Despite significant recent advances in the field of face recognition [10, 14, 15, 17], implementing face verification and recognition efficiently at scale presents serious challenges to current approaches. In this paper we present a system, called FaceNet, that directly learns a mapping from face images to a compact Euclidean space where distances directly correspond to a measure of face similarity. Once this space has been produced, tasks such as face recognition, verification and clustering can be easily implemented using standard techniques with FaceNet embeddings as feature vectors.
The works of @cite_10 @cite_4 @cite_12 all employ a complex system of multiple stages, that combines the output of a deep convolutional network with PCA for dimensionality reduction and an SVM for classification.
@cite_10 @cite_12 @cite_4
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This paper introduces the use of single-layer and deep convolutional networks for remote sensing data analysis. Direct application to multi- and hyperspectral imagery of supervised (shallow or deep) convolutional networks is very challenging given the high input data dimensionality and the relatively small amount of available labeled data. Therefore, we propose the use of greedy layerwise unsupervised pretraining coupled with a highly efficient algorithm for unsupervised learning of sparse features. The algorithm is rooted on sparse representations and enforces both population and lifetime sparsity of the extracted features, simultaneously. We successfully illustrate the expressive power of the extracted representations in several scenarios: classification of aerial scenes, as well as land-use classification in very high resolution or land-cover classification from multi- and hyperspectral images. The proposed algorithm clearly outperforms standard principal component analysis (PCA) and its kernel counterpart (kPCA), as well as current state-of-the-art algorithms of aerial classification, while being extremely computationally efficient at learning representations of data. Results show that single-layer convolutional networks can extract powerful discriminative features only when the receptive field accounts for neighboring pixels and are preferred when the classification requires high resolution and detailed results. However, deep architectures significantly outperform single-layer variants, capturing increasing levels of abstraction and complexity throughout the feature hierarchy. In this paper, we propose a very simple deep learning network for image classification that is based on very basic data processing components: 1) cascaded principal component analysis (PCA); 2) binary hashing; and 3) blockwise histograms. In the proposed architecture, the PCA is employed to learn multistage filter banks. This is followed by simple binary hashing and block histograms for indexing and pooling. This architecture is thus called the PCA network (PCANet) and can be extremely easily and efficiently designed and learned. For comparison and to provide a better understanding, we also introduce and study two simple variations of PCANet: 1) RandNet and 2) LDANet. They share the same topology as PCANet, but their cascaded filters are either randomly selected or learned from linear discriminant analysis. We have extensively tested these basic networks on many benchmark visual data sets for different tasks, including Labeled Faces in the Wild (LFW) for face verification; the MultiPIE, Extended Yale B, AR, Facial Recognition Technology (FERET) data sets for face recognition; and MNIST for hand-written digit recognition. Surprisingly, for all tasks, such a seemingly naive PCANet model is on par with the state-of-the-art features either prefixed, highly hand-crafted, or carefully learned [by deep neural networks (DNNs)]. Even more surprisingly, the model sets new records for many classification tasks on the Extended Yale B, AR, and FERET data sets and on MNIST variations. Additional experiments on other public data sets also demonstrate the potential of PCANet to serve as a simple but highly competitive baseline for texture classification and object recognition. We show an exponential separation between two well-studied models of algebraic computation, namely read-once oblivious algebraic branching programs (ROABPs) and multilinear depth three circuits. In particular we show the following: 1. There exists an explicit n-variate polynomial computable by linear sized multilinear depth three circuits (with only two product gates) such that every ROABP computing it requires 2^ Omega(n) size. 2. Any multilinear depth three circuit computing IMM_ n,d (the iterated matrix multiplication polynomial formed by multiplying d, n * n symbolic matrices) has n^ Omega(d) size. IMM_ n,d can be easily computed by a poly(n,d) sized ROABP. 3. Further, the proof of 2 yields an exponential separation between multilinear depth four and multilinear depth three circuits: There is an explicit n-variate, degree d polynomial computable by a poly(n,d) sized multilinear depth four circuit such that any multilinear depth three circuit computing it has size n^ Omega(d) . This improves upon the quasi-polynomial separation result by Raz and Yehudayoff [2009] between these two models. The hard polynomial in 1 is constructed using a novel application of expander graphs in conjunction with the evaluation dimension measure used previously in Nisan [1991], Raz [2006,2009], Raz and Yehudayoff [2009], and Forbes and Shpilka [2013], while 2 is proved via a new adaptation of the dimension of the partial derivatives measure used by Nisan and Wigderson [1997]. Our lower bounds hold over any field. In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in [11] to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in [4].