A semi-supervised learning framework using the feedforward-designed convolutional neural networks (FF-CNNs) is proposed for image classification in this work. One unique property of FF-CNNs is that no backpropagation is used in model parameters determination. Since unlabeled data may not always enhance semi-supervised learning, we define an effective quality score and use it to select a subset of unlabeled data in the training process. We conduct experiments on the MNIST, SVHN, and CIFAR-10 datasets, and show that the proposed semi-supervised FF-CNN solution outperforms the CNN trained by backpropagation (BP-CNN) when the amount of labeled data is reduced. Furthermore, we develop an ensemble system that combines the output decision vectors of different semi-supervised FF-CNNs to boost classification accuracy. The ensemble systems can achieve further performance gains on all three benchmarking datasets.
The construction of conv layers is realized by multi-stage Saab transforms @cite_19 . The Saab transform is a variant of the principal component analysis (PCA) with a constant bias vector to annihilate activation's nonlinearity. The Saab transform can reduce feature redundancy in the spectral domain, yet there still exists correlation among spatial dimensions of the same spectral component. This is especially true in low-frequency spectral components. Thus, a channel-wise PCA (C-PCA) was proposed in @cite_1 to reduce spatial redundancy of Saab coefficients furthermore. Since the construction of conv layers is unsupervised, they can be fully adopted in an SSL system.
@cite_19 @cite_1
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The model parameters of convolutional neural networks (CNNs) are determined by backpropagation (BP). In this work, we propose an interpretable feedforward (FF) design without any BP as a reference. The FF design adopts a data-centric approach. It derives network parameters of the current layer based on data statistics from the output of the previous layer in a one-pass manner. To construct convolutional layers, we develop a new signal transform, called the Saab (Subspace Approximation with Adjusted Bias) transform. It is a variant of the principal component analysis (PCA) with an added bias vector to annihilate activation's nonlinearity. Multiple Saab transforms in cascade yield multiple convolutional layers. As to fully-connected (FC) layers, we construct them using a cascade of multi-stage linear least squared regressors (LSRs). The classification and robustness (against adversarial attacks) performances of BP- and FF-designed CNNs applied to the MNIST and the CIFAR-10 datasets are compared. Finally, we comment on the relationship between BP and FF designs. High correlation among the neighboring pixels both spatially and spectrally in a multispectral image makes it necessary to use an efficient data transformation approach before performing pan-sharpening. Wavelets and principal component analysis (PCA) methods have been a popular choice for spatial and spectral transformations, respectively. Current PCA-based pan-sharpening methods make an assumption that the first principal component (PC) of high variance is an ideal choice for replacing or injecting it with high spatial details from the high-resolution histogram-matched panchromatic (PAN) image. This paper presents a combined adaptive PCA-contourlet approach for pan-sharpening, where the adaptive PCA is used to reduce the spectral distortion and the use of nonsubsampled contourlets for spatial transformation in pan-sharpening is incorporated to overcome the limitation of the wavelets in representing the directional information efficiently and capturing intrinsic geometrical structures of the objects. The efficiency of the presented method is tested by performing pan-sharpening of the high-resolution (IKONOS and QuickBird) and the medium-resolution (Landsat-7 Enhanced Thematic Mapper Plus) datasets. The evaluation of the pan-sharpened images using global validation indexes reveal that the adaptive PCA approach helps reducing the spectral distortion, and its merger with contourlets provides better fusion results. Abstract Being motivated by the multilayer RECOS (REctified-COrrelations on a Sphere) transform, we develop a data-driven Saak (Subspace approximation with augmented kernels) transform in this work. The Saak transform consists of three steps: (1) building the optimal linear subspace approximation with orthonormal bases using the second-order statistics of input vectors, (2) augmenting each transform kernel with its negative, (3) applying the rectified linear unit (ReLU) to the transform output. The Karhunen-Loeve transform (KLT) is used in the first step. The integration of Steps 2 and 3 is powerful since they resolve the sign confusion problem, remove the rectification loss and allow a straightforward implementation of the inverse Saak transform at the same time. Multiple Saak transforms are cascaded to transform images of a larger size. All Saak transform kernels are derived from the second-order statistics of input random vectors in a one-pass feedforward manner. Neither data labels nor backpropagation is used in kernel determination. Multi-stage Saak transforms offer a family of joint spatial-spectral representations between two extremes; namely, the full spatial-domain representation and the full spectral-domain representation. We select Saak coefficients of higher discriminant power to form a feature vector for pattern recognition, and use the MNIST dataset classification problem as an illustrative example. In this study, we propose the application of principal components analysis (PCA) to scale-spaces. PCA is a standard method used in computer vision. The translation of an input image into scale-space is a continuous operation, which requires the extension of conventional finite matrix- based PCA to an infinite number of dimensions. In this study, we use spectral decomposition to resolve this infinite eigenproblem by integration and we propose an approximate solution based on polynomial equations. To clarify its eigensolutions, we apply spectral decomposition to the Gaussian scale-space and scale-normalized Laplacian of Gaussian (LoG) space. As an application of this proposed method, we introduce a method for generating Gaussian blur images and scale-normalized LoG images, where we demonstrate that the accuracy of these images can be very high when calculating an arbitrary scale using a simple linear combination. We also propose a new Scale Invariant Feature Transform (SIFT) detector as a more practical example.