Underactuation is widely used when designing anthropomorphic hand, which involves fewer degrees of actuation than degrees of freedom. However, the similarities between coordinated joint movements and movement variances across different grasp tasks have not been suitably examined. This work suggests a systematic approach to identify the actuation strategy with the minimum number for degrees of actuation for anthropomorphic hands. This work evaluates the correlations of coordinated movements in human hands during 23 grasp tasks to suggest actuation strategies for anthropomorphic hands. Our approach proceeds as follows: first, we find the best description for each coordinated joint movement in each grasp task by using multiple linear regression; then, based on the similarities between joint movements, we classify hand joints into groups by using hierarchical cluster analysis; finally, we reduce the dimensionality of each group of joints by employing principal components analysis. The metacarpophalangeal joints and proximal interphalangeal joints have the best and most consistent description of their coordinated movements across all grasp tasks. The thumb metacarpophalangeal and abduction/adduction between the ring and little fingers exhibit relatively high independence of movement. The distal interphalangeal joints show a high degree of independent movement but not for all grasp tasks. Analysis of the results indicates that for the distal interphalangeal joints, their coordinated movements are better explained when all fingers wrap around the object. Our approach fails to provide more information for the other joints. We conclude that 19 degrees of freedom for an anthropomorphic hand can be reduced to 13 degrees of actuation distributed between six groups of joints. The number of degrees of actuation can be further reduced to six by relaxing the dimensionality reduction criteria. Other resolutions are as follows: (a) the joint coupling scheme should be joint-based rather than finger-based and (b) hand designs may need to include finger abduction/adduction movements. Keywords Anthropomorphic hand, prosthetic hand, degrees of freedom, dimensionality of hand movements, hand kinematics, degrees of actuation Date

Using hierarchies of classes is one of the standard methods to solve multi-class classification problems. In the literature, selecting the right hierarchy is considered to play a key role in improving classification performance. Although different methods have been proposed, there is still a lack of understanding of what makes one method to extract hierarchies perform better or worse.To this effect, we analyze and compare some of the most popular approaches to extracting hierarchies. We identify some common pitfalls that may lead practitioners to make misleading conclusions about their methods. In addition, to address some of these problems, we demonstrate that using random hierarchies is an appropriate benchmark to assess how the hierarchy's quality affects the classification performance.In particular, we show how the hierarchy's quality can become irrelevant depending on the experimental setup: when using powerful enough classifiers, the final performance is not affected by the quality of the hierarchy. We also show how comparing the effect of the hierarchies against non-hierarchical approaches might incorrectly indicate their superiority.Our results confirm that datasets with a high number of classes generally present complex structures in how these classes relate to each other. In these datasets, the right hierarchy can dramatically improve classification performance.

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In classification problems, as the number of classes increases, correctly classifying a new instance into one of them is assumed to be more challenging than making the same decision in the presence of fewer classes. The essence of the problem is that using the learning algorithm on each decision boundary individually is better than using the same learning algorithm on several of them simultaneously. However, why and when it happens is still not well-understood today. This work's main contribution is to introduce the concept of heterogeneity of decision boundaries as an explanation of this phenomenon. Based on the definition of heterogeneity of decision boundaries, we analyze and explain the differences in the performance of state of the art approaches to solve multi-class classification. We demonstrate that as the heterogeneity increases, the performances of all approaches, except one-vs-one, decrease. We show that by correctly encoding the knowledge of the heterogeneity of decision boundaries in a decomposition of the multi-class problem, we can obtain better results than state of the art decompositions. The benefits can be an increase in classification performance or a decrease in the time it takes to train and evaluate the models. We first provide intuitions and illustrate the effects of the heterogeneity of decision boundaries using synthetic datasets and a simplistic classifier. Then, we demonstrate how a real dataset exhibits these same principles, also under realistic learning algorithms. In this setting, we devise a method to quantify the heterogeneity of different decision boundaries, and use it to decompose the multi-class problem. The results show significant improvements over state-of-the-art decompositions that do not take the heterogeneity of decision boundaries into account.

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