=Paper=
{{Paper
|id=Vol-1751/AICS_2016_paper_58
|storemode=property
|title=Investigating the Impact of Unsupervised Feature-Extraction from Multi-Wavelength Image Data for Photometric Classification of Stars, Galaxies and QSOs
|pdfUrl=https://ceur-ws.org/Vol-1751/AICS_2016_paper_58.pdf
|volume=Vol-1751
|authors=Annika Lindh
|dblpUrl=https://dblp.org/rec/conf/aics/Lindh16
}}
==Investigating the Impact of Unsupervised Feature-Extraction from Multi-Wavelength Image Data for Photometric Classification of Stars, Galaxies and QSOs==
https://ceur-ws.org/Vol-1751/AICS_2016_paper_58.pdf
Investigating the Impact of Unsupervised Feature-
Extraction from Multi-Wavelength Image Data for
Photometric Classification of Stars, Galaxies and QSOs
Annika Lindh
Dublin Institute of Technology, Ireland
Abstract. Accurate classification of astronomical objects currently relies on
spectroscopic data. Acquiring this data is time-consuming and expensive com-
pared to photometric data. Hence, improving the accuracy of photometric classi-
fication could lead to far better coverage and faster classification pipelines. This
paper investigates the benefit of using unsupervised feature-extraction from
multi-wavelength image data for photometric classification of stars, galaxies and
QSOs. An unsupervised Deep Belief Network is used, giving the model a higher
level of interpretability thanks to its generative nature and layer-wise training. A
Random Forest classifier is used to measure the contribution of the novel features
compared to a set of more traditional baseline features.
1 Introduction
With the vast amounts of data gathered by today’s astronomical surveys, it is no
longer feasible to inspect the observations manually, making the role of Machine Learn-
ing (ML) in the field of Astronomy highly relevant at present [1,2]. However, incorpo-
rating this approach is an ongoing effort which Djorgovski et al. [3] describe as a
change of culture in the field. Borne [4] also discusses this, and concludes that it is
essential that the ML techniques be such that they are interpretable enough to allow for
human astronomers to work in collaboration with them on the analysis. This would also
allow for verification of their quality and would contribute more to the understanding
of the underlying models of our universe than a black-box technique could do.
This paper takes these concerns into account while investigating a novel approach
to the feature generation problem in the photometric classification of stars, galaxies and
quasi-stellar objects (QSOs); the latter term referring to the highly active galactic nuclei
believed to be caused by supermassive black holes [5]. The data source used is the
Sloan Digital Sky Survey (SDSS) Data Release 12 (DR12) – a recent ground-based
astronomical survey covering roughly a third of the sky [6].
The approach used in this paper is an unsupervised ML technique from the Deep
Learning field called Deep Belief Networks (DBN) which has some interesting quali-
ties when it comes to interpretability [7]. DBNs have been used successfully in Com-
puter Vision tasks with unlabeled image data [8], which makes it a good candidate con-
sidering the vast amounts of this type of data available from recent surveys such as the
SDSS.
The purpose of this paper is to provide an evaluation of the approach presented here.
Conclusions drawn from this can be used either directly when designing the methodol-
ogy for future classification tasks, or as a basis for future research in a similar direction.
It is outside the scope of this paper to investigate different classification algorithms
in which the unsupervised features could be used, so this is left as a recommendation
for future work. Further, while some exploration into different hyper-parameter settings
was carried out during the development of the unsupervised model, extensive tuning
was not a prioritized task, leaving some room for improvement on this aspect.
2 Photometric Classification
The golden record for object class labels in Astronomy is obtained by inspecting the
object’s spectra, i.e. the light emitted as a function of wavelength. From this, it is pos-
sible to analyze the physical qualities of the object that are highly relevant when deter-
mining its class [9]. A problem with using these spectroscopic measurements is that
they are far more time-consuming to obtain than photometric measurements such as
images and the parameters derived thereof [3]. In SDSS DR12, the number of objects
with spectroscopic observations are roughly 1% of those with photometric observations
[6]. Considering this, accurate automated classification using photometric data alone
would increase both the coverage and speed of the classification task [1], [10].
While spectroscopic classification defines the golden record, photometric classifica-
tion is an active area of research with promising results. The SDSS dataset in particular
has become something of a standard for this type of research thanks to its publicly
available dataset consisting of photometric observations of around 470 million objects,
and spectroscopic measurements for around 5.3 million of these in SDSS DR12 [6],
[11]. Current state-of-the-art on the three-way classification of stars, galaxies and QSOs
in the SDSS dataset has reached rather high levels of accuracy, but still suffers from
some problems, mainly with regards to the feature generation process and the interpret-
ability of the models.
2.1 Current State-of-the-Art
Brescia et al. [11] used a 2-layer Multi-Layer Perceptron with Quasi Newton Algo-
rithm to simultaneously classify stars, galaxies and QSOs in the SDSS dataset, using
only photometric features, with the spectroscopic class labels as the true labels. Their
best result gave a precision of 93.82% for stars, 93.49% for galaxies and 86.90% for
QSOs, with recall values of 86.40% for stars, 97.02% for galaxies and 90.49% for
QSOs. For this model, the input features were the magnitude values that SDSS derives
from the image data, representing the apparent strength of the source as seen from our
planet. One problem with this feature set is that the magnitude values are dependent on
the distance to the source, such that a closer source will have higher magnitude values
than an identical source that is further away. While there is some correlation between
the distance to an object and its class label due to cosmological reasons, the magnitude
values themselves do not represent an accurate definition of the physical attributes of
the source. However, the difference in magnitudes from multiple wavelength bands of
the same object does carry relevant information, essentially forming a very low-resolu-
tion spectra of the object [3], [12]. As such, it is possible that the classifier in [11]
managed to find such correlations between differences in the magnitudes. There is also
the risk, though, that it potentially overfits to irrelevant aspects of the individual mag-
nitudes that might be correlated to the instrument quality or the target selection pipeline
for the spectroscopic observations. This is a situation where a higher interpretability of
the model would have been useful to investigate what the model based its decisions on.
In a separate experiment from the same paper, instead of using all the magnitude
values directly, only one of them was used as-is, while the rest were used to generate a
set of features from the differences between them [11]. These differences, referred to
as color values, are commonly used in photometric classification tasks [13]. They are
referred to by two-letter names based on the wavelength bands they compare, such as
B-V or u-g; which wavelength bands are available depend on the photometric system
that is used [12]. These color values should not be confused with the single-color terms
used to describe subclasses of stars (e.g. red giants, white dwarves).
In this second experiment, 10 color values were used along with the magnitude value
from the u-band and r-band respectively in two different models. The results from this
experiment were slightly lower: for stars the precisions were 90.21% and 89.93% with
recalls of 82.57% and 82.27%, for galaxies the precisions were 88.00% and 88.03%
with recalls of 92.69% and 92.64%, and for QSOs the precisions were 85.56% and
85.60% with recall values of 87.83% and 87.77% [11]. It is difficult to say whether the
results from the first experiment were higher due to the model’s ability to find more
complex correlations in the magnitude differences, or whether it was due to overfitting
on aspects of the data that might not generalize to the full photometric population.
It should be mentioned that higher accuracies have been reported for specific classes
under specific circumstances. In [14], QSO point-sources were separated from other
point-sources to a precision of 96.96% and a recall of 99.01% for the QSO class. How-
ever, the sample selection resulted in a proportion of QSOs of 86.14% in contrast to
12.88% in the full dataset. While this might be useful for certain scenarios, the focus of
the present work is on developing a model that generalizes well to all classes.
2.2 Gaps
Accurate object type classification still relies on spectroscopic measurements which
are far less abundant than image data and its derived photometric parameters, but pho-
tometric classification results are reaching fairly high accuracies. Current state-of-the-
art results have been obtained through the use of advanced ML algorithms. However,
the interpretability of these techniques is often lacking, making it hard to say what they
base their decisions on. For the methods to become more useful to astronomers, this
needs to be addressed.
Another problem is the way features are derived from the original measurements.
Often, this is done by handcrafted rules, increasing the risk of introducing a human bias.
In the SDSS photometric pipeline, magnitude values are calculated based on assump-
tions about the nature of the object they measure, without actually knowing the nature
of that source; because of this, multiple values are derived for the same parameter,
leaving it up to individual researchers which ones to use [15]. Coughlin et al. [16] argue
for the use of methods that treat all sources in the same way, so that results can be
compared more easily and biases be more readily quantified. Since the photometric
parameters in SDSS are derived from the image data, using that data directly, in the
same way for all objects, might be a step in the right direction.
Further, there might be useful information in the image data that is not captured by
the parameters from the current pipelines. Support for this has been demonstrated on
the task of galaxy morphology classification in [17] and [18]. While [17] used a novel
set of handcrafted rules as input features for a Multi-Layer Perceptron, [18] used a Con-
volutional Neural Network where the algorithm decides which details are relevant in
describing the images, potentially reducing the human bias of the model. Additionally,
thanks to the deep layer-wise training of the model on image data, they were able to
visualize what was learned by the model, thus making it more interpretable. These qual-
ities would be beneficial to the classification task in this paper as well, and their results
lend some support to the approach of using unsupervised feature-extraction from astro-
nomical image data, which is an approach that has not been well-explored when it
comes to photometric classification of stars, galaxies and QSOs.
2.3 Deep Learning as a Potential Solution
Deep Learning is an area of ML that covers the use of multi-layered non-linear mod-
els [8]. It builds on previous research into Neural Networks which is a technique in-
spired by our understanding of the biological learning process in humans and other
animals. The breakthrough that led to a surge of interest into Neural Networks in the
early 2000s came from a combination of the rapid increase in processing power at a
lower price scale, along with the work of Hinton, Osindero & Ten [7] who proposed a
more efficient way of training Deep Neural Networks than the previous standard of
using backpropagation [8]. Their approach was to pre-train a network through an unsu-
pervised approach that made it possible to leverage large amounts of unlabeled data –
a trait that is highly relevant in the Astronomy domain. The network was trained layer-
by-layer so that increasingly sophisticated features could be found at each level. This
not only improved the final result and the training speed – it also made the model more
interpretable since the features learned in each layer could be visualized separately.
Their motivation for using such an approach was that it should be possible to find a
clearer link between what causes the image (i.e. the actual object being imaged) and its
class label than there would be between individual pixel values and the class label of
the object [19]; in practice, such a model learns the underlying features that cause the
pixel values to take on certain distributions, which agrees well with the intention of the
astronomical classification task.
To achieve the layer-wise training described above, a deep model was constructed
by stacking a set of two-layer Restricted Boltzmann Machines (RBMs), each trained in
isolation starting with the one closest to the input layer [7]. Each RBM is a network
where all the units of one layer are connected to all the units of the next, with no con-
nections between units within the same layer. The weights are symmetrically tied in
both directions: in a two-layer RBM, the weight matrix from the visible (input) layer to
the hidden layer is the transpose of the weight matrix from the hidden layer to the visi-
ble. In addition to the weights, the two layers have their own set of bias units corre-
sponding to the connected units of that layer. Training is carried out by using a learning
technique called Contrastive Divergence (CD) which was introduced in [20] as an effi-
cient approximation of maximum likelihood learning. As a final step, the weights of
the RBMs can be unfolded into a single network where the symmetrical ties are
dropped; this network can then be fine-tuned through a contrastive version of the wake-
sleep algorithm that was introduced in [21]. This type of deep model is referred to in
the literature as a DBN; however, the term is used somewhat ambiguously as it some-
times implies that the network includes a supervised softmax layer on top of the stack
of RBMs, while at other times it refers to the fully unsupervised version, and yet other
times it is used for a Multi-Layer Perceptron that has been pre-trained by CD and then
fine-tuned by traditional backpropagation [8]. In this work, DBN refers to an unsuper-
vised model trained by CD and fine-tuned in an unsupervised manner through the con-
trastive version of the wake-sleep algorithm.
2.4 Suitability of Using a DBN for Photometric Feature-Extraction
Feature-extraction by a DBN provides an unsupervised method that can be used di-
rectly on the image data. It is a data-driven method that avoids the use of handcrafted
rules. Hence, the extracted features are chosen by the model to best represent the actual
data, avoiding the human bias of handcrafted rules based on the researcher’s assump-
tions about the data. Since it uses unsupervised training, it can potentially leverage the
vast amounts of unlabeled data available from modern Astronomy surveys. Further,
DBN is a generative model, meaning that what it learns is actually to generate new data
samples from its understanding of the training data; this can be used to visualize what
type of data the model has learnt to recognize. Additionally, thanks to its layer-wise
training, it provides a straightforward way to visualize what sort of structures each unit
is sensitive to in the images. These points address the gaps discussed here, while still
providing a technique that has been shown capable of handling complex ML tasks.
3 Methodology
3.1 Experiment Design
The classification task was to use photometric data to classify each astronomical
object as either a star, galaxy or QSO according to its spectroscopic class label. To
measure the advantage of using the features extracted by the unsupervised DBN, an
experiment was designed where the result of two models could be compared. The base-
line model uses the 10 color values introduced in section 2, which are easily derived
from the existing dataset; this gives a baseline result which can already be obtained
with little effort. The DBN model uses the novel features, in addition to the baseline
features, to measure what added benefit they might provide. Both models use a Random
Forest (RF) classifier to assign the class labels. For the baseline model, this is the entire
model; for the DBN model, the RF classifier is the final stage where the DBN features
and the baseline features are used as inputs.
Each sample of input data for the DBN consisted of the pixel values from all 5 wave-
length bands of one object with a resolution of 20 by 20 pixels each, making each sam-
ple 2000 pixels in total. Some preprocessing was necessary to ensure the images were
cropped, centered and resized to the same dimensions. After this, the images were nor-
malized in each wavelength band individually since the difference in signal strength
between the bands is already covered by the color features; if a future experiment were
to use the DBN features alone, the author recommends calibrating the images according
to the information given in [22].
3.2 DBN Design
The DBN was constructed from two RBMs: the first with 2000 visible and 1000
hidden units, and the second with 1000 visible and 100 hidden units. The output from
the DBN is thus 100 features, referred to here as the DBN features. Each layer was
trained greedily in isolation, after which the symmetry of the generative and recognition
weights were dropped and the RBMs were unfolded into a single network; the structure
of these networks are shown in Fig. 1. The resulting network was globally fine-tuned
through the contrastive wake-sleep algorithm where the generative weights were
trained separately from the recognition weights [7], [21].
Fig. 1. The network used for unsupervised feature-extraction, with the RBM layers on the left
and the combined DBN network on the right
3.3 Sample
The dataset for the experiments was acquired from the SDSS dataset by random
sampling stratified on the spectroscopic class labels. Table 1 shows the class label pro-
portions and sizes of the full set of spectroscopic observations (which can contain du-
plicates and failed observations), the clean population (where objects must have valid
spectroscopic and photometric observations and not contain duplicates) and the actual
sample. The criteria for the clean sample was based on SDSS flags only; no extra in-
spection was carried out on the images themselves. Specifically, only the primary pho-
tometric and spectroscopic observations were used. Spectroscopic observations were
not allowed to have zWarning flags of UNPLUGGED, BAD_TARGET or NODATA.
Photometric observations were required to have the PHOTOMETRIC flag set for its
calibStatus in all wavelength bands, in addition to having the clean flag set. More de-
tails on the meaning of these flags can be found on the SDSS DR12 website 1 and the
CasJobs2 site where most of the numerical data can be downloaded from. The images
were obtained separately through the DR12 Science Archive Server3.
Table 1. Spectroscopic class proportions in the sample and the relevant populations
Clean Full
Sample population population
n = 10,000 n = 3,140,923 n = 3,537,411
STAR 23.97% 23.97 % 22.83 %
GALAXY 62.10% 62.10 % 64.29 %
QSO 13.93% 13.93 % 12.88 %
Due to resource limitations, the sample size is quite small compared to the total da-
taset, but as the experiments are meant to test the approach rather than draw conclusions
about the class labels of the total dataset, this limitation should not be of great concern.
The sample was split into training and test sets by first splitting the dataset in half
for use in the DBN and RF training each. The DBN data was split into 70% training
and 30% cross-validation of the cost monitoring; the RF data was split into 40% for
training, 30% for cross-validation of the number of trees for the RF and some hyper-
parameter tuning for the DBN, with 30% reserved for the final test results.
3.4 Evaluation
To assess the model’s performance on the individual classes, the individual F1 scores
were used. For the overall performance, the macro-averaged F1 score was used, calcu-
lated to prefer a model that generalizes well to all classes [23]. This was used since one
of the strengths of unsupervised learning is that it can leverage unlabeled data, but by
doing so, there’s a risk of biasing the model towards data with a more common profile.
The final training and testing of the models was performed 100 times with different
random number generator seeds to ensure that any differences between the models were
not due to chance. The difference in means was tested for statistical significance with
a one-tailed two-sample independent t-test in PSPP with a 95% confidence interval and
a p-value cut-off of .05.
1 http://www.sdss.org/dr12/
2 http://cas.sdss.org/dr12/en/home.aspx
3 http://data.sdss3.org/
3.5 Limitations
Since the absolute true labels of distant astronomical objects are unknown, the
golden record will inevitably be an approximation based on current theories [3]. For
this paper, the SDSS spectroscopic class labels were used, so any biases in the SDSS
spectroscopic pipeline and target selection criteria are inherited here.
The strongest human bias of this work was the image preprocessing which unfortu-
nately could not be avoided. Attempts have been made to keep this to a minimum by
using threshold values relative to the measurements in each individual image.
4 Results
The DBN model performed better than the baseline model both overall and on each
of the three classes. The differences in means were statistically significant (p < .001)
when tested in a one-tailed independent two-sample t-test in PSPP with a confidence
interval of 95% and no assumption of equal variance. Table 2 shows the results along
with the differences in means. The relative performance increase when adding the novel
features is also given, calculated by taking the absolute performance increase divided
by the means from the baseline model.
Table 2. Results from the baseline model and DBN model, the absolute difference between them,
and the relative improvment of the DBN model compared to the baseline model
baseline DBN Absolute Relative
model model increase increase
Macro-averaged F1 score 0.8321 0.8682 0.0361 4.35%
F1 score, STAR 0.8037 0.8664 0.0627 7.81%
F1 score, GALAXY 0.9376 0.9582 0.0206 2.20%
F1 score, QSO 0.7549 0.7801 0.0252 3.32%
5 Discussion
The results confirm the usefulness of unsupervised feature-extraction from image
data in photometric classification of stars, galaxies and QSOs. The model generalizes
fairly well to the different classes, but could potentially be improved on this aspect by
training the classifier on a weighted sample to counter the class-imbalance.
Comparing to current state-of-the-art, the results reported in [11] can be converted
into the same metrics used for this work, giving a macro-averaged F1 score of 0.9135,
with the F1 score for stars at 0.8996, galaxies at 0.9522 and QSOs at 0.8866. The DBN
model performs slightly better on the galaxy class but is otherwise below the state-of-
the-art results, with mainly the QSO class lagging behind in performance. This leaves
room for improvement, possibly by combining the classifier used in [11] and the novel
features presented in this work.
For the interpretability of the model, however, a simpler classifier makes it possible
to not only understand the extracted features but also how they were used in the classi-
fication task. This was done for the present work by examining the feature contribution
values obtained from the RF classifier, averaged over the 100 training runs. The 10
color features were the top 10 contributors, while the total contribution of the 100 DBN
features added up to 28.43%. A visualization of the top 10 DBN features is shown in
Fig. 2 where brighter areas represent a preference for the presence of signal, and darker
areas represent the preference of an absence of signal. Since the images are normalized,
they do not show where the zero-point of the weights are, but the contrast shows the
type of shapes the model has learned to recognize. This visualization technique is pos-
sible regardless of the classifier, but the RF classifier can help by measuring their con-
tributions.
Fig. 2. Normalized visualizations of the top 10 contributing DBN features
Another way to provide some insight into what the model learned is by generating
samples from the joint distribution learned by the model [7]. Fig. 3 shows some of the
actual data samples after the image preprocessing on the left, with samples generated
from the model on the right-hand side, in both cases taken from different wavelength
bands and different object types. The samples on either side are unrelated to each other
and to the other samples in the same rows and columns.
Fig. 3. Actual data samples after image preprocessing (left) and samples generated from the
model’s joint distribution (right). Individual images are 20x20 pixels and are taken from different
wavelength bands and classes.
6 Conclusions
6.1 Contributions
The main contribution of this work is the finding that unsupervised feature-extrac-
tion from image data can provide a measurable advantage for photometric classification
of stars, galaxies and QSOs. The approach makes it possible to leverage the large
amounts of unlabeled image data captured by modern Astronomy surveys, and it ad-
dresses the concern in the field regarding the interpretability of ML models. Addition-
ally, thanks to the unsupervised training, the DBN features could be re-used even if the
golden record for the class labels was expanded or re-evaluated.
As a side-product of this work, scalable implementations of the RBM and DBN al-
gorithms have been constructed for running the experiments. These implementations
are not tied to the task presented in this paper but can be applied to any domain with
high-dimensionality (labeled or unlabeled) data. The source code has been made avail-
able online as free software under the GPLv3 license.4
6.2 Future Work
The approach presented in this paper could be used directly in future research with
relevant classification objectives. The weakness in the QSO class could potentially be
addressed by training the RF classifier on a weighted sample, or by using the DBN
features in a more complex classifier such as the one from [11] at the expense of some
of the model’s interpretability.
A more specific recommendation regarding the quality of the DBN features would
be to train the DBN with a sparsity target; sparser features take on more specific roles
which improves their interpretability [24]. Potentially, this could also reduce the com-
plexity of the DBN’s learning, especially in the second layer and beyond where the
features from previous layers would provide clearer building blocks.
A limitation to what can be concluded from this paper, which could be addressed by
future research, is that it is not clear whether the image data from all five wavelength
bands contributed to the results. More insight into this aspect could be provided by
comparing these results to a model using only images from the wavelength band with
the highest signal-to-noise ratio.
Finally, and perhaps the most interesting direction, would be for future work to in-
vestigate the usefulness of the DBN features for Transfer Learning. Previous work by
[25] has shown that unsupervised feature-extraction can provide useful intermediate
features for different classification tasks within the same domain. If the DBN features
were to show promising results in this area, then building a database of such general-
izable features could provide the Astronomy community with a set of ready-to-use
lower-dimensionality features that would be more accessible than the full image data.
Acknowledgements
The author would like to thank the supervisor of the project, Robert J. Ross, along
with the staff and lecturers at Dublin Institute of Technology.
The author also would like to thank Gabriele Angeletti for making his Deep Learning
implementation available online.5 This was of great help when learning the relevant
framework and for starting off the implementation of the algorithms.
4 https://github.com/AnnikaLindh/DBNTensorFlow
5 https://github.com/blackecho/Deep-Learning-TensorFlow
Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Par-
ticipating Institutions, the National Science Foundation, and the U.S. Department of
Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/.
SDSS-III is managed by the Astrophysical Research Consortium for the Participat-
ing Institutions of the SDSS-III Collaboration including the University of Arizona, the
Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon Uni-
versity, University of Florida, the French Participation Group, the German Participation
Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan
State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence
Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck In-
stitute for Extraterrestrial Physics, New Mexico State University, New York Univer-
sity, Ohio State University, Pennsylvania State University, University of Portsmouth,
Princeton University, the Spanish Participation Group, University of Tokyo, University
of Utah, Vanderbilt University, University of Virginia, University of Washington, and
Yale University.
References
1. Ž. Ivezić, J. A. Tyson, B. Abel, E. Acosta, R. Allsman, Y. AlSayyad, ... H. Zhan,
“LSST: from Science Drivers to Reference Design and Anticipated Data Prod-
ucts,” arXiv:0805.2366 [astro-ph], Aug. 2014.
2. A. M. Mickaelian, “Astronomical Surveys and Big Data,” arXiv:1511.07322 [as-
tro-ph], Nov. 2015.
3. S. G. Djorgovski, A. A. Mahabal, A. J. Drake, M. J. Graham, and C. Donalek,
“Sky Surveys,” arXiv:1203.5111 [astro-ph, physics:physics], pp. 223–281,
2013.
4. K. D. Borne, “Scientific Data Mining in Astronomy,” arXiv:0911.0505 [astro-
ph, physics:physics], Nov. 2009.
5. D. Richstone, E. A. Ajhar, R. Bender, G. Bower, A. Dressler, S. M. Faber, … S.
Tremaine, “Supermassive Black Holes and the Evolution of Galaxies,” arXiv:as-
tro-ph/9810378, Oct. 1998.
6. S. Alam, F. D. Albareti, C. A. Prieto, F. Anders, S. F. Anderson, B. H. Andrews,
… H. Zou, “The Eleventh and Twelfth Data Releases of the Sloan Digital Sky
Survey: Final Data from SDSS-III,” The Astrophysical Journal Supplement Se-
ries, vol. 219, no. 1, pp. 12–43, Jul. 2015.
7. G. E. Hinton, S. Osindero, and Y.-W. Teh, “A fast learning algorithm for deep
belief nets,” Neural Computation, vol. 18, no. 7, pp. 1527–1554, Jul. 2006.
8. L. Deng, “A tutorial survey of architectures, algorithms, and applications for
deep learning,” APSIPA Transactions on Signal and Information Processing,
vol. 3, no. e2, pp. 1–29, 2014.
9. K. S. Dawson, D. J. Schlegel, C. P. Ahn, S. F. Anderson, É. Aubourg, S. Bailey,
… Z. Zheng, “The Baryon Oscillation Spectroscopic Survey of SDSS-III,” The
Astronomical Journal, vol. 145, no. 10, pp. 1–41, Jan. 2013.
10. M. Brescia, S. Cavuoti, S. G. Djorgovski, C. Donalek, G. Longo, and M. Paolillo,
“Extracting Knowledge From Massive Astronomical Data Sets,”
arXiv:1109.2840 [astro-ph], pp. 31–45, 2012.
11. M. Brescia, S. Cavuoti, and G. Longo, “Automated physical classification in the
SDSS DR10. A catalogue of candidate Quasars,” Monthly Notices of the Royal
Astronomical Society, vol. 450, no. 4, pp. 3893–3903, May 2015.
12. M. S. Bessell, “Standard Photometric Systems,” Annual Review of Astronomy
and Astrophysics, vol. 43, no. 1, pp. 293–336, Sep. 2005.
13. N. M. Ball and R. J. Brunner, “Data Mining and Machine Learning in Astron-
omy,” International Journal of Modern Physics D, vol. 19, no. 7, pp. 1049–1106,
Jul. 2010.
14. S. Abraham and N. S. Philip, “Photometric Determination of Quasar Candi-
dates,” presented at the Astronomical Data Analysis Software and Systems XIX,
2010, vol. 434, pp. 147–150.
15. C. Stoughton, R. H. Lupton, M. Bernardi, M. R. Blanton, S. Burles, F. J.
Castander, … W. Zheng, “Sloan Digital Sky Survey: Early Data Release,” The
Astronomical Journal, vol. 123, pp. 485–548, Jan. 2002.
16. J. L. Coughlin, F. Mullally, S. E. Thompson, J. F. Rowe, C. J. Burke, D. W.
Latham, … K. A. Zamudio, “Planetary Candidates Observed by Kepler. VII. The
First Fully Uniform Catalog Based on The Entire 48 Month Dataset (Q1-Q17
DR24),” arXiv:1512.06149 [astro-ph], Dec. 2015.
17. M. Banerji, O. Lahav, C. J. Lintott, F. B. Abdalla, K. Schawinski, S. P. Bamford,
... J. Vandenberg, “Galaxy Zoo: reproducing galaxy morphologies via machine
learning,” MNRAS, vol. 406, no. 1, pp. 342–353, Jul. 2010.
18. S. Dieleman, K. W. Willett, and J. Dambre, “Rotation-invariant convolutional
neural networks for galaxy morphology prediction,” Monthly Notices of the
Royal Astronomical Society, vol. 450, no. 2, pp. 1441–1459, Apr. 2015.
19. G. E. Hinton, “Learning to represent visual input,” Philos Trans R Soc Lond B
Biol Sci, vol. 365, no. 1537, pp. 177–184, Jan. 2010.
20. G. E. Hinton, “Training products of experts by minimizing contrastive diver-
gence,” Neural Computation, vol. 14, no. 8, pp. 1771–1800, Aug. 2002.
21. G. E. Hinton, P. Dayan, B. J. Frey, and R. M. Neal, “The ‘wake-sleep’ algorithm
for unsupervised neural networks,” Science, vol. 268, no. 5214, pp. 1158–1161,
May 1995.
22. J. A. Smith, D. L. Tucker, S. Kent, M. W. Richmond, M. Fukugita, T. Ichikawa,
… D. G. York, “The u’g’r’i’z’ Standard Star Network,” The Astronomical Jour-
nal, vol. 123, no. 4, pp. 2121–2144, Apr. 2002.
23. M. Sokolova and G. Lapalme, “A systematic analysis of performance measures
for classification tasks,” Information Processing & Management, vol. 45, no. 4,
pp. 427–437, Jul. 2009.
24. G. E. Hinton, “A practical guide to training restricted Boltzmann machines,” Mo-
mentum, vol. 9, no. 1, p. 926, 2010.
25. Y. Bengio, A. Courville, and P. Vincent, “Representation Learning: A Review
and New Perspectives,” IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol. 35, no. 8, pp. 1798–1828, Aug. 2013.