Extended Predictable Feature Analysis (PFAx) [Richthofer and Wiskott, 2017] is an extension of PFA [Richthofer and Wiskott, 2015] that allows generating a goal-directed control signal of an agent whose dynamics has previously been learned during a training phase in an unsupervised manner. PFAx hardly requires assumptions or prior knowledge of the agent's sensor or control mechanics, or of the environment. It selects features from a high-dimensional input by intrinsic predictability and organizes them into a reasonably low-dimensional model. While PFA obtains a well predictable model, PFAx yields a model ideally suited for manipulations with predictable outcome. This allows for goal-directed manipulation of an agent and thus for local navigation, i.e. for reaching states where intermediate actions can be chosen by a permanent descent of distance to the goal. The approach is limited when it comes to global navigation, e.g. involving obstacles or multiple rooms. In this article, we extend theoretical results from [Sprekeler and Wiskott, 2008], enabling PFAx to perform stable global navigation. So far, the most widely exploited characteristic of Slow Feature Analysis (SFA) was that slowness yields invariances. We focus on another fundamental characteristics of slow signals: They tend to yield monotonicity and one significant property of monotonicity is that local optimization is sufficient to find a global optimum. We present an SFA-based algorithm that structures an environment such that navigation tasks hierarchically decompose into subgoals. Each of these can be efficiently achieved by PFAx, yielding an overall global solution of the task. The algorithm needs to explore and process an environment only once and can then perform all sorts of navigation tasks efficiently. We support this algorithm by mathematical theory and apply it to different problems.
@cite_8 gives an overview of methods for autonomous RL directly based on sensor-observations. The mainly discussed algorithms are deep auto encoders and SFA. They mention slow distractors (e.g. the position of a slowly moving sun in an outdoor scenario) as a typical issue of SFA. This supports our idea of a combination of SFA with predictability in form of PFAx, which should be able to discard slow distractors. However, PFAx can be affected by predictable distractors, but these can be identified by the coefficients of the matrix incorporating the control signal. Finally they explicitly point out the idea of combining notions of slowness with predictability, referencing the follwoing work:
@cite_8
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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. 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. Recent development of compressive sensing has greatly benefited radar imaging problems. In this paper, we investigate the problem of obtaining enhanced targets such as ships and airplanes, where targets often exhibit structured sparsity. A novel structured sparsity-driven autofocus algorithm is proposed based on sparse Bayesian framework.The structured sparse prior is imposed on the target scene in a statistical manner. Based on a statistical framework, the proposed algorithm can simultaneously cope with structured sparse recovery and phase error correction problem. The focused high-resolution radar image can be obtained by iteratively estimating scattering coefficients and phase. Due to the structured sparse constraint, the proposed algorithm can desirably preserve the target region and alleviate over-shrinkage problem, compared to previous sparsity-driven auto-focus approaches.Moreover, to accelerate convergence rate of the algorithm, we propose to adaptively eliminate noise-only range cells in estimating phase errors. The selection is conveniently conducted based on the parameters controlling sparsity degree of the signal in the proposed hierarchical model.The simulated and real data experimental results demonstrate that the proposed algorithm can obtain more concentrated images with much smaller number of iterations, particularly in low SNR and highly under-sampling scenarios. HighlightsA novel structured sparsity-driven autofocus algorithm is proposed based on sparse Bayesian framework.To accelerate convergence rate of the algorithm, we propose to adaptively eliminate noise-only range cells in phase error estimation stage.The proposed algorithm can obtain more concentrated images with much smaller number of iterations, particularly in low SNR and highly under-sampling scenarios. The Slow Feature Analysis (SFA) unsupervised learning framework extracts features representing the underlying causes of the changes within a temporally coherent high-dimensional raw sensory input signal. We develop the first online version of SFA, via a combination of incremental Principal Components Analysis and Minor Components Analysis. Unlike standard batch-based SFA, online SFA adapts along with non-stationary environments, which makes it a generally useful unsupervised preprocessor for autonomous learning agents. We compare online SFA to batch SFA in several experiments and show that it indeed learns without a teacher to encode the input stream by informative slow features representing meaningful abstract environmental properties. We extend online SFA to deep networks in hierarchical fashion, and use them to successfully extract abstract object position information from high-dimensional video.