Most of the data science use cases are relatively well established by now: a goal is defined, a target class is selected, a model is trained to recognize/predict the target, and the same model is applied to new never-seen-before productive data. An anomaly is an event that is not part of the system's past; an event that cannot be found in the system's historical data. In the case of network data, an anomaly can be an intrusion, in medicine a sudden pathological status, in sales or credit card businesses a fraudulent payment, and, finally, in machinery a mechanical piece breakdown. In the manufacturing industry, the goal is to keep a mechanical pieceworking as long as possible–mechanical pieces are expensive – and at the same time to predict its breaking point before it actually occurs–a machine breakoften triggers a chain reaction of expensive damages. Therefore, a high value is usually associated with the early discovery, warning, prediction, and/or prevention of anomalies.Specifically, the prediction of "unknown" disruptive events in the field of mechanical maintenance takes the name of "anomaly detection".

One intuitive way to make forecasts would be to refer to recent time points. Today's stock prices would likely be more similar to yesterday's prices than those from five years ago. Hence, we would give more weight to recent than to older prices in predicting today's price. These correlations between past and present values demonstrate temporal dependence, which forms the basis of a popular time series analysis technique called ARIMA (Autoregressive Integrated Moving Average). ARIMA accounts for both seasonal variability and one-off'shocks' in the past to make future predictions.

The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued signal into its quadrature component. In this paper, we define a probabilistic generalization of this approach. We model the observable real-valued signal as the real part of a latent complex-valued Gaussian process. In order to obtain the appropriate statistical relationship between its real and imaginary parts, we define two new classes of complex-valued covariance functions. Through an analysis of simulated chirplets and stochastic oscillations, we show that the resulting Gaussian process complex-valued signal provides a better estimate of the instantaneous amplitude and frequency than the established approaches. Furthermore, the complex-valued Gaussian process regression allows to incorporate prior information about the structure in signal and noise and thereby to tailor the analysis to the features of the signal. As a example, we analyze the non-stationary dynamics of brain oscillations in the alpha band, as measured using magneto-encephalography.

Now I am going to use CNN or RNN to extract features in a time sequence, for example, a sequence related to user clicks, (Oct 10 19:20:30 click page 10, Oct 10 19:20:35 click page 22, etc). Simply, I can represent the two clicks as 000...10.....22...000 (0 for no click). As you can see, if use one number for the action in one second, that will generate a quite long sequence with a lot of blank fragments, which is not good for RNN or CNN. But we remove all zeros, only with 10-22 we don't know the time interval between two clicks. So, can anyone give a suggestion on how to express this kind of sequence properly so that we can combine it with neural networks easily?

Whenever you spot a trend plotted against time, you would be looking at a time series. The de facto choice for studying financial market performance and weather forecasts, time series are one of the most pervasive analysis techniques because of its inextricable relation to time--we are always interested to foretell the future.

For those that may have missed it, every day this week we are demo-ing an R package: tidyquant (Monday), timetk (Tuesday), sweep (Wednesday), tibbletime (Thursday) and h2o (Friday)! Let's take tibbletime for a spin! This allows the user to easily aggregate data to a less granular level. This can be used for rolling averages and other rolling calculations inside the tidyverse framework. The tibbletime package is under active development, and because of this we recommend downloading the package from GitHub using devtools.

This is part 3 of a multi-part guide on working with time series data in R. You can find the previous parts here: Part 1, Part 2. Generated data like that used in Parts 1 and 2 is great for sake of example, but not very interesting to work with. So let's get some real-world data that we can work with for the rest of this tutorial. There are countless sources of time series data that we can use including some that are already included in R and some of its packages. But I'd like to expand our horizons a bit.

In the first part in a series on Tidy Time Series Analysis, we'll use tidyquant to investigate CRAN downloads. Most people think of tidyquant as purely a financial package and rightfully so. However, because of its integration with xts, zoo and TTR, it's naturally suited for "tidy" time series analysis. We'll primarily be using two libraries today. As you can tell from my laptop stickers, I'm a bit of a tidyverse fan.

Whenever you spot a trend plotted against time, you would be looking at a time series. The de facto choice for studying financial market performance and weather forecasts, time series are one of the most pervasive analysis techniques because of its inextricable relation to time--we are always interested to foretell the future. One intuitive way to make forecasts would be to refer to recent time points. Today's stock prices would likely be more similar to yesterday's prices than those from five years ago. Hence, we would give more weight to recent than to older prices in predicting today's price.

As a first step, Understand the data visually, for this purpose, the data is converted to time series object using ts(), and plotted visually using plot() functions available in R. Forecast package is written by Rob J Hyndman and is available from CRAN here. All these forecasting models returns objects which contain original series, point forecasts, forecasting methods used residuals.