Recently, a number of works have studied clustering strategies that combine classical clustering algorithms and deep learning methods. These approaches follow either a sequential way, where a deep representation is learned using a deep autoencoder before obtaining clusters with k-means, or a simultaneous way, where deep representation and clusters are learned jointly by optimizing a single objective function. Both strategies improve clustering performance, however the robustness of these approaches is impeded by several deep autoencoder setting issues, among which the weights initialization, the width and number of layers or the number of epochs. To alleviate the impact of such hyperparameters setting on the clustering performance, we propose a new model which combines the spectral clustering and deep autoencoder strengths in an ensemble learning framework. Extensive experiments on various benchmark datasets demonstrate the potential and robustness of our approach compared to state-of-the art deep clustering methods.
Within this framework, classical dimensionality reduction approaches, e.g., Principal Component Analysis (PCA), have been widely considered for the embedding task. However, the linear nature of such techniques makes it challenging to infer faithful representations of real-world data, which typically lie on highly non-linear manifolds. This motivates the investigation of deep learning models (e.g., autoencoders, convolutional neural networks), which have been shown so far to be successful in extracting highly non-linear features from complex data, such as text, images or graphs @cite_16 @cite_44 @cite_12 .
@cite_44 @cite_16 @cite_12
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Mining useful clusters from high dimensional data have received significant attention of the computer vision and pattern recognition community in the recent years. Linear and nonlinear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with three different problems: high computational complexity (usually associated with the nuclear norm minimization), nonconvexity (for matrix factorization methods), and susceptibility to gross corruptions in the data. In this paper, we propose a principal component analysis (PCA) based solution that overcomes these three issues and approximates a low-rank recovery method for high dimensional datasets. We target the low-rank recovery by enforcing two types of graph smoothness assumptions, one on the data samples and the other on the features by designing a convex optimization problem. The resulting algorithm is fast, efficient, and scalable for huge datasets with O(n log(n)) computational complexity in the number of data samples. It is also robust to gross corruptions in the dataset as well as to the model parameters. Clustering experiments on 7 benchmark datasets with different types of corruptions and background separation experiments on 3 video datasets show that our proposed model outperforms 10 state-of-the-art dimensionality reduction models. Our theoretical analysis proves that the proposed model is able to recover approximate low-rank representations with a bounded error for clusterable data. Recently deep Convolutional Neural Networks have been successfully applied in many computer vision tasks and achieved promising results. So some works have introduced the deep learning into face anti-spoofing. However, most approaches just use the final fully-connected layer to distinguish the real and fake faces. Inspired by the idea of each convolutional kernel can be regarded as a part filter, we extract the deep partial features from the convolutional neural network (CNN) to distinguish the real and fake faces. In our prosed approach, the CNN is fine-tuned firstly on the face spoofing datasets. Then, the block principle component analysis (PCA) method is utilized to reduce the dimensionality of features that can avoid the over-fitting problem. Lastly, the support vector machine (SVM) is employed to distinguish the real the real and fake faces. The experiments evaluated on two public available databases, Replay-Attack and CASIA, show the proposed method can obtain satisfactory results compared to the state-of-the-art methods. When faced with high-dimensional data, one often uses principal component analysis (PCA) for dimension reduction. Classical PCA constructs a set of uncorrelated variables, which correspond to eigenvectors of the sample covariance matrix. However, it is well-known that this covariance matrix is strongly affected by anomalous observations. It is therefore necessary to apply robust methods that are resistant to possible outliers. Li and Chen [J. Am. Stat. Assoc. 80 (1985) 759] proposed a solution based on projection pursuit (PP). The idea is to search for the direction in which the projected observations have the largest robust scale. In subsequent steps, each new direction is constrained to be orthogonal to all previous directions. This method is very well suited for high-dimensional data, even when the number of variables p is higher than the number of observations n. However, the algorithm of Li and Chen has a high computational cost. In the references [C. Croux, A. Ruiz-Gazen, in COMPSTAT: Proceedings in Computational Statistics 1996, Physica-Verlag, Heidelberg, 1996, pp. 211–217; C. Croux and A. Ruiz-Gazen, High Breakdown Estimators for Principal Components: the Projection-Pursuit Approach Revisited, 2000, submitted for publication.], a computationally much more attractive method is presented, but in high dimensions (large p) it has a numerical accuracy problem and still consumes much computation time. In this paper, we construct a faster two-step algorithm that is more stable numerically. The new algorithm is illustrated on a data set with four dimensions and on two chemometrical data sets with 1200 and 600 dimensions. The paper addresses large scale image retrieval with short vector representations. We study dimensionality reduction by Principal Component Analysis (PCA) and propose improvements to its different phases. We show and explicitly exploit relations between i) mean subtraction and the negative evidence, i.e., a visual word that is mutually missing in two descriptions being compared, and ii) the axis de-correlation and the co-occurrences phenomenon. Finally, we propose an effective way to alleviate the quantization artifacts through a joint dimensionality reduction of multiple vocabularies. The proposed techniques are simple, yet significantly and consistently improve over the state of the art on compact image representations. Complementary experiments in image classification show that the methods are generally applicable.