System: Based on the search results given, can you provide a concise overview of the main hypothesis or research question addressed in the article, along with the key methodologies used by the researchers to investigate it? Additionally, could you summarize the main findings obtained from the experiments and discuss their implications for advancing state-of-the-art research in the field? Lastly, please identify any limitations of the study and suggest potential areas for future research, while also evaluating the strengths and weaknesses of the presented conclusions. The answer should be well structured and between 300 and 400 words.

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[Page no. 6] "included as parameters of the network and optimized via back-propagation. • Alternatingly updated with the network model: Clustering assignments are strict and updated in a different step than the one where the network model is updated. In this case, several scenarios are possible, dependent on two main factors: – Number of iterations: Number of iterations of the chosen clustering algorithm, that are executed at every cluster update step. For instance, in Xie et al. (2016), at each cluster update step, the algorithm runs until a ﬁxed percentage of points change as- signments between two consecutive iterations. – Frequency of updates: How often are cluster updates started. For instance in Yang et al. (2016b), for every P network model update steps, one cluster updates step hap- pens. 2.7 AFTER NETWORK TRAINING After the training is ﬁnished, even if a clustering result was produced in the process, it can make sense to re-run a clustering algorithm from scratch using the learned features, for one of several reasons: • Clustering a similar dataset: The general and the most trivial case is to reuse the learned features representation mapping on another dataset which is similar to the one that has been used but has different data. • Obtaining better results: Under certain circumstances, it is possible that the results of clustering after the training are better than the ones obtained during the learning procedure. For instance, in Yang et al. (2016b), such a behavior is reported. One possible reason for this to happen is that the cluster update step during the training doesn’t go all the way till the end (see Number of iterations in Section 2.6). 3 RELATED METHODS In this section we give a systematic overview of related work and analyze it within the framework of the proposed taxonomy. In Table 1"

[Page no. 10] "instance, while TAGNet (Wang et al., 2016) deﬁnes the state of the art on the COIL20 dataset, it performs quite bad on MNIST. Our results show that the taxonomy enables the creation of high-performing methods in a structured and analytical way. Researches are now able to selectively recombine or replace distinct aspects of existing methods instead of relying on a experiment and discovery based approach. Figure 3 and 4 visualize the clustering spaces at different training stages of the proposed network. The clustering spaces are 120-dimensional and 320-dimensional for MNIST and COIL20, respec- tively. The true cluster labels are indicated by the different colors. The visualizations show that the proposed method results in a more clustering-friendly space compared to the original image space and the space before jointly training with the clustering loss. 6 CONCLUSION In this paper, we proposed a universal taxonomy for clustering methods that utilize deep neural networks. The taxonomy was created by decomposing existing methods and analyzing the building blocks for properties that are indicative of desirable or undesirable results. Our case study shows that by using this taxonomy, researches and practitioners can derive new clustering methods in a systematic and analytical way to suit their task. The method we constructed as part of the case study was able to outperform the previous state of the art method on the MNIST dataset. Following the same approach, the proposed taxonomy can thus inspire a myriad of new methods. REFERENCES Cai, D., He, X., and Han, J. (2011). Locally consistent concept factorization for document clustering. IEEE Transactions on Knowledge and Data Engineering, 23(6):902–913. Chen, D., Lv, J., and Yi, Z. (2017). Unsupervised multi-manifold clustering by learning deep repre- sentation. In Workshops at the AAAI Conference on Artiﬁcial Intelligence, pages 385–391. Chen, G. (2015). Deep learning with nonparametric clustering."

[Page no. 2] "al. (2013); Xie et al. (2016); Yang et al. (2016a;b); Li et al. (2017). The main contribution of this paper is the formulation of a taxonomy for clustering methods that rely on a deep neural network for representation learning. The proposed taxonomy enables researchers to create new methods in a structured and analytical way by selectively recombining or replacing distinct aspects of existing methods to improve their performance or mitigate limitations. The tax- onomy is in particular also valuable for practitioners who want to create a method from existing building blocks that suits their task at hand. To illustrate the value of the proposed taxonomy, we conducted a case study in which we fuse a new method based on insights from the taxonomy. In this case study, we use a fully convolutional autoencoder to learn clustering-friendly represen- tations of the data by optimizing it with a two-phased training procedure. In the ﬁrst phase, the 1 arXiv:1801.07648v2 [cs.LG] 13 Sep 2018  2.1 Main network branch 2.2 Features for clustering Input 2.3 Side branch with 2.4 Clustering loss non -clustering loss 2.5 Training 2.6 Cluster updates 2.7 Re-run clustering (optional) Figure 1: The general pipeline of most deep-learning-based clustering methods accodring to the proposed taxonomy, with building blocks as described in Sections 2.1–2.7. autoencoder is trained with the standard mean squared error reconstruction loss. In the second phase, the autoencoder is then ﬁne-tuned with a combined loss function consisting of the autoen- coder reconstruction loss and a clustering-speciﬁc loss. The rest of this paper is organized as follows: At ﬁrst, we introduce the taxonomy and its building blocks in Section 2. In Section 3, we then present a comprehensive review of clustering methods and analyze them with respect to the proposed taxonomy. Subsequently, in Section 4, we propose a new method"

[Page no. 1] "Clustering with Deep Learning: Taxonomy and New Methods Elie Aljalbout, Vladimir Golkov, Yawar Siddiqui, Maximilian Strobel & Daniel Cremers Computer Vision Group Technical University of Munich {firstname.lastname, <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS> September 17, 2018 ABSTRACT Clustering methods based on deep neural networks have proven promising for clustering real-world data because of their high representational power. In this paper we propose a systematic taxonomy of clustering methods that utilize deep neural networks. We base our taxonomy on a comprehensive review of recent work and validate the taxonomy in a case study. In this case study, we show that the taxonomy enables researchers and practitioners to systematically create new clustering methods by selectively recombining and replacing distinct aspects of previous methods with the goal of overcoming their individual limitations. The experimental evaluation conﬁrms this and shows that the method created for the case study achieves state-of-the-art clustering quality and surpasses it in some cases. 1 INTRODUCTION The main objective of clustering is to separate data into groups of similar data points. Having a good separation of data points into clusters is fundamental for many applications in data analysis and data visualization. The performance of current clustering methods is however highly dependent on the input data. Dif- ferent datasets usually require different similarity measures and separation techniques. As a result, dimensionality reduction and representation learning have been extensively used alongside cluster- ing in order to map the input data into a feature space where separation is easier. By utilizing deep neural networks (DNNs), it is possible to learn non-linear mappings that allow transforming data into more clustering-friendly representations without manual feature extraction/selection. In the past, feature extraction and clustering were applied sequentially Ding and He (2004); Trige- orgis et al. (2014). However, recent work shows that jointly optimizing for both can yield better results Song et"

[Page no. 3] "of several layers of latent variables. It is composed of several shallow networks such as restricted Boltzmann machines, such that the hidden layer of each sub-network serves as the visible layer of the next sub-network. • Generative Adversarial Network (GAN): A system of two competing neural network models G and D that engage in a zero-sum game. The generator G learns a distribution of interest to produce samples. The discriminator D learns to distinguish between real samples and generated ones (Goodfellow et al., 2014). 2  • Variational Autoencoder (VAE): A Bayesian network with an autoencoder architecture that learns the data distribution (generative model). 2.2 SET OF DEEP FEATURES USED FOR CLUSTERING After transforming the input to a more clustering-friendly representation, the features that are then used for clustering can be taken from one or more layers of the deep neural network: • One layer: Refers to the case where only one layer of the network is used which is beneﬁ- cial because of its low dimensionality. In most cases the output of the last layer is used. • Several layers: Refers to the case where the representation is a combination of the out- puts of several layers. Thus, the representation is richer and allows the embedded space to represent more complex semantic representations, which might enhance the separation process and help in the similarity computation (Saito and Tan, 2017). 2.3 NON-CLUSTERING LOSS The non-clustering loss is independent of the clustering algorithm and usually enforces a desired constraint on the learned model. Possible options are as follows: • No non-clustering loss: No additional non-clustering loss function is used and the network model is only constrained by the clustering loss. For most clustering losses, the absence of a non-clustering loss can have a danger of worse representations/results, or theoretically even collapsing"

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