Human action recognition is one of the important fields of computer vision and machine learning. Although various methods have been proposed for 3D action recognition, some of which are basic and some use deep learning, the need of basic methods based on generalized eigenvalue problem is sensed for action recognition. This need is especially sensed because of having similar basic methods in the field of face recognition such as eigenfaces and Fisherfaces. In this paper, we propose Roweisposes which uses Roweis discriminant analysis for generalized subspace learning. This method includes Fisherposes, eigenposes, supervised eigenposes, and double supervised eigenposes as its special cases. Roweisposes is a family of infinite number of action recongition methods which learn a discriminative subspace for embedding the body poses. Experiments on the TST, UTKinect, and UCFKinect datasets verify the effectiveness of the proposed method for action recognition.

We propose a new embedding method, named Quantile-Quantile Embedding (QQE), for distribution transformation, manifold embedding, and image embedding with the ability to choose the embedding distribution. QQE, which uses the concept of quantile-quantile plot from visual statistical tests, can transform the distribution of data to any theoretical desired distribution or empirical reference sample. Moreover, QQE gives the user a choice of embedding distribution in embedding manifold of data into the low dimensional embedding space. It can also be used for modifying the embedding distribution of different dimensionality reduction methods, either basic or deep ones, for better representation or visualization of data. We propose QQE in both unsupervised and supervised manners. QQE can also transform the distribution to either the exact reference distribution or shape of the reference distribution; and one of its many applications is better discrimination of classes. Our experiments on different synthetic and image datasets show the effectiveness of the proposed embedding method.

Standard reinforcement learning (RL) algorithms assume that the observation of the next state comes instantaneously and at no cost. In a wide variety of sequential decision making tasks ranging from medical treatment to scientific discovery, however, multiple classes of state observations are possible, each of which has an associated cost. We propose the active measure RL framework (Amrl) as an initial solution to this problem where the agent learns to maximize the costed return, which we define as the discounted sum of rewards minus the sum of observation costs. Our empirical evaluation demonstrates that Amrl-Q agents are able to learn a policy and state estimator in parallel during online training. During training the agent naturally shifts from its reliance on costly measurements of the environment to its state estimator in order to increase its reward. It does this without harm to the learned policy. Our results show that the Amrl-Q agent learns at a rate similar to standard Q-learning and Dyna-Q. Critically, by utilizing an active strategy, Amrl-Q achieves a higher costed return.

We present a new method which generalizes subspace learning based on eigenvalue and generalized eigenvalue problems. This method, Roweis Discriminant Analysis (RDA), is named after Sam Roweis to whom the field of subspace learning owes significantly. RDA is a family of infinite number of algorithms where Principal Component Analysis (PCA), Supervised PCA (SPCA), and Fisher Discriminant Analysis (FDA) are special cases. One of the extreme special cases, which we name Double Supervised Discriminant Analysis (DSDA), uses the labels twice; it is novel and has not appeared elsewhere. We propose a dual for RDA for some special cases. We also propose kernel RDA, generalizing kernel PCA, kernel SPCA, and kernel FDA, using both dual RDA and representation theory. Our theoretical analysis explains previously known facts such as why SPCA can use regression but FDA cannot, why PCA and SPCA have duals but FDA does not, why kernel PCA and kernel SPCA use kernel trick but kernel FDA does not, and why PCA is the best linear method for reconstruction. Roweisfaces and kernel Roweisfaces are also proposed generalizing eigenfaces, Fisherfaces, supervised eigenfaces, and their kernel variants. We also report experiments showing the effectiveness of RDA and kernel RDA on some benchmark datasets.

This paper proposes a new subspace learning method, named Quantized Fisher Discriminant Analysis (QFDA), which makes use of both machine learning and information theory. There is a lack of literature for combination of machine learning and information theory and this paper tries to tackle this gap. QFDA finds a subspace which discriminates the uniformly quantized images in the Discrete Cosine Transform (DCT) domain at least as well as discrimination of non-quantized images by Fisher Discriminant Analysis (FDA) while the images have been compressed. This helps the user to throw away the original images and keep the compressed images instead without noticeable loss of classification accuracy. We propose a cost function whose minimization can be interpreted as rate-distortion optimization in information theory. We also propose quantized Fisherfaces for facial analysis in QFDA.

Despite the advances of deep learning in specific tasks using images, the principled assessment of image fidelity and similarity is still a critical ability to develop. As it has been shown that Mean Squared Error (MSE) is insufficient for this task, other measures have been developed with one of the most effective being Structural Similarity Index (SSIM). Such measures can be used for subspace learning but existing methods in machine learning, such as Principal Component Analysis (PCA), are based on Euclidean distance or MSE and thus cannot properly capture the structural features of images. In this paper, we define an image structure subspace which discriminates different types of image distortions. We propose Image Structural Component Analysis (ISCA) and also kernel ISCA by using SSIM, rather than Euclidean distance, in the formulation of PCA. This paper provides a bridge between image quality assessment and manifold learning opening a broad new area for future research.

However, for the problem of image quality assessment, these are not promising measure. In this paper, we introduce the concept of an image structure manifold which captures image structure features and discriminates image distortions. We propose a new manifold learning method, Locally Linear Image Structural Embedding (LLISE), and kernel LLISE for learning this manifold. The LLISE is inspired by Locally Linear Embedding (LLE) but uses SSIM rather than MSE. This paper builds a bridge between manifold learning and image fidelity assessment and it can open a new area for future investigations.

This is a detailed tutorial paper which explains the Fisher discriminant Analysis (FDA) and kernel FDA. We start with projection and reconstruction. Then, one- and multi-dimensional FDA subspaces are covered. Scatters in two- and then multi-classes are explained in FDA. Then, we discuss on the rank of the scatters and the dimensionality of the subspace. A real-life example is also provided for interpreting FDA. Then, possible singularity of the scatter is discussed to introduce robust FDA. PCA and FDA directions are also compared. We also prove that FDA and linear discriminant analysis are equivalent. Fisher forest is also introduced as an ensemble of fisher subspaces useful for handling data with different features and dimensionality. Afterwards, kernel FDA is explained for both one- and multi-dimensional subspaces with both two- and multi-classes. Finally, some simulations are performed on AT&T face dataset to illustrate FDA and compare it with PCA.

This tutorial explains Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) as two fundamental classification methods in statistical and probabilistic learning. We start with the optimization of decision boundary on which the posteriors are equal. Then, LDA and QDA are derived for binary and multiple classes. The estimation of parameters in LDA and QDA are also covered. Then, we explain how LDA and QDA are related to metric learning, kernel principal component analysis, Mahalanobis distance, logistic regression, Bayes optimal classifier, Gaussian naive Bayes, and likelihood ratio test. We also prove that LDA and Fisher discriminant analysis are equivalent. We finally clarify some of the theoretical concepts with simulations we provide.

This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection directions, properties of the projection matrix, reconstruction error minimization, and we connect to auto-encoder. Then, PCA with singular value decomposition, dual PCA, and kernel PCA are covered. SPCA using both scoring and Hilbert-Schmidt independence criterion are explained. Kernel SPCA using both direct and dual approaches are then introduced. We cover all cases of projection and reconstruction of training and out-of-sample data. Finally, some simulations are provided on Frey and AT&T face datasets for verifying the theory in practice.