Multivariate time series (MTS) arise when multiple interconnected sensors record data over time. Dealing with this high-dimensional data is challenging for every classifier for at least two aspects: First, a MTS is not only characterized by individual feature values, but also by the co-occurrence of features in different dimensions. Second, this typically adds large amounts of irrelevant data and noise. We present our novel MTS classifier WEASEL+MUSE (Word ExtrAction for time SEries cLassification + MUltivariate Symbols and dErivatives) which addresses both challenges. WEASEL+MUSE builds a multivariate feature vector, first using a sliding-window approach applied to each dimension of the MTS, then extracts discrete features per window and dimension. The feature vector is subsequently fed through feature selection, removing non-discriminative features, and analysed by a machine learning classifier. The novelty of WEASEL+MUSE lies in its specific way of extracting and filtering multivariate features from MTS by encoding context information into each feature, resulting in a small, yet very discriminative feature set useful for MTS classification. Based on a popular benchmark of @math MTS datasets, we found that WEASEL+MUSE is the most accurate domain agnostic classifier, when compared to the state of the art. The outstanding robustness of WEASEL+MUSE is further confirmed based on motion gesture recognition data, where it out-of-the-box achieved similar accuracies as domain-specific methods.
@cite_4 extracts segments from an MTS. It then trains regression trees to identify structural dependencies between segments. The regression trees trained in this manner represent a non-linear AR model. LPS next builds a BOW representation based on the labels of the leaf nodes similar to SMTS. Finally a similarity measure is defined on the BOW representations of the MTS. LPS showed better performance than DTW in a benchmark using 15 MTS datasets. @cite_24 proposes an AR kernel-based distance measure for MTSC.
@cite_24 @cite_4
2436453945 2066224818 789250018 2762016725
This paper presents a novel deep architecture, called neural regression forest (NRF), for depth estimation from a single image. NRF combines random forests and convolutional neural networks (CNNs). Scanning windows extracted from the image represent samples which are passed down the trees of NRF for predicting their depth. At every tree node, the sample is filtered with a CNN associated with that node. Results of the convolutional filtering are passed to left and right children nodes, i.e., corresponding CNNs, with a Bernoulli probability, until the leaves, where depth estimations are made. CNNs at every node are designed to have fewer parameters than seen in recent work, but their stacked processing along a path in the tree effectively amounts to a deeper CNN. NRF allows for parallelizable training of all "shallow" CNNs, and efficient enforcing of smoothness in depth estimation results. Our evaluation on the benchmark Make3D and NYUv2 datasets demonstrates that NRF outperforms the state of the art, and gracefully handles gradually decreasing training datasets. Multivariate time series (MTS) classification has gained importance with the increase in the number of temporal datasets in different domains (such as medicine, finance, multimedia, etc.). Similarity-based approaches, such as nearest-neighbor classifiers, are often used for univariate time series, but MTS are characterized not only by individual attributes, but also by their relationships. Here we provide a classifier based on a new symbolic representation for MTS (denoted as SMTS) with several important elements. SMTS considers all attributes of MTS simultaneously, rather than separately, to extract information contained in the relationships. Symbols are learned from a supervised algorithm that does not require pre-defined intervals, nor features. An elementary representation is used that consists of the time index, and the values (and first differences for numerical attributes) of the individual time series as columns. That is, there is essentially no feature extraction (aside from first differences) and the local series values are fused to time position through the time index. The initial representation of raw data is quite simple conceptually and operationally. Still, a tree-based ensemble can detect interactions in the space of the time index and time values and this is exploited to generate a high-dimensional codebook from the terminal nodes of the trees. Because the time index is included as an attribute, each MTS is learned to be segmented by time, or by the value of one of its attributes. The codebook is processed with a second ensemble where now implicit feature selection is exploited to handle the high-dimensional input. The constituent properties produce a distinctly different algorithm. Moreover, MTS with nominal and missing values are handled efficiently with tree learners. Experiments demonstrate the effectiveness of the proposed approach in terms of accuracy and computation times in a large collection multivariate (and univariate) datasets. Time series data mining has received much greater interest along with the increase in temporal data sets from different domains such as medicine, finance, multimedia, etc. Representations are important to reduce dimensionality and generate useful similarity measures. High-level representations such as Fourier transforms, wavelets, piecewise polynomial models, etc., were considered previously. Recently, autoregressive kernels were introduced to reflect the similarity of the time series. We introduce a novel approach to model the dependency structure in time series that generalizes the concept of autoregression to local autopatterns. Our approach generates a pattern-based representation along with a similarity measure called learned pattern similarity (LPS). A tree-based ensemble-learning strategy that is fast and insensitive to parameter settings is the basis for the approach. Then, a robust similarity measure based on the learned patterns is presented. This unsupervised approach to represent and measure the similarity between time series generally applies to a number of data mining tasks (e.g., clustering, anomaly detection, classification). Furthermore, an embedded learning of the representation avoids pre-defined features and an extraction step which is common in some feature-based approaches. The method generalizes in a straightforward manner to multivariate time series. The effectiveness of LPS is evaluated on time series classification problems from various domains. We compare LPS to eleven well-known similarity measures. Our experimental results show that LPS provides fast and competitive results on benchmark datasets from several domains. Furthermore, LPS provides a research direction and template approach that breaks from the linear dependency models to potentially foster other promising nonlinear approaches. Like other machine learning paradigms, multi-label learning also suffers from the curse of dimensionality problem. Multi-label dimensionality reduction can alleviate the problem but they generally ask for sufficient labeled samples. Nevertheless, we often may only have scarce labeled samples and abundant unlabeled samples. In this paper, we propose a @math emi-supervised @math ulti-label @math imensionality @math eduction based on @math ependence @math aximization approach (SMDRdm in short). SDMRdm assumes the semantic similarity and feature similarity of multi-label samples are inter-depended. SMDRdm first applies label propagation on a neighborhood graph composed with labeled and unlabeled samples to obtain the soft labels of unlabeled samples, and then measures the semantic similarity between all the training samples (including unlabeled ones) based on these soft labels and available labels of labeled samples. Next, it measures the feature similarity between samples in the subspace projected by the target projective matrix, instead of the original high-dimensional feature space. After that, it maximizes the dependence between these two types of similarities and incorporates the dependence into linear discriminant analysis to optimize the target projective matrix. Experiments on publicly accessible multi-label data sets demonstrate that SMDRdm achieves more prominent results than other related approaches across various evaluation metrics. In addition, the empirical study also shows the semantic similarity between samples derived from soft labels works better than that derived from scarce available labels.