Oceanic variability on interannual, interdecadal, and longer timescales plays a key role in climate variability and climate change. Paleoclimatic records suggest major changes in the location and rate of deepwater formation in the Atlantic and Southern oceans on timescales from millennia to millions of years. Instrumental records of increasing duration and spatial coverage document substantial variability in the path and intensity of ocean surface currents on timescales of months to decades. We review recent theoretical and numerical results that help explain the physical processes governing the large-scale ocean circulation and its intrinsic variability. To do so, we apply systematically the methods of dynamical systems theory. The dynamical systems approach is proving successful for more and more detailed and realistic

[1] Methods in multivariate statistical analysis are essential for working with large amounts of geophysical data, data from observational arrays, from satellites, or from numerical model output. In classical multivariate statistical analysis, there is a hierarchy of methods, starting with linear regression at the base, followed by principal component analysis (PCA) and finally canonical correlation analysis (CCA). A multivariate time series method, the singular spectrum analysis (SSA), has been a fruitful extension of the PCA technique. The common drawback of these classical methods is that only linear structures can be correctly extracted from the data. Since the late 1980s, neural network methods have become popular for performing nonlinear regression and classification. More recently, neural network methods have been extended to perform nonlinear PCA (NLPCA), nonlinear CCA (NLCCA), and nonlinear SSA (NLSSA). This paper presents a unified view of the NLPCA, NLCCA, and NLSSA techniques and their applications to various data sets of the atmosphere and the ocean (especially for the El Niño-Southern Oscillation and the stratospheric quasi-biennial oscillation). These data sets reveal that the linear methods are often too simplistic to describe real-world systems, with a tendency to scatter a single oscillatory phenomenon into numerous unphysical modes or higher harmonics, which can be largely alleviated in the new nonlinear paradigm. INDEX TERMS: 3299

Most of the stream mining techniques presented so far have primary paid attention to discovering association rules by direct comparison between time-series data sets. However, their utility is very limited for heterogeneous systems, where time series of various types (discrete, continuous, oscillatory, noisy, etc.) act dynamically in a strongly correlated manner. In this paper, we introduce a new nonlinear transformation, singular spectrum transformation (SST), to address the problem of knowledge discovery of causal relationships from a set of time series. SST is a transformation that transforms a time series into the probability density function that represents a chance to observe some particular change. For an automobile data set, we demonstrate that SST enables us to discover a hidden and useful dependency between variables.

We introduce a method to discover optimal local patterns, which concisely describe the main trends in a time series. Our approach examines the time series at multiple time scales (i.e., window sizes) and efficiently discovers the key patterns in each. We also introduce a criterion to select the best window sizes, which most concisely capture the key oscillatory as well as aperiodic trends. Our key insight lies in learning an optimal orthonormal transform from the data itself, as opposed to using a predetermined basis or approximating function (such as piecewise constant, shortwindow Fourier or wavelets), which essentially restricts us to a particular family of trends. Our method lifts that limitation, while lending itself to fast, incremental estimation in a streaming setting. Experimental evaluation shows that our method can capture meaningful patterns in a variety of settings. Our streaming approach requires order of magnitude less time and space, while still producing concise and informative patterns. 1.

We address the problem of capturing and tracking local correlations among time evolving time series. Our approach is based on comparing the local auto-covariance matrices (via their spectral decompositions) of each series and generalizes the notion of linear cross-correlation. In this way, it is possible to concisely capture a wide variety of local patterns or trends. Our method produces a general similarity score, which evolves over time, and accurately reflects the changing relationships. Finally, it can also be estimated incrementally, in a streaming setting. We demonstrate its usefulness, robustness and efficiency on a wide range of real datasets. 1

The historical records of the low- and high-water levels of the Nile River are among the longest climatic records that have near-annual resolution. There are few gaps in the first part of the records (A.D. 622–1470) and larger gaps later (A.D. 1471–1922). We apply advanced spectral methods, Singular-Spectrum Analysis (SSA) and the Multi-Taper Method (MTM), to fill the gaps and to locate interannual and interdecadal periodicities. The gap filling uses a novel, iterative version of SSA. Our analysis reveals several statistically significant features of the records: a nonlinear, data-adaptive trend that includes a 256-yr cycle, a quasi-quadriennial (4.2-yr) and a quasi-biennial (2.2-yr) mode, as well as additional periodicities of 64, 19, 12 and, most strikingly, 7 years. The quasi-quadriennial and quasibiennial modes support the long-established connection between the Nile River discharge and the El-Niño/Southern Oscillation (ENSO) phenomenon in the Indo-Pacific Ocean. The longest periods might be of astronomical origin. The 7-yr periodicity, possibly related to the biblical cycle of lean and fat years, seems to be due to North-Atlantic influences. 1.

We address the problem of preserving privacy in streams, which has received surprisingly limited attention. For static data, a well-studied and widely used approach is based on random perturbation of the data values. However, streams pose additional challenges. First, analysis of the data has to be performed incrementally, using limited processing time and buffer space, making batch approaches unsuitable. Second, the characteristics of streams evolve over time. Consequently, approaches based on global analysis of the data are not adequate. We show that it is possible to efficiently and effectively track the correlation and autocorrelation structure of multivariate streams and leverage it to add noise which maximally preserves privacy, in the sense that it is very hard to remove. Our techniques achieve much better results than previous static, global approaches, while requiring limited processing time and memory. We provide both a mathematical analysis and experimental evaluation on real data to validate the correctness, efficiency, and effectiveness of our algorithms. 1.

The dating of the cores we drilled from the Gallipoli terrace in the Gulf of Taranto (Ionian Sea), previously obtained by tephroanalysis, is checked by applying a method to objectively recognize volcanic events. This automatic statistical procedure allows identifying pulse-like features in a series and evaluating quantitatively the confidence level at which the significant peaks are detected. We applied it to the 2000-years-long pyroxenes series of the GT89-3 core, on which the dating is based. The method confirms the dating previously performed by detecting at a high confidence level the peaks originally used and indicates a few possible undocumented eruptions. Moreover, a spectral analysis, focussed on the long-term variability of the pyroxenes series and performed by several advanced methods, reveals that the volcanic pulses are superimposed to a millennial trend and a 400 years oscillation.

Abstract—With the proliferation of motion capture data, interest in removing noise and outliers from motion capture data has increased. In this paper, we introduce an efficient motion denoising technique for simultaneous removal of noise and outliers in corrupted human motion data. The key idea of our approach is to construct a series of filter bases from prerecorded human motion data and use them along with robust statistics to filter corrupted human motion data. Mathematically, we formulate the motion denoising in an optimization framework. The objective function measures distance between the filtered motion and noisy input as well as how well the filtered motion matches spatial-temporal patterns embedded in natural human motion. Optimizing the cost function not only filters noise and outliers in corrupted motion but also preserves spatial-temporal patterns of natural human motion. We demonstrate the effectiveness of our system by experimenting with both real and simulated motion data, and by comparing with baseline methods and existing commercial softwares such as Vicon Blade. We also show the effectiveness of our algorithm on filling in missing values of motion capture data. Index Terms—motion capture data, motion data processing, statistical data analysis, filtering, optimization, robust statistics 1

In the present article, we combine two data analysis methods --principal component analysis and spectral analysis-- to analyze the dynamics of eleven North-American species. This combination allows us to determine the importance of different factors that affect this dynamics, such as hunting pressure, climate change, and biological interactions. Our datasets include fur counts and climatic indices that represent the North Atlantic Oscillation, the El Nio-Southern Oscillation, and Northern Hemisphere temperatures. Our results show that all three climatic indices influence the animal-population dynamics, first because they explain a substantial part of the variance in the fur counts and second because they share characteristic periods with the fur-count dataset. In addition to these climate-related periods, the fur-count time series also contain a significant 3-year period that is, in all likelihood, caused by biological interactions.