SlowGuess/ACL_2020_OCR huggingface dataset:
where  $P(a^{(s)}|s) = P(a_{1}^{(s)}|s)\prod_{i = 2}^{n}P(a_{i}^{(s)}|a_{i - 1}^{(s)})$  is the probability of the suffix group conditioned on the POS of the stem.  $P(a^{(p)}|s)$  is defined analogously for prefix groups.
We train all models on the nine SRs using the same split of  $\mathcal{E}$  into training ( $n_{train}^{(p)} = 0.85 \cdot |\mathcal{E}|$ ), validation ( $n_{val}^{(p)} = 0.05 \cdot |\mathcal{E}|$ ), and test ( $n_{test}^{(p)} = 0.1 \cdot |\mathcal{E}|$ ) edges. For validation and test, we randomly sample  $n_{val}^{(n)} = n_{val}^{(p)}$  and  $n_{test}^{(n)} = n_{test}^{(p)}$  non-edges ( $s, a) \notin \mathcal{E}$  as negative examples such that both sets are balanced (0.5 positive, 0.5 negative).
For training, we sample  $n_{train}^{(n)} = n_{train}^{(p)}$  non-edges  $(s,a) \notin \mathcal{E}$  in every epoch (i.e., the set of sampled non-edges changes in every epoch). Nodes are sampled according to their degree with  $P(n) \propto d(n)$ , a common strategy in bipartite link prediction (Chen et al., 2017). We make sure non-edges sampled in training are not in the validation or test sets. During the test phase, we rank all edges according to their predicted scores.
Model	np
DGA+	30,200
DGA	20,200
CM	349,301
NC+	30,200
NC	20,200
Table 2: Number of trainable parameters for neural models.  $n_p$ : number of trainable parameters.
We evaluate the models using average precision (AP) and area under the ROC curve (AUC), two common evaluation measures in link prediction that do not require a decision threshold. AP emphasizes the correctness of the top-ranked edges (Su et al., 2015) more than AUC.
5.2 Training Details
DGA, DGA+: We use binary cross entropy as loss function. Hyperparameter tuning is performed on the validation set. We train the DGA for 600 epochs using Adam (Kingma and Ba, 2015) with a learning rate of 0.01. We use  $L = 2$  hidden layers in the DGA with a dimension of 100. For regularization, we apply dropout of 0.1 after the input layer and 0.7 after the hidden layers. For  $\mathbf{x}_s$  and  $\mathbf{x}_a$ , we use 100-dimensional GloVe embeddings (Pennington et al., 2014) trained on the segmented text of the individual SRs with a window size of 10. These can be seen as GloVe variants of traditional morpheme embeddings as proposed, e.g., by Qiu et al. (2014), with the sole difference that we use affix groups instead of individual affixes. For training the embeddings, derivatives are segmented into prefix group, stem, and suffix group. In the case of both prefix and suffix groups, we add prefix and suffix group embeddings.
Since the window size impacts the information represented by the embeddings, with larger windows tending to capture topical and smaller windows morphosyntactic information (Lison and Kutuzov, 2017), we also train the DGA with 200-dimensional embeddings consisting of concatenated 100-dimensional embeddings trained with window sizes of 10 and 1, respectively  $(\mathrm{DGA}+)$ .<sup>7</sup> Since DGA already receives associative informa
The number of epochs until convergence lies within the typical range of values for graph convolutional networks.
<sup>7</sup>We experimented with using vectors trained on isolated pairs of stems and affix groups instead of window-1 vectors trained on the full text, but the performance was comparable. We also implemented the DGA using only window-1 vectors (without concatenating them with window-10 vectors), but it performed considerably worse.
Model	sports	entertainment	knowledge	μ±σ
cfb	nba	nfl	gam	lol	mov	pol	sci	tec	AP	AUC
AP	AUC	AP	AUC	AP	AUC	AP	AUC	AP	AUC	AP	AUC	AP	AUC	AP	AUC	AP	AUC	AP	AUC
DGA+	.783	.754	.764	.749	.773	.751	.775	.759	.758	.740	.772	.749	.777	.766	.809	.795	.799	.778	.779±.015	.760±.016
DGA	.760	.730	.754	.731	.762	.740	.762	.743	.752	.738	.765	.747	.764	.750	.783	.770	.781	.761	.765±.010	.746±.012
CM	.745	.745	.751	.759	.764	.766	.768	.776	.766	.773	.769	.780	.776	.786	.793	.804	.768	.775	.767±.013	.774±.016
NC+	.737	.739	.729	.733	.737	.740	.722	.728	.730	.733	.732	.741	.725	.731	.772	.781	.758	.756	.738±.016	.742±.016
NC	.704	.710	.705	.715	.719	.728	.709	.714	.699	.711	.709	.720	.695	.708	.731	.743	.734	.737	.712±.013	.721±.012
JS	.632	.593	.617	.582	.626	.588	.619	.588	.609	.584	.622	.589	.614	.591	.649	.617	.638	.608	.625±.012	.593±.011
BM	.598	.602	.592	.597	.600	.600	.592	.592	.583	.585	.596	.594	.583	.584	.610	.601	.589	.596	.594±.008	.595±.006
Table 3: Performance on MWF prediction. The table shows AP and AUC of the models for the nine SRs as well as averaged scores. Grey highlighting illustrates the best score in a column, light grey the second-best.
tion from the DG and semantic information from the embeddings trained with window size 10, the main advantage of DGA+ should lie in additional syntactic information.
CM: We use binary cross entropy as loss function. We train the CM for 20 epochs using Adam with a learning rate of 0.001. Both input character embeddings and hidden states of the bidirectional LSTMs have 100 dimensions. The output of the first feed-forward layer has 50 dimensions. We apply dropout of 0.2 after the embedding layer as well as the first feed-forward layer.
NC, NC+: All hyperparameters are identical to the DGA and the DGA+, respectively.
JS: Similarity scores are computed on the SR training sets.
BM: Transition probabilities are maximum likelihood estimates from the SR training sets. If a stem is assigned several POS tags by the tagger, we take the most frequent one.
Table 2 summarizes the number of trainable parameters for the neural models. Notice that CM has more than 10 times as many trainable parameters as DGA+, DGA, NC+, and NC.
The overall best performing models are DGA+ and CM (see Table 3). While DGA+ beats CM on all SRs except for lol in AP, CM beats DGA+ on all SRs except for cfb and tec in AUC. Except for CM, DGA+ beats all other models on all SRs in both AP and AUC, i.e., it is always the best or second-best model. DGA beats all models except for DGA+ and CM on all SRs in AP but has lower AUC than NC+ on three SRs. It also outperforms CM on three SRs in AP. NC+ and NC mostly have scores above 0.7, showing that traditional morpheme embeddings also capture information about the compatibility of affixes and stems (albeit to a lesser degree than models with associative or orthographic
information). Among the non-neural methods, JS outperforms BM (and the other non-neural link prediction models, see Appendix A.4) in AP, but is beaten by BM in AUC on six SRs.
The fact that DGA+ performs on par with CM while using less than  $10\%$  of CM's parameters demonstrates the power of incorporating associative information from the mental lexicon in modeling the MWF of derivatives. This result is even more striking since DGA+, as opposed to CM, has no direct access to orthographic (i.e., phonological) information. At the same time, CM's high performance indicates that orthographic information is an important predictor of MWF.
6 Derivational Embeddings
6.1 Comparison with Input Vectors
To understand better how associative information from the DG increases performance, we examine how DGA+ changes the shape of the vector space by comparing input vs. learned embeddings (X vs.  $\mathbf{Z}_{DGA+}$ ), and contrast that with NC+ (X vs.  $\mathbf{Z}_{NC+}$ ). A priori, there are two opposing demands the embeddings need to respond to: (i) as holds for bipartite graphs in general (Gao et al., 2018), the two node sets (stems and affix groups) should form two separated clusters in embedding space; (ii) stems associated with the same affix group should form clusters in embedding space that are close to the embedding of the respective affix group.
For this analysis, we define  $\delta(\mathcal{N},\mathbf{v})$  as the mean cosine similarity between the embeddings of a node set  $\mathcal{N}$  and an individual embedding  $\mathbf{v}$ ,
$$
\delta (\mathcal {N}, \mathbf {v}) = \frac {1}{| \mathcal {N} |} \sum_ {n \in \mathcal {N}} \cos \left(\mathbf {u} _ {n}, \mathbf {v}\right), \tag {11}
$$
where  $\mathbf{u}_n$  is the embedding of node  $n$ . We calculate  $\delta$  for the set of stem nodes  $\mathcal{S}$  and their centroid  $\mathbf{c}_{\mathcal{S}} = \frac{1}{|\mathcal{S}|} \sum_{s \in \mathcal{S}} \mathbf{u}_s$  as well as the set of affix group
(a)  $\mathbf{X}$
(b)  $\mathbf{Z}_{NC + }$
Figure 5: Comparison of input embeddings X with learned representations  $Z_{NC+}$  and  $Z_{DGA+}$ . The plots are t-SNE projections (van der Maaten and Hinton, 2008) of the embedding spaces. We highlight two example sets of stems occurring with a common affix: the blue points are stems occurring with  $\$esque$ , the orange points stems occurring with  $\$ful$ .  $\times$  marks the embedding of  $\$esque$ , + the embedding of  $\$ful$ .
(c)  $\mathbf{Z}_{DGA + }$
Measure	X	ZNC+	ZDGA+
δ(S, cS)	.256 ± .026	.500 ± .027	.487 ± .022
δ(A, cA)	.377 ± .017	.522 ± .016	.322 ± .030
δ(Sa, cSa)	.281 ± .006	.615 ± .017	.671 ± .024
δ(Sa, ua)	.133 ± .006	.261 ± .022	.278 ± .033
Table 4: Comparison of  $\mathbf{X}$  with  ${\mathbf{Z}}_{NC + }$  and  ${\mathbf{Z}}_{DGA + }$  . The table shows topological measures highlighting differences between the input and learned embeddings.
nodes  $\mathcal{A}$  and their centroid  $\mathbf{c}_{\mathcal{A}} = \frac{1}{|\mathcal{A}|}\sum_{a\in \mathcal{A}}\mathbf{u}_a$  . Table 4 shows that while NC  $^+$  makes the embeddings of both S and A more compact (higher similarity in  $\mathbf{Z}_{NC + }$  than in X), DGA  $^+$  makes S more compact, too, but decreases the compactness of  $\mathcal{A}$  (lower similarity in  $\mathbf{Z}_{DGA + }$  than in X).  $\mathbf{Z}_{NC + }$  meets (i) to a greater extent than  $\mathbf{Z}_{DGA + }$
We then calculate  $\delta$  for all sets of stems  $S_{a}$  occurring with a common affix group  $a$  and their centroids  $\mathbf{c}_{S_a} = \frac{1}{|\mathcal{S}_a|}\sum_{s\in S_a}\mathbf{u}_s$ . We also compute  $\delta$  for all  $S_{a}$  and the embeddings of the corresponding affix groups  $\mathbf{u}_a$ . As Table 4 shows, both values are much higher in  $\mathbf{Z}_{DGA + }$  than in  $\mathbf{X}$ , i.e., DGA+ brings stems with a common affix group  $a$  (lexical clusters in the mental lexicon) close to each other while at the same time moving  $a$  into the direction of the stems. The embeddings  $\mathbf{Z}_{NC + }$  exhibit a similar pattern, but more weakly than  $\mathbf{Z}_{DGA + }$  (see Table 4 and Figure 5).  $\mathbf{Z}_{DGA + }$  meets (ii) to a greater extent than  $\mathbf{Z}_{NC + }$ .
Thus, DGA+ and NC+ solve the tension between (i) and (ii) differently; the associative information from the mental lexicon allows DGA+ to put a greater emphasis on (ii), leading to higher performance in MWF prediction.
6.2 Comparison between SRs
Another reason for the higher performance of the models with associative information could be that their embeddings capture differences in derivational patterns between the SR communities. To examine this hypothesis, we map the embeddings  $\mathbf{Z}_{DGA+}$  of all SRs into a common vector space by means of orthogonal procrustes alignment (Schönenmann, 1966), i.e., we optimize
$$
\mathbf {R} ^ {(i)} = \underset {\mathbf {T} ^ {\top} \mathbf {T} = \mathbf {I}} {\arg \min } | | \mathbf {Z} _ {D G A +} ^ {(i)} \mathbf {T} - \mathbf {Z} _ {D G A +} ^ {(0)} | | _ {F} \tag {12}
$$
for every SR, where  $\mathbf{Z}_{DGA+}^{(i)}$  is the embedding matrix of the SR  $i$ , and  $\mathbf{Z}_{DGA+}^{(0)}$  is the embedding matrix of a randomly chosen SR (which is the same for all projections). We then compute the intersection of stem and affix group nodes from all SRs  $S_{\cap} = \bigcap_{i} S^{(i)}$  and  $\mathcal{A}_{\cap} = \bigcap_{i} \mathcal{A}^{(i)}$ , where  $S^{(i)}$  and  $\mathcal{A}^{(i)}$  are the stem and affix group sets of SR  $i$ , respectively. To probe whether differences between SRs are larger or smaller for affix embeddings as compared to stem embeddings, we define
$$
\Delta \left(\mathcal {S} ^ {(i)}, \mathcal {S} ^ {(j)}\right) = \sum_ {s \in \mathcal {S} _ {\cap}} \frac {\cos \left(\hat {\mathbf {z}} _ {s} ^ {(i)} , \hat {\mathbf {z}} _ {s} ^ {(j)}\right)}{\left| \mathcal {S} _ {\cap} \right|}, \tag {13}
$$
i.e., the mean cosine similarity between projected embedding pairs  $\hat{\mathbf{z}}_s^{(i)}$  and  $\hat{\mathbf{z}}_s^{(j)}$  from two SRs  $i$  and  $j$  representing the same stem  $s$  in the intersection set  $S_{\cap}$ , with  $\hat{\mathbf{z}}_s^{(i)} = \mathbf{z}_s^{(i)}\mathbf{R}^{(i)}$ .  $\Delta (\mathcal{A}^{(i)},\mathcal{A}^{(j)})$  is defined analogously for affix groups.
The mean value for  $\Delta (\mathcal{A}^{(i)},\mathcal{A}^{(j)})$ $(0.723\pm$  0.102) is lower than that for  $\Delta (S^{(i)},S^{(j)})$ $(0.760\pm$  0.087), i.e., differences between affix group embeddings are more pronounced than between stem embeddings. Topically connected SRs are more similar to each other than SRs of different topic groups,
(a)  $\Delta (\mathcal{S}^{(i)},\mathcal{S}^{(j)})$
(b)  $\Delta (\mathcal{A}^{(i)},\mathcal{A}^{(j)})$
Figure 6: Comparison of embedding spaces across SRs. The plots show color-coded values of  $\Delta(S^{(i)}, S^{(j)})$  and  $\Delta(\mathcal{A}^{(i)}, \mathcal{A}^{(j)})$  for all pairs of SRs, respectively. The block-diagonal structure highlights the impact of topical relatedness on embedding similarities.
with the differences being larger in  $\Delta (\mathcal{A}^{(i)},\mathcal{A}^{(j)})$  than in  $\Delta (S^{(i)},S^{(j)})$  (see Figure 6).
These results can be related to Section 6.1: affix groups are very close to the stems they associate with in  $\mathbf{Z}_{DGA+}$ , i.e., if an affix group is used with stems of meaning  $p$  in one SR and stems with meaning  $q$  in the other SR, then the affix groups also have embeddings close to  $p$  and  $q$  in the two SRs. Most technical vocabulary, on the other hand, is specific to a SR and does not make it into  $S_{\square}$ .
A qualitative analysis supports this hypothesis: affix groups with low cosine similarities between SRs associate with highly topical stems; e.g., the affix group  $\$ 0$ ocracy has a low cosine similarity of -0.189 between the SRs nba and pol, and it occurs with stems such as kobe, jock in nba but left, wealth in pol.
Much recent computational research on derivational morphology in NLP has focused on two related problems: predicting the meaning of a derivative given its form, and predicting the form of a derivative given its meaning.
The first group of studies models the meaning of derivatives as a function of their morphological structure by training embeddings directly on text segmented into morphemes (Luong et al., 2013; Qiu et al., 2014) or by inferring morpheme embeddings from whole-word vector spaces, e.g., using the vector offset method (Lazaridou et al., 2013; Padó et al., 2016). Formally, given a derived form  $f_{d}$ , this line of research tries to find the meaning  $m_{d}$  that maximizes  $P(m_{d}|f_{d})$ .
The second group of studies models the form
of derivatives as a function of their meaning. The meaning is represented by the base word and a semantic tag (Cotterell et al., 2017; Deutsch et al., 2018) or the sentential context (Vylomova et al., 2017). Formally, given a meaning  $m_d$ , these studies try to find the derived form  $f_d$  of a word that maximizes  $P(f_d|m_d)$ .
Our study differs from these two approaches in that we model  $P(W|f_d, m_d)$ , i.e., we predict the overall likelihood of a derivative to exist. For future research, it would be interesting to apply derivational embeddings in studies of the second type by using them as pretrained input.
Neural link prediction is the task of inferring the existence of unknown connections between nodes in a graph. Advances in deep learning have prompted various neural models for link prediction that learn distributed node representations (Tang et al., 2015; Grover and Leskovec, 2016). Kipf and Welling (2016, 2017) proposed a convolutional graph auto-encoder that allows to include feature vectors for each node. The model was adapted to bipartite graphs by van den Berg et al. (2018).
Previous studies on neural link prediction for bipartite graphs have shown that the embeddings of the two node sets should ideally form separated clusters (Gao et al., 2018). Our work demonstrates that relations transcending the two-mode graph structure can lead to a trade-off between clustering and dispersion in embedding space.
We have introduced a derivational graph autoencoder (DGA) that combines syntactic and semantic information with associative information from the mental lexicon to predict morphological well-formedness (MWF), a task that has not been addressed before. The model achieves good results and performs on par with a character-based LSTM at a fraction of the number of trainable parameters (less than  $10\%$ ). Furthermore, the model learns embeddings capturing information about the compatibility of affixes and stems in derivation.
Acknowledgements. Valentin Hofmann was funded by the Arts and Humanities Research Council and the German Academic Scholarship Foundation. This research was also supported by the European Research Council (Grant No. 740516). We thank the reviewers for their helpful and very constructive comments.
One SR standing out in Figure 6 is lol, a multiplayer online video game, in which many common stems such as fame and range have highly idiosyncratic meanings.
Paolo Acquaviva. 2016. Morphological semantics. In Andrew Hippisley and Gregory Stump, editors, The Cambridge handbook of morphology, pages 117-148. Cambridge University Press, Cambridge.
Lada A. Adamic and Eytan Adar. 2003. Friends and neighbors on the web. Social Networks, 25:211-230.
Maria Alegre and Peter Gordon. 1999. Rule-based versus associative processes in derivational morphology. *Brain and Language*, 68(1-2):347-354.
Margaret R. Allen. 1979. Morphological investigations. University of Connecticut, Mansfield, CT.
Frank Anshen and Mark Aronoff. 1999. Using dictionaries to study the mental lexicon. *Brain and Language*, 68:16-26.
Mark Aronoff. 1976. Word formation in generative grammar. MIT Press, Cambridge, MA.
Laurie Bauer. 2001. Morphological productivity. Cambridge University Press, Cambridge, UK.
Laurie Bauer. 2019. Rethinking morphology. Edinburgh University Press, Edinburgh, UK.
Joan Bybee. 1995. Regular morphology and the lexicon. Language and Cognitive Processes, 10(425-455).
Ting Chen, Yizhou Sun, Yue Shi, and Liangjie Hong. 2017. On sampling strategies for neural network-based collaborative filtering. In International Conference on Knowledge Discovery and Data Mining (KDD) 23.
Ryan Cotterell, Ekaterina Vylomova, Huda Khayral-lah, Christo Kirov, and David Yarowsky. 2017. Paradigm completion for derivational morphology. In Conference on Empirical Methods in Natural Language Processing (EMNLP) 2017.
David Crystal. 1997. The Cambridge encyclopedia of the English language. Cambridge University Press, Cambridge, UK.
Hanjun Dai, Bo Dai, and Le Song. 2016. Discriminative embeddings of latent variable models for structured data. In International Conference on Machine Learning (ICML) 33.
Marco del Tredici and Raquel Fernández. 2018. The road to success: Assessing the fate of linguistic innovations in online communities. In International Conference on Computational Linguistics (COLING) 27.
Daniel Deutsch, John Hewitt, and Dan Roth. 2018. A distributional and orthographic aggregation model for english derivational morphology. In Annual Meeting of the Association for Computational Linguistics (ACL) 56.
Nigel Fabb. 1988. English suffixation is constrained only by selectional restrictions. Natural Language & Linguistic Theory, 6(4):527-539.
Ming Gao, Leihui Chen, Xiangnan He, and Aoying Zhou. 2018. BiNE: Bipartite network embedding. In International Conference on Research and Development in Information Retrieval (SIGIR) 41.
Albert Gatt and Emiel Krahmer. 2018. Survey of the state of the art in natural language generation: Core tasks, applications and evaluation. Journal of Artificial Intelligence Research, 61:65-170.
Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, and George E. Dahl. 2017. Neural message passing for quantum chemistry. In International Conference on Machine Learning (ICML) 34.
Aditya Grover and Jure Leskovec. 2016. node2vec: Scalable feature learning for networks. In International Conference on Knowledge Discovery and Data Mining (KDD) 22.
Bo Han and Timothy Baldwin. 2011. Lexical normalisation of short text messages: Makn sens a #twitter. In Annual Meeting of the Association for Computational Linguistics (ACL) 49.
Martin Haspelmath and Andrea D. Sims. 2010. Understanding morphology. Routledge, New York, NY.
Jennifer Hay. 2001. Lexical frequency in morphology: Is everything relative? Linguistics, 39(6):1041-1070.
Jennifer Hay and Ingo Plag. 2004. What constrains possible suffix combinations? on the interaction of grammatical and processing restrictions in derivational morphology. Natural Language & Linguistic Theory, 22(3):565-596.
Valentin Hofmann, Janet B. Pierrehumbert, and Hinrich Schütze. 2020. Predicting the growth of morphological families from social and linguistic factors. In Annual Meeting of the Association for Computational Linguistics (ACL) 58.
Diederik P. Kingma and Jimmy L. Ba. 2015. Adam: A method for stochastic optimization. In International Conference on Learning Representations (ICLR) 3.
Thomas N. Kipf and Max Welling. 2016. Variational graph auto-encoders. In NIPS Bayesian Deep Learning Workshop.
Thomas N. Kipf and Max Welling. 2017. Semi-supervised classification with graph convolutional networks. In International Conference on Learning Representations (ICLR) 5.
Angeliki Lazaridou, Marco Marelli, Roberto Zamparelli, and Marco Baroni. 2013. Compositional-ly derived representations of morphologically complex words in distributional semantics. In Annual Meeting of the Association for Computational Linguistics (ACL) 51.
David Liben-Nowell and Jon Kleinberg. 2003. The link prediction problem for social networks. In ACM Conference on Information and Knowledge Management (CIKM) 12.
Pierre Lison and Andrey Kutuzov. 2017. Redefining context windows for word embedding models: An experimental study. In arXiv 1704.05781.
Minh-Thang Luong, Richard Socher, and Christopher D. Manning. 2013. Better word representations with recursive neural networks for morphology. In Conference on Computational Natural Language Learning (CoNLL) 17.
Einat Minkov, Kristina Toutanova, and Hisami Suzuki. 2007. Generating complex morphology for machine translation. In Annual Meeting of the Association for Computational Linguistics (ACL) 45.
Vinod Nair and Geoffrey E. Hinton. 2010. Rectified linear units improve restricted Boltzmann machines. In International Conference on Machine Learning (ICML) 27.
Sebastian Padó, Aurélie Herbelot, Max Kisselew, and Jan Šnajder. 2016. Predictability of distributional semantics in derivational word formation. In International Conference on Computational Linguistics (COLING) 26.
Jeffrey Pennington, Richard Socher, and Christopher D. Manning. 2014. GloVe: Global vectors for word representation. In Conference on Empirical Methods in Natural Language Processing (EMNLP) 2014.
Janet Pierrehumbert. 2012. The dynamic lexicon. In Abigail Cohn, Cecile Fougeron, and Marie Huffman, editors, *The Oxford handbook of laboratory phonology*, pages 173–183. Oxford University Press, Oxford.
Janet Pierrehumbert and Ramon Granell. 2018. On hapax legomena and morphological productivity. In Workshop on Computational Research in Phonetics, Phonology, and Morphology (SIGMORPHON) 15.
Ingo Plag. 2003. Word-formation in English. Cambridge University Press, Cambridge, UK.
Siyu Qiu, Qing Cui, Jiang Bian, Bin Gao, and Tie-Yan Liu. 2014. Co-learning of word representations and morpheme representations. In International Conference on Computational Linguistics (COLING) 25.
Peter H. Schonemann. 1966. A generalized solution of the orthogonal procrustes problem. Psychometrika, 36(1).
Ingrid Sonnenstuhl and Axel Huth. 2002. Processing and representation of german -n plurals: A dual mechanism approach. *Brain and Language*, 81(1-3):276-290.