In this paper we study the problem of image representation learning without human annotation. By following the principles of self-supervision, we build a convolutional neural network (CNN) that can be trained to solve Jigsaw puzzles as a pretext task, which requires no manual labeling, and then later repurposed to solve object classification and detection. To maintain the compatibility across tasks we introduce the context-free network (CFN), a siamese-ennead CNN. The CFN takes image tiles as input and explicitly limits the receptive field (or context) of its early processing units to one tile at a time. We show that the CFN includes fewer parameters than AlexNet while preserving the same semantic learning capabilities. By training the CFN to solve Jigsaw puzzles, we learn both a feature mapping of object parts as well as their correct spatial arrangement. Our experimental evaluations show that the learned features capture semantically relevant content. Our proposed method for learning visual representations outperforms state of the art methods in several transfer learning benchmarks.
If the data structure suggests that data points might concentrate around a manifold, then techniques can be employed @cite_18 @cite_10 . This representation allows to map directly smooth variations of the factors to smooth variations of the observations. Some of the issues with manifold learning techniques are that they might require computing nearest neighbors (which scales quadratically with the number of samples) and that they need a sufficiently high density of samples around the manifold (and this becomes more difficult to achieve with high-dimensional manifolds).
@cite_18 @cite_10
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In this paper, we study a family of semisupervised learning algorithms for “aligning” different data sets that are characterized by the same underlying manifold. The optimizations of these algorithms are based on graphs that provide a discretized approximation to the manifold. Partial alignments of the data sets—obtained from prior knowledge of their manifold structure or from pairwise correspondences of subsets of labeled examples— are completed by integrating supervised signals with unsupervised frameworks for manifold learning. As an illustration of this semisupervised setting, we show how to learn mappings between different data sets of images that are parameterized by the same underlying modes of variability (e.g., pose and viewing angle). The curse of dimensionality in these problems is overcome by exploiting the low dimensional structure of image manifolds. Recently, manifold learning has been widely exploited in pattern recognition, data analysis, and machine learning. This paper presents a novel framework, called Riemannian manifold learning (RML), based on the assumption that the input high-dimensional data lie on an intrinsically low-dimensional Riemannian manifold. The main idea is to formulate the dimensionality reduction problem as a classical problem in Riemannian geometry, that is, how to construct coordinate charts for a given Riemannian manifold? We implement the Riemannian normal coordinate chart, which has been the most widely used in Riemannian geometry, for a set of unorganized data points. First, two input parameters (the neighborhood size k and the intrinsic dimension d) are estimated based on an efficient simplicial reconstruction of the underlying manifold. Then, the normal coordinates are computed to map the input high-dimensional data into a low- dimensional space. Experiments on synthetic data, as well as real-world images, demonstrate that our algorithm can learn intrinsic geometric structures of the data, preserve radial geodesic distances, and yield regular embeddings. Previous efforts in hashing intend to preserve data variance or pairwise affinity, but neither is adequate in capturing the manifold structures hidden in most visual data. In this paper, we tackle this problem by reconstructing the locally linear structures of manifolds in the binary Hamming space, which can be learned by locality-sensitive sparse coding. We cast the problem as a joint minimization of reconstruction error and quantization loss, and show that, despite its NP-hardness, a local optimum can be obtained efficiently via alternative optimization. Our method distinguishes itself from existing methods in its remarkable ability to extract the nearest neighbors of the query from the same manifold, instead of from the ambient space. On extensive experiments on various image benchmarks, our results improve previous state-of-the-art by 28-74 typically, and 627 on the Yale face data. Many applications in computer vision and pattern recognition involve drawing inferences on certain manifold-valued parameters. In order to develop accurate inference algorithms on these manifolds we need to a) understand the geometric structure of these manifolds b) derive appropriate distance measures and c) develop probability distribution functions (pdf) and estimation techniques that are consistent with the geometric structure of these manifolds. In this paper, we consider two related manifolds - the Stiefel manifold and the Grassmann manifold, which arise naturally in several vision applications such as spatio-temporal modeling, affine invariant shape analysis, image matching and learning theory. We show how accurate statistical characterization that reflects the geometry of these manifolds allows us to design efficient algorithms that compare favorably to the state of the art in these very different applications. In particular, we describe appropriate distance measures and parametric and non-parametric density estimators on these manifolds. These methods are then used to learn class conditional densities for applications such as activity recognition, video based face recognition and shape classification.