
Full-text available
Real-world tasks in computer vision often touch upon open set recognition: multi-class recognition with incomplete knowledge of the world and many unknown inputs. Recent work on this problem has proposed a model incorporating an open space risk term to account for the space beyond the reasonable support of known classes. This paper extends the general idea of open space risk limiting classification to accommodate non-linear classifiers in a multi-class setting. We introduce a new open set recognition model called compact abating probability (CAP), where the probability of class membership decreases in value (abates) as points move from known data toward open space. We show that CAP models improve open set recognition for multiple algorithms. Leveraging the CAP formulation, we go on to describe the novel Weibull-calibrated SVM (W-SVM) algorithm, which combines the useful properties of statistical extreme value theory for score calibration with one-class and binary support vector machines. Our experiments show that the W-SVM is significantly better for open set object detection and OCR problems when compared to the state-of-the-art for the same tasks.
Article
Full-text available
Several recent publications have proposed methods for mapping images into continuous semantic embedding spaces. In some cases the semantic embedding space is trained jointly with the image transformation, while in other cases the semantic embedding space is established independently by a separate task, such as a natural language processing task on a text corpus, and then the image transformation into that space is learned in a second stage. Proponents of these image embedding systems have stressed their advantages over the traditional n-way classification framing of image understanding, particularly in terms of the promise of zero-shot learning -- the ability to correctly annotate images of previously unseen object categories. Here we propose a simple method for constructing an image embedding system from any existing n-way image classification mechanism and any existing semantic embedding space which contains the n class labels in its vocabulary. Our method maps images into the semantic embedding space via convex combination of the class label embedding vectors, and requires no additional learning. We show that this simple and direct method confers many of the advantages associated with more complex image embedding schemes, and indeed outperforms state of the art methods on the ImageNet zero-shot learning task.
Article
Full-text available
To date, almost all experimental evaluations of machine learning-based recognition algorithms in computer vision have taken the form of "closed set" recognition, whereby all testing classes are known at training time. A more realistic scenario for vision applications is "open set" recognition, where incomplete knowledge of the world is present at training time, and unknown classes can be submitted to an algorithm during testing. This paper explores the nature of open set recognition and formalizes its definition as a constrained minimization problem. The open set recognition problem is not well addressed by existing algorithms because it requires strong generalization. As a step toward a solution, we introduce a novel "1-vs-set machine," which sculpts a decision space from the marginal distances of a 1-class or binary SVM with a linear kernel. This methodology applies to several different applications in computer vision where open set recognition is a challenging problem, including object recognition and face verification. We consider both in this work, with large scale cross-dataset experiments performed over the Caltech 256 and ImageNet sets, as well as face matching experiments performed over the Labeled Faces in the Wild set. The experiments highlight the effectiveness of machines adapted for open set evaluation compared to existing 1-class and binary SVMs for the same tasks.
Conference Paper
Full-text available
We study the problem of object classification when training and test classes are disjoint, i.e. no training examples of the target classes are available. This setup has hardly been studied in computer vision research, but it is the rule rather than the exception, because the world contains tens of thousands of different object classes and for only a very few of them image, collections have been formed and annotated with suitable class labels. In this paper, we tackle the problem by introducing attribute-based classification. It performs object detection based on a human-specified high-level description of the target objects instead of training images. The description consists of arbitrary semantic attributes, like shape, color or even geographic information. Because such properties transcend the specific learning task at hand, they can be pre-learned, e.g. from image datasets unrelated to the current task. Afterwards, new classes can be detected based on their attribute representation, without the need for a new training phase. In order to evaluate our method and to facilitate research in this area, we have assembled a new largescale dataset, "Animals with Attributes", of over 30,000 animal images that match the 50 classes in Osherson's classic table of how strongly humans associate 85 semantic attributes with animal classes. Our experiments show that by using an attribute layer it is indeed possible to build a learning object detection system that does not require any training images of the target classes.
Conference Paper
Full-text available
For many KDD applications, such as detecting criminal activities in E-commerce, finding the rare instances or the outliers, can be more interesting than finding the common patterns. Existing work in outlier detection regards being an outlier as a binary property. In this paper, we contend that for many scenarios, it is more meaningful to assign to each object a degree of being an outlier. This degree is called the local outlier factor (LOF) of an object. It is local in that the degree depends on how isolated the object is with respect to the surrounding neighborhood. We give a detailed formal analysis showing that LOF enjoys many desirable properties. Using real-world datasets, we demonstrate that LOF can be used to find outliers which appear to be meaningful, but can otherwise not be identified with existing approaches. Finally, a careful performance evaluation of our algorithm confirms we show that our approach of finding local outliers can be practical.
Article
Full-text available
Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a “simple” subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified value between 0 and 1. We propose a method to approach this problem by trying to estimate a function f that is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabeled data.
Article
Full-text available
In this paper, we define meta-recognition, a performance prediction method for recognition algorithms, and examine the theoretical basis for its post-recognition score analysis form through the use of the statistical extreme value theory (EVT). The ability to predict the performance of a recognition system based on its outputs for each match instance is desirable for a number of important reasons, including automatic threshold selection for determining matches and non-matches, and automatic algorithm selection or weighting for multi-algorithm fusion. The emerging body of literature on post-recognition score analysis has been largely constrained to biometrics, where the analysis has been shown to successfully complement or replace image quality metrics as a predictor. We develop a new statistical predictor based upon the Weibull distribution, which produces accurate results on a per instance recognition basis across different recognition problems. Experimental results are provided for two different face recognition algorithms, a fingerprint recognition algorithm, a SIFT-based object recognition system, and a content-based image retrieval system.
Article
Full-text available
Under fairly general assumptions on the underlying distribution function, the bootstrap process, pertaining to the sample $q$-quantile, converges weakly in $D_\mathbb{R}$ to the standard Brownian motion. Furthermore, weak convergence of a smoothed bootstrap quantile estimate is proved which entails that in this particular case the smoothed bootstrap estimate outperforms the nonsmoothed one.
Article
Full-text available
Kolmogorov's goodness-of-fit measure, D_n , for a sample CDF has consistently been set aside for methods such as the D^+_n or D^-_n of Smirnov, primarily, it seems, because of the difficulty of computing the distribution of D_n . As far as we know, no easy way to compute that distribution has ever been provided in the 70+ years since Kolmogorov's fundamental paper. We provide one here, a C procedure that provides Pr(D_n < d) with 13-15 digit accuracy for n ranging from 2 to at least 16000. We assess the (rather slow) approach to limiting form, and because computing time can become excessive for probabilities>.999 with n's of several thousand, we provide a quick approximation that gives accuracy to the 7th digit for such cases.
Conference Paper
Zero-shot learning consists in learning how to recognize new concepts by just having a description of them. Many sophisticated approaches have been proposed to address the challenges this problem comprises. In this paper we describe a zero-shot learning approach that can be implemented in just one line of code, yet it is able to outperform state of the art approaches on standard datasets. The approach is based on a more general framework which models the relationships between features, attributes, and classes as a two linear layers network, where the weights of the top layer are not learned but are given by the environment. We further provide a learning bound on the generalization error of this kind of approaches, by casting them as domain adaptation methods. In experiments carried out on three standard real datasets, we found that our approach is able to perform significantly better than the state of art on all of them, obtaining a ratio of improvement up to 17%17$backslash$%.
Article
Due to the importance of zero-shot learning, the number of proposed approaches has increased steadily recently. We argue that it is time to take a step back and to analyze the status quo of the area. The purpose of this paper is three-fold. First, given the fact that there is no agreed upon zero-shot learning benchmark, we first define a new benchmark by unifying both the evaluation protocols and data splits. This is an important contribution as published results are often not comparable and sometimes even flawed due to, e.g. pre-training on zero-shot test classes. Second, we compare and analyze a significant number of the state-of-the-art methods in depth, both in the classic zero-shot setting but also in the more realistic generalized zero-shot setting. Finally, we discuss limitations of the current status of the area which can be taken as a basis for advancing it.
Conference Paper
Conference Paper
We investigate the problem of generalized zero-shot learning (GZSL). GZSL relaxes the unrealistic assumption in conventional zero-shot learning (ZSL) that test data belong only to unseen novel classes. In GZSL, test data might also come from seen classes and the labeling space is the union of both types of classes. We show empirically that a straightforward application of classifiers provided by existing ZSL approaches does not perform well in the setting of GZSL. Motivated by this, we propose a surprisingly simple but effective method to adapt ZSL approaches for GZSL. The main idea is to introduce a calibration factor to calibrate the classifiers for both seen and unseen classes so as to balance two conflicting forces: recognizing data from seen classes and those from unseen ones. We develop a new performance metric called the Area Under Seen-Unseen accuracy Curve to characterize this trade-off. We demonstrate the utility of this metric by analyzing existing ZSL approaches applied to the generalized setting. Extensive empirical studies reveal strengths and weaknesses of those approaches on three well-studied benchmark datasets, including the large-scale ImageNet with more than 20,000 unseen categories. We complement our comparative studies in learning methods by further establishing an upper bound on the performance limit of GZSL. In particular, our idea is to use class-representative visual features as the idealized semantic embeddings. We show that there is a large gap between the performance of existing approaches and the performance limit, suggesting that improving the quality of class semantic embeddings is vital to improving ZSL.
Article
Modern visual recognition systems are often limited in their ability to scale to large numbers of object categories. This limitation is in part due to the increasing difficulty of acquiring sufficient training data in the form of labeled images as the number of object categories grows. One remedy is to leverage data from other sources - such as text data - both to train visual models and to constrain their predictions. In this paper we present a new deep visual-semantic embedding model trained to identify visual objects using both labeled image data as well as semantic information gleaned from unannotated text. We demonstrate that this model matches state-of-the-art performance on the 1000-class ImageNet object recognition challenge while making more semantically reasonable errors, and also show that the semantic information can be exploited to make predictions about tens of thousands of image labels not observed during training. Semantic knowledge improves such zero-shot predictions achieving hit rates of up to 18% across thousands of novel labels never seen by the visual model.
Article
The test is based on the maximum difference between an empirical and a hypothetical cumulative distribution. Percentage points are tabled, and a lower bound to the power function is charted. Confidence limits for a cumulative distribution are described. Examples are given. Indications that the test is superior to the chi-square test are cited.
Conference Paper
We consider the problem of semi-supervised bootstrap learning for scene categorization. Existing semi-supervised approaches are typically unreliable and face semantic drift because the learning task is under-constrained. This is primarily because they ignore the strong interactions that often exist between scene categories, such as the common attributes shared across categories as well as the attributes which make one scene different from another. The goal of this paper is to exploit these relationships and constrain the semi-supervised learning problem. For example, the knowledge that an image is an auditorium can improve labeling of amphitheaters by enforcing constraint that an amphitheater image should have more circular structures than an auditorium image. We propose constraints based on mutual exclusion, binary attributes and comparative attributes and show that they help us to constrain the learning problem and avoid semantic drift. We demonstrate the effectiveness of our approach through extensive experiments, including results on a very large dataset of one million images.
Conference Paper
Recent work has shown that visual attributes are a powerful approach for applications such as recognition, image description and retrieval. However, fusing multiple attribute scores - as required during multi-attribute queries or similarity searches - presents a significant challenge. Scores from different attribute classifiers cannot be combined in a simple way; the same score for different attributes can mean different things. In this work, we show how to construct normalized “multi-attribute spaces” from raw classifier outputs, using techniques based on the statistical Extreme Value Theory. Our method calibrates each raw score to a probability that the given attribute is present in the image. We describe how these probabilities can be fused in a simple way to perform more accurate multiattribute searches, as well as enable attribute-based similarity searches. A significant advantage of our approach is that the normalization is done after-the-fact, requiring neither modification to the attribute classification system nor ground truth attribute annotations. We demonstrate results on a large data set of nearly 2 million face images and show significant improvements over prior work. We also show that perceptual similarity of search results increases by using contextual attributes.
Article
We study the problem of object recognition for categories for which we have no training examples, a task also called zero--data or zero-shot learning. This situation has hardly been studied in computer vision research, even though it occurs frequently; the world contains tens of thousands of different object classes, and image collections have been formed and suitably annotated for only a few of them. To tackle the problem, we introduce attribute-based classification: Objects are identified based on a high-level description that is phrased in terms of semantic attributes, such as the object's color or shape. Because the identification of each such property transcends the specific learning task at hand, the attribute classifiers can be prelearned independently, for example, from existing image data sets unrelated to the current task. Afterward, new classes can be detected based on their attribute representation, without the need for a new training phase. In this paper, we also introduce a new data set, Animals with Attributes, of over 30,000 images of 50 animal classes, annotated with 85 semantic attributes. Extensive experiments on this and two more data sets show that attribute-based classification indeed is able to categorize images without access to any training images of the target classes.
Article
A simple method for testing the probability that a set of numbers is a sample from a known distribution consists of comparing the empirical cumulative distribution function of the sample, Sn(x), with the known cumulative distribution function F(x). Both Dn = maximum {Sn(x) – F{x)} and Dn* = maximum | Sn(x) – F(x) | are random variables, independent of the special form of F(x), if F(x) is continuous. This paper contains more extensive tables of the percentage points in the distributions of Dn and Dn* than have been published previously. These values are obtained by empirical modification of a known asymptotic formula.* This study was supported in part by funds granted to Ohio State University by the Research Foundation for aid in fundamental research. The author acknowledges the assistance of Nelson Prentiss, Vincent Donato, Milton Glanz, and Richard Thomas in carrying out numerical computations.
Conference Paper
Remarkable performance has been reported to recognize single object classes. Scalability to large numbers of classes however remains an important challenge for today's recognition methods. Several authors have promoted knowledge transfer between classes as a key ingredient to address this challenge. However, in previous work the decision which knowledge to transfer has required either manual supervision or at least a few training examples limiting the scalability of these approaches. In this work we explicitly address the question of how to automatically decide which information to transfer between classes without the need of any human intervention. For this we tap into linguistic knowledge bases to provide the semantic link between sources (what) and targets (where) of knowledge transfer. We provide a rigorous experimental evaluation of different knowledge bases and state-of-the-art techniques from Natural Language Processing which goes far beyond the limited use of language in related work. We also give insights into the applicability (why) of different knowledge sources and similarity measures for knowledge transfer.
Article
We discuss the following problem given a random sample X = (X 1, X 2,…, X n) from an unknown probability distribution F, estimate the sampling distribution of some prespecified random variable R(X, F), on the basis of the observed data x. (Standard jackknife theory gives an approximate mean and variance in the case R(X, F) = $$\theta \left( {\hat F} \right) - \theta \left( F \right)$$, θ some parameter of interest.) A general method, called the “bootstrap”, is introduced, and shown to work satisfactorily on a variety of estimation problems. The jackknife is shown to be a linear approximation method for the bootstrap. The exposition proceeds by a series of examples: variance of the sample median, error rates in a linear discriminant analysis, ratio estimation, estimating regression parameters, etc.
Towards open world recognition
• Abhijit Bendale
• Terrance Boult
Abhijit Bendale and Terrance Boult. Towards open world recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1893-1902, 2015. 2
Zero-shot learning through cross-modal transfer
• Richard Socher
• Milind Ganjoo
• D Christopher
• Andrew Manning
• Ng
Richard Socher, Milind Ganjoo, Christopher D Manning, and Andrew Ng. Zero-shot learning through cross-modal transfer. In Advances in neural information processing systems, pp. 935-943, 2013. (document), 3.3, 3.3, 6.3