Predictable Feature Analysis (PFA) (Richthofer, Wiskott, ICMLA 2015) is an algorithm that performs dimensionality reduction on high dimensional input signal. It extracts those subsignals that are most predictable according to a certain prediction model. We refer to these extracted signals as predictable features. In this work we extend the notion of PFA to take supplementary information into account for improving its predictions. Such information can be a multidimensional signal like the main input to PFA, but is regarded external. That means it won't participate in the feature extraction - no features get extracted or composed of it. Features will be exclusively extracted from the main input such that they are most predictable based on themselves and the supplementary information. We refer to this enhanced PFA as PFAx (PFA extended). Even more important than improving prediction quality is to observe the effect of supplementary information on feature selection. PFAx transparently provides insight how the supplementary information adds to prediction quality and whether it is valuable at all. Finally we show how to invert that relation and can generate the supplementary information such that it would yield a certain desired outcome of the main signal. We apply this to a setting inspired by reinforcement learning and let the algorithm learn how to control an agent in an environment. With this method it is feasible to locally optimize the agent's state, i.e. reach a certain goal that is near enough. We are preparing a follow-up paper that extends this method such that also global optimization is feasible.
A related SFA-inspired approach for RL is Contingent Feature Analysis (CFA) @cite_11 . The main difference to the PFAx based approach presented here is that CFA assumes a discrete action set and uses a different selection criterion. PFAx assumes a continuous signal for control -- think of pressing buttons (discrete control) compared to turning a steering wheel or moving levers (continuous control). CFA requires a no-operation (NOP) among the possible actions and then selects features to behave as uncorrelated as possible to NOP induced behavior. Given that continuous control is discretely sampled in digital processing, a comparison of PFAx and CFA would be an interesting exercise in the future, but is not in the scope of this work.
@cite_11
1977814411 2342036932 1897029691 2111616957
Slow Feature Analysis (SFA) extracts slowly varying features from a quickly varying input signal [1]. It has been successfully applied to modeling the visual receptive fields of the cortical neurons. Sufficient experimental results in neuroscience suggest that the temporal slowness principle is a general learning principle in visual perception. In this paper, we introduce the SFA framework to the problem of human action recognition by incorporating the discriminative information with SFA learning and considering the spatial relationship of body parts. In particular, we consider four kinds of SFA learning strategies, including the original unsupervised SFA (U-SFA), the supervised SFA (S-SFA), the discriminative SFA (D-SFA), and the spatial discriminative SFA (SD--SFA), to extract slow feature functions from a large amount of training cuboids which are obtained by random sampling in motion boundaries. Afterward, to represent action sequences, the squared first order temporal derivatives are accumulated over all transformed cuboids into one feature vector, which is termed the Accumulated Squared Derivative (ASD) feature. The ASD feature encodes the statistical distribution of slow features in an action sequence. Finally, a linear support vector machine (SVM) is trained to classify actions represented by ASD features. We conduct extensive experiments, including two sets of control experiments, two sets of large scale experiments on the KTH and Weizmann databases, and two sets of experiments on the CASIA and UT-interaction databases, to demonstrate the effectiveness of SFA for human action recognition. Experimental results suggest that the SFA-based approach (1) is able to extract useful motion patterns and improves the recognition performance, (2) requires less intermediate processing steps but achieves comparable or even better performance, and (3) has good potential to recognize complex multiperson activities. A recently introduced latent feature learning technique for time-varying dynamic phenomena analysis is the so-called slow feature analysis (SFA). SFA is a deterministic component analysis technique for multidimensional sequences that, by minimizing the variance of the first-order time derivative approximation of the latent variables, finds uncorrelated projections that extract slowly varying features ordered by their temporal consistency and constancy. In this paper, we propose a number of extensions in both the deterministic and the probabilistic SFA optimization frameworks. In particular, we derive a novel deterministic SFA algorithm that is able to identify linear projections that extract the common slowest varying features of two or more sequences. In addition, we propose an expectation maximization (EM) algorithm to perform inference in a probabilistic formulation of SFA and similarly extend it in order to handle two and more time-varying data sequences. Moreover, we demonstrate that the probabilistic SFA (EM-SFA) algorithm that discovers the common slowest varying latent space of multiple sequences can be combined with dynamic time warping techniques for robust sequence time-alignment. The proposed SFA algorithms were applied for facial behavior analysis, demonstrating their usefulness and appropriateness for this task. Slow feature analysis (SFA) extracts slowly varying signals from input data and has been used to model complex cells in the primary visual cortex (V1). It transmits information to both ventral and dorsal pathways to process appearance and motion information, respectively. However, SFA only uses slowly varying features for local feature extraction, because they represent appearance information more effectively than motion information. To better utilize temporal information, we propose temporal variance analysis (TVA) as a generalization of SFA. TVA learns a linear transformation matrix that projects multidimensional temporal data to temporal components with temporal variance. Inspired by the function of V1, we learn receptive fields by TVA and apply convolution and pooling to extract local features. Embedded in the improved dense trajectory framework, TVA for action recognition is proposed to: 1) extract appearance and motion features from gray using slow and fast filters, respectively; 2) extract additional motion features using slow filters from horizontal and vertical optical flows; and 3) separately encode extracted local features with different temporal variances and concatenate all the encoded features as final features. We evaluate the proposed TVA features on several challenging data sets and show that both slow and fast features are useful in the low-level feature extraction. Experimental results show that the proposed TVA features outperform the conventional histogram-based features, and excellent results can be achieved by combining all TVA features. This paper proposes a reinforcement ant optimized fuzzy controller (FC) design method, called RAOFC, and applies it to wheeled-mobile-robot wall-following control under reinforcement learning environments. The inputs to the designed FC are range-finding sonar sensors, and the controller output is a robot steering angle. The antecedent part in each fuzzy rule uses interval type-2 fuzzy sets in order to increase FC robustness. No a priori assignment of fuzzy rules is necessary in RAOFC. An online aligned interval type-2 fuzzy clustering (AIT2FC) method is proposed to generate rules automatically. The AIT2FC not only flexibly partitions the input space but also reduces the number of fuzzy sets in each input dimension, which improves controller interpretability. The consequent part of each fuzzy rule is designed using Q-value aided ant colony optimization (QACO). The QACO approach selects the consequent part from a set of candidate actions according to ant pheromone trails and Q-values, both of whose values are updated using reinforcement signals. Simulations and experiments on mobile-robot wall-following control show the effectiveness and efficiency of the proposed RAOFC.