Avoiding vincular patterns on alternating words

A word $w=w_1w_2\cdots w_n$ is alternating if either $w_1w_3\cdots$ (when the word is up-down) or $w_1>w_2w_4<\cdots$ (when the word is down-up). The study of alternating words avoiding classical permutation patterns was initiated by the authors in~\cite{GKZ}, where, in particular, it was shown that 123-avoiding up-down words of even length are counted by the Narayana numbers. However, not much was understood on the structure of 123-avoiding up-down words. In this paper, we fill in this gap by introducing the notion of a cut-pair that allows us to subdivide the set of words in question into equivalence classes. We provide a combinatorial argument to show that the number of equivalence classes is given by the Catalan numbers, which induces an alternative (combinatorial) proof of the corresponding result in~\cite{GKZ}. Further, we extend the enumerative results in~\cite{GKZ} to the case of alternating words avoiding a vincular pattern of length 3. We show that it is sufficient to enumerate up-down words of even length avoiding the consecutive pattern $\underline{132}$ and up-down words of odd length avoiding the consecutive pattern $\underline{312}$ to answer all of our enumerative questions. The former of the two key cases is enumerated by the Stirling numbers of the second kind.Comment: 25 pages; To appear in Discrete Mathematic

Pattern-avoiding alternating words

A word $w=w_1w_2\cdots w_n$ is alternating if either $w_1w_3\cdots$ (when the word is up-down) or $w_1>w_2w_4<\cdots$ (when the word is down-up). In this paper, we initiate the study of (pattern-avoiding) alternating words. We enumerate up-down (equivalently, down-up) words via finding a bijection with order ideals of a certain poset. Further, we show that the number of 123-avoiding up-down words of even length is given by the Narayana numbers, which is also the case, shown by us bijectively, with 132-avoiding up-down words of even length. We also give formulas for enumerating all other cases of avoidance of a permutation pattern of length 3 on alternating words

Mining Mid-level Features for Action Recognition Based on Effective Skeleton Representation

Recently, mid-level features have shown promising performance in computer vision. Mid-level features learned by incorporating class-level information are potentially more discriminative than traditional low-level local features. In this paper, an effective method is proposed to extract mid-level features from Kinect skeletons for 3D human action recognition. Firstly, the orientations of limbs connected by two skeleton joints are computed and each orientation is encoded into one of the 27 states indicating the spatial relationship of the joints. Secondly, limbs are combined into parts and the limb's states are mapped into part states. Finally, frequent pattern mining is employed to mine the most frequent and relevant (discriminative, representative and non-redundant) states of parts in continuous several frames. These parts are referred to as Frequent Local Parts or FLPs. The FLPs allow us to build powerful bag-of-FLP-based action representation. This new representation yields state-of-the-art results on MSR DailyActivity3D and MSR ActionPairs3D

Multilabel Consensus Classification

In the era of big data, a large amount of noisy and incomplete data can be collected from multiple sources for prediction tasks. Combining multiple models or data sources helps to counteract the effects of low data quality and the bias of any single model or data source, and thus can improve the robustness and the performance of predictive models. Out of privacy, storage and bandwidth considerations, in certain circumstances one has to combine the predictions from multiple models or data sources to obtain the final predictions without accessing the raw data. Consensus-based prediction combination algorithms are effective for such situations. However, current research on prediction combination focuses on the single label setting, where an instance can have one and only one label. Nonetheless, data nowadays are usually multilabeled, such that more than one label have to be predicted at the same time. Direct applications of existing prediction combination methods to multilabel settings can lead to degenerated performance. In this paper, we address the challenges of combining predictions from multiple multilabel classifiers and propose two novel algorithms, MLCM-r (MultiLabel Consensus Maximization for ranking) and MLCM-a (MLCM for microAUC). These algorithms can capture label correlations that are common in multilabel classifications, and optimize corresponding performance metrics. Experimental results on popular multilabel classification tasks verify the theoretical analysis and effectiveness of the proposed methods

Large-scale Continuous Gesture Recognition Using Convolutional Neural Networks

This paper addresses the problem of continuous gesture recognition from sequences of depth maps using convolutional neutral networks (ConvNets). The proposed method first segments individual gestures from a depth sequence based on quantity of movement (QOM). For each segmented gesture, an Improved Depth Motion Map (IDMM), which converts the depth sequence into one image, is constructed and fed to a ConvNet for recognition. The IDMM effectively encodes both spatial and temporal information and allows the fine-tuning with existing ConvNet models for classification without introducing millions of parameters to learn. The proposed method is evaluated on the Large-scale Continuous Gesture Recognition of the ChaLearn Looking at People (LAP) challenge 2016. It achieved the performance of 0.2655 (Mean Jaccard Index) and ranked $3^{rd}$ place in this challenge

Large-scale Isolated Gesture Recognition Using Convolutional Neural Networks

This paper proposes three simple, compact yet effective representations of depth sequences, referred to respectively as Dynamic Depth Images (DDI), Dynamic Depth Normal Images (DDNI) and Dynamic Depth Motion Normal Images (DDMNI). These dynamic images are constructed from a sequence of depth maps using bidirectional rank pooling to effectively capture the spatial-temporal information. Such image-based representations enable us to fine-tune the existing ConvNets models trained on image data for classification of depth sequences, without introducing large parameters to learn. Upon the proposed representations, a convolutional Neural networks (ConvNets) based method is developed for gesture recognition and evaluated on the Large-scale Isolated Gesture Recognition at the ChaLearn Looking at People (LAP) challenge 2016. The method achieved 55.57\% classification accuracy and ranked $2^{nd}$ place in this challenge but was very close to the best performance even though we only used depth data.Comment: arXiv admin note: text overlap with arXiv:1608.0633