Context. In astronomy, new approaches to process and analyze the exponentially increasing amount of data are inevitable. For spectra, such as in the Sloan Digital Sky Survey spectral database, usually templates of well-known classes are used for classification. In case the fitting of a template fails, wrong spectral properties (e.g. redshift) are derived. Validation of the derived properties is the key to understand the caveats of the template-based method. Aims. In this paper we present a method for statistically computing the redshift z based on a similarity approach. This allows us to determine redshifts in spectra for emission and absorption features without using any predefined model. Additionally, we show how to determine the redshift based on single features. As a consequence we are, for example, able to filter objects that show multiple redshift components. Methods. The redshift calculation is performed by comparing predefined regions in the spectra and individually applying a nearest neighbor regression model to each predefined emission and absorption region. Results. The choice of the model parameters controls the quality and the completeness of the redshifts. For ≈90% of the analyzed 16 000 spectra of our reference and test sample, a certain redshift can be computed that is comparable to the completeness of SDSS (96%). The redshift calculation yields a precision for every individually tested feature that is comparable to the overall precision of the redshifts of SDSS. Using the new method to compute redshifts, we could also identify 14 spectra with a significant shift between emission and absorption or between emission and emission lines. The results already show the immense power of this simple machine-learning approach for investigating huge databases such as the SDSS.

Context.Deep optical surveys open the avenue for finding large numbers of BL Lac objects that are hard to identify because they lack the unique properties classifying them as such. While radio or X-ray surveys typically reveal dozens of sources, recent compilations based on optical criteria alone have increased the number of BL Lac candidates considerably. However, these compilations are subject to biases and may contain a substantial number of contaminating sources. Aims. In this paper we extend our analysis of 182 optically selected BL Lac object candidates from the SDSS with respect to an earlier study. The main goal is to determine the number of bona fide BL Lac objects in this sample. Methods. We examine their variability characteristics, determine their broad-band radio-UV spectral energy distributions (SEDs), and search for the presence of a host galaxy. In addition we present new optical spectra for 27 targets with improved signal-to-noise ratio with respect to the SDSS spectra. Results. At least 59% of our targets have shown variability between SDSS DR2 and our observations by more than 0.1-0.27 mag depending on the telescope used. A host galaxy was detected in 36% of our targets. The host galaxy type and luminosities are consistent with earlier studies of BL Lac host galaxies. Simple fits to broad-band SEDs for 104 targets of our sample derived synchrotron peak frequencies between 13.5 ≤ log 10 (ν peak ) ≤ 16 with a peak at log 10 ∼ 14.5. Our new optical spectra do not reveal any new redshift for any of our objects. Thus the sample contains a large number of bona fide BL Lac objects and seems to contain a substantial fraction of intermediate-frequency peaked BL Lacs.

In the era of rapidly increasing amounts of time series data, classification of variable objects has become the main objective of time-domain astronomy. Classification of irregularly sampled time series is particularly difficult because the data cannot be represented naturally as a vector which can be directly fed into a classifier. In the literature, various statistical features serve as vector representations.In this work, we represent time series by a density model. The density model captures all the information available, including measurement errors. Hence, we view this model as a generalisation to the static features which directly can be derived, e.g., as moments from the density. Similarity between each pair of time series is quantified by the distance between their respective models. Classification is performed on the obtained distance matrix.In the numerical experiments, we use data from the OGLE and ASAS surveys and demonstrate that the proposed representation performs up to par with the best currently used feature-based approaches. The density representation preserves all static information present in the observational data, in contrast to a less complete description by features. The density representation is an upper boundary in terms of information made available to the classifier. Consequently, the predictive power of the proposed classification depends on the choice of similarity measure and classifier, only. Due to its principled nature, we advocate that this new approach of representing time series has potential in tasks beyond classification, e.g., unsupervised learning.

We present an approach for the visualisation of a set of time series that combines an echo state network with an autoencoder. For each time series in the dataset we train an echo state network, using a common and fixed reservoir of hidden neurons, and use the optimised readout weights as the new representation. Dimensionality reduction is then performed via an autoencoder on the readout weight representations. The crux of the work is to equip the autoencoder with a loss function that correctly interprets the reconstructed readout weights by associating them with a reconstruction error measured in the data space of sequences. This essentially amounts to measuring the predictive performance that the reconstructed readout weights exhibit on their corresponding sequences when plugged back into the echo state network with the same fixed reservoir. We demonstrate that the proposed visualisation framework can deal both with real valued sequences as well as binary sequences. We derive magnification factors in order to analyse distance preservations and distortions in the visualisation space. The versatility and advantages of the proposed method are demonstrated on datasets of time series that originate from diverse domains.

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