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Title: Neural Clustering By Predicting And Copying Noise

Paper content:
We propose a neural clustering model that jointly learns both latent features and how they cluster.
Unlike similar methods our model does not require a predefined number of clusters.
Using a supervised approach, we agglomerate latent features towards randomly sampled targets within the same space whilst progressively removing the targets until we are left with only targets which represent cluster centroids.
To show the behavior of our model across different modalities we apply our model on both text and image data and very competitive results on MNIST.
Finally, we also provide results against baseline models for fashion-MNIST, the 20 newsgroups dataset, and a Twitter dataset we ourselves create.
Clustering is one of the fundamental problems of unsupervised learning.
It involves the grouping of items into clusters such that items within the same cluster are more similar than items in different clusters.
Crucially, the ability to do this often hinges upon learning latent features in the input data which can be used to differentiate items from each other in some feature space.
Two key questions thus arise: How do we decide upon cluster membership?
and How do we learn good representations of data in feature space?Spurred
initially by studies into the division of animals into taxa BID31 , cluster analysis matured as a field in the subsequent decades with the advent of various models. These included
distribution-based models, such as Gaussian mixture models BID9 ; densitybased models, such as DBSCAN BID11 ; centroid-based models, such as k-means.2 and hierarchical models, including agglomerative BID29 and divisive models BID13 .While the cluster
analysis community has focused on the unsupervised learning of cluster membership, the deep learning community has a long history of unsupervised representation learning, yielding models such as variational autoencoders BID21 , generative adversarial networks BID12 , and vector space word models BID28 .In this paper, we
propose using noise as targets for agglomerative clustering (or NATAC). As in BID1 we begin
by sampling points in features space called noise targets which we match with latent features. During training we
progressively remove targets and thus agglomerate latent features around fewer and fewer target centroids using a simple heuristic. To tackle the instability
of such training we augment our objective with an auxiliary loss which prevents the model from collapsing and helps it learn better representations. We explore the performance
of our model across different modalities in Section 3.Recently, there have been several attempts at jointly learning both cluster membership and good representations using end-to-end differentiable methods. Similarly to us, BID37 use
a policy to agglomerate points at each training step but they require a given number of clusters to stop agglomerating at. BID23 propose a form of supervised
neural clustering which can then be used to cluster new data containing different categories. BID25 propose jointly learning representations
and clusters by using a k-means style objective. BID36 introduce deep embedding clustering (DEC
) which learns a mapping from data space to a lower-dimensional feature space in which it iteratively optimizes a clustering objective (however, as opposed to the hard assignment we use, they optimize based on soft assignment).Additionally, there have been unsupervised clustering
methods using nonnegative low-rank approximations BID40 which perform competitively to current neural methods on datasets such as MNIST.Unlike all of the above papers, our method does not require a predefined number of clusters.
In this paper, we present a novel neural clustering method which does not depend on a predefined number of clusters.
Our empirical evaluation shows that our model works well across modalities.
We show that NATAC has competitive performance to other methods which require a pre-defined number of clusters.
Further, it outperforms powerful baselines on Fashion-MNIST and text datasets (20 Newsgroups and a Twitter hashtag dataset).
However, NATAC does require some hyperparameters to be tuned, namely the dimensionality of the latent space, the length of warm-up training and the values for the loss coefficient λ.
However, our experiments indicate that NATAC models are fairly robust to hyperparameter changes.Future work Several avenues of investigation could flow from this work.
Firstly, the effectiveness of this method in a semi-supervised setting could be explored using a joint reconstruction and classi-fication auxiliary objective.
Another interesting avenue to explore would be different agglomerative policies other than delete-and-copy.
Different geometries of the latent space could also be considered other than a unit normalized hypersphere.
To remove the need of setting hyperparameters by hand, work into automatically controlling the coefficients (e.g. using proportional control) could be studied.
Finally, it would be interesting to see whether clustering jointly across different feature spaces would help with learning better representations.B EXAMPLES FROM THE FASHION-MNIST DATASET.
We experimented with using polar coordinates early on in our experiments.
Rather than using euclidean coordinates as the latent representation, z is considered a list of angles θ 1 , θ 2 · · · θ n where θ 1 · · · θ n−1 ∈ [0, π] and θ n ∈ [0, 2π].
However, we found that the models using polar geometry performed significantly worse than those with euclidean geometry.Additionally, we also experimented with not L2 normalizing the output of the encoder network.
We hypothesized that the model would learn a better representation of the latent space by also "learning" the geometry of the noise targets.
Unfortunately, the unnormalized representation caused the noise targets to quickly collapse to a single point.

assistant: text: Neural clustering without needing a number of clusters