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COMPARATIVE MUSIC SIMILARITY MODELLING USING TRANSFER LEARNING ACROSS USER GROUPS Daniel Wolff, Andrew MacFarlane and Tillman Weyde Music Informatics Research Group – Department of Computer Science City University London approach of transfer learning in music similarity that im-proves results of specialised models, using our We introduce a new application of transfer learning for extension of Information-Theoretic Metric Learning (ITML).
training and comparing music similarity models based on The template-based optimisation in relative user data: The proposed Relative Information-The- W0-RITML allows for a comparison of the general and specialised models – it oretic Metric Learning (RITML) algorithm adapts a Maha- derives the latter from the former – which we suggest as lanobis distance using an iterative application of the ITML a tool for comparative analysis of similarity data by (e.g.
algorithm, thereby extending it to relative similarity data.
RITML supports transfer learning by training models withrespect to a given template model that can provide prior We are particularly interested in modelling relative similar- information for regularisation. With this feature we use in- ity ratings collected from participants during Games With a formation from larger datasets to build better models for Purpose (GWAPs). Using similarity data from user groups more specific datasets, such as user groups from differ- promises to provide tailored model performance and the ent cultures or of different age. We then evaluate what opportunity to compare such groups via the trained sim- model parameters, in this case acoustic features, are rele- ilarity models. The new CASimIR dataset presented in vant for the specific models when compared to the general Section 3 contains such similarity ratings and information about the contributing subjects. We use this extra data togroup users and here exemplarily train age-specific music We to this end introduce the new CASimIR dataset, the similarity models based on age-bounded subsets. How- first openly available relative similarity dataset with user ever, the relatively small size of the CASimIR dataset re- attributes. With two age-related subsets, we show that trans- quires a different approach to training the group-specific fer learning with RITML leads to better age-specific mod- models as existing algorithms are not sufficiently effective els. RITML here improves learning on small datasets. Us- for this purpose.
ing the larger MagnaTagATune dataset, we show that RITMLperforms as well as state-of-the-art algorithms in terms of We contribute a solution to this problem with a novel generic general similarity estimation.
algorithm for transfer learning with similarity models: TheRITML algorithm (see Section 5.2) extends on ITML toallow for learning a Mahalanobis metric from relative sim- ilarity data like in CASimIR. With W0-RITML, informa- tion learnt from remaining data can be successfully trans- Music similarity models are a central part of many ap- ferred to an age-bounded dataset via a Mahalanobis ma- plications in music research, particularly Music Informa- trix. This transfer-learning increases performance on small tion Retrieval (MIR). When training similarity models, it datasets and provides interpretable values in the Mahala- turns out that learnt models vary considerably for differ- nobis matrix. The Mahalanobis matrix provides a compact ent data sets and application scenarios. Recently, context- representation of similarity information in a dataset. This sensitive models have been introduced, e.g. for the task of is useful in scenarios where the music data is difficult to music recommendation (Stober [9] provides an overview).
access due to its data volume or copyright restrictions. The The main problem with context-sensitive similarity mod- CASimIR dataset and code used in this paper are available els is currently to obtain enough data to train the models for each context. Transfer learning promises to enable ef-fective training of models for specific contexts by includ- 2. RESEARCH BACKGROUND ing information from related datasets. We here present an Transfer learning relates to many areas and approaches inmachine learning. A general overview of transfer learning c Daniel Wolff, Andrew MacFarlane and Tillman Weyde.
Licensed under a Creative Commons Attribution 4.0 International Li- is given in Pan and Yang [6]. In their categorisation, our cense (CC BY 4.0). Attribution: Daniel Wolff, Andrew MacFarlane task is an inductive knowledge transfer from one similarity and Tillman Weyde. "Comparative Music Similarity Modelling using modelling task to another via model parameters. Note that Transfer Learning Across User Groups", 16th International Society forMusic Information Retrieval Conference, 2015.
Proceedings of the 16th ISMIR Conference, M´ alaga, Spain, October 26-30, 2015 in our example the tasks differ only in the dataset, but our the odd one out (of the triplet Ci, Cj, Ck) results in 2 rela- method can also be used for more divergent tasks.
tive similarity constraints: clips Ci and Cj are more similar In MIR, transfer learning is a relatively new method. In Ci and Ck, and clips Cj and Ci are more similar than 2013, [2] described multi-task learning using a shared la- Cj and Ck. These constraints are denoted as (i, j, k) and tent representation for auto-tagging, genre classification and (j, i, k), respectively which are contained in the constraintset ˆ genre-based music similarity. This representation includes both the features and the labels for the different tasks. In Human ratings regularly produce inconsistent constraints.
experiments on several datasets they showed improvement We use the graph representation of the similarity data as of classification accuracy and modelling similarity accord- suggested by [5] to analyse and filter inconsistencies: Each ing to genre.
constraint (i, j, k) is represented by an edge connecting We here work with relative similarity ratings from humans two vertices (i, j) ! (i, k) corresponding to two clip in our new CASimIR dataset for group-specific modelling.
pairs, with the edge weight ↵ijk = 1. When combining Furthermore, we use the MagnaTagATune dataset [3] for all constraints in a graph, the weights ↵ijk are accumu- comparison on non-specific similarity learning. Here, the lated. Inconsistencies then appear as cycles in the graph, Support Vector Machine (SVM) approach developed by which in their most common form are of length 2: Schultz and Joachims [7] and applied in [10, 11] is used as state-of-the art baseline.
Another state-of-the-art algorithm for learning from rela-tive similarity data is Metric Learning To Rank (MLR).
We remedy such cycles by removing the edge with the McFee et al. [4] introduce MLR for parametrising a lin- smaller weight and assigning the weight ↵ijk ↵ikj to ear combination of content-based features using collabo- the remaining edge. For both the MagnaTagATune and rative filtering data. Their post-training analysis of feature CASimIR datasets this already creates a cycle-free graph weights revealed that tags relating to genre or radio stations Q as no larger cycles remain. The cycle-free sets Q are were assigned greater weights than those related to music used in this study for training and evaluation.
theoretical terms.
Compared to the MagnaTagATune dataset, the CASimIRdataset features more frequent recurrences of clips between 3. A DATASET FOR USER-AWARE SIMILARITY the triplets presented to the users. Recurring clips relate thecorresponding similarity data, and result in large connected In order to perform a related analysis and comparisons of components in the CASimIR similarity graph: While the models between different user groups, we have collected maximal number of clips directly or transitively related the CASimIR datasets using Spot the Odd Song Out [13], to each other through similarity data in the MagnaTagA- an online 2 multi-player Game With a Purpose (GWAP).
Tune dataset was 3 (see [11]), most clips in the CASimIR The similarity module of the Spot the Odd Song Out game similarity data are related to at least 5 other clips. The collects relative similarity data using an odd-one-out sur- repetition of clips across triplets results in fewer unique vey: From a set of three music clips, participants are asked referenced clips: the current CASimIR similarity dataset to choose the clip most dissimilar to the remaining clips, contains only 180 clips referenced by 2102 ratings, while i.e. the odd song out. The game motivates players by MagnaTagATune references 2000 ratings with about 500 rewarding blind agreement. For various reasons, includ- clips, and has 1019 clips with 7650 ratings in total.
ing personal data protection, little music annotation data ispublicly available with information about the provider of 3.2 Analysis of Age-bounded Similarity Ratings the data and their context.
The additional participant attributes allow us to select sub- Although the game can collect anonymised personal in- sets of similarity data according to specific profiles of the formation including gender, nationality, spoken languages participants. This enables the training of more specific and musical experience, the amount and type information models that support better similarity predictions for the rel- available varies between participants, as data provision is evant group of users, and allows for comparison of differ- voluntary. Our overarching goal is to study the relation between similarity and culture and we thus link annota-tions to cultural profiles rather than indexing specific par- As an example of group-based similarity modelling we ticipants. With this paper we publish the first set of simi- choose age as a separating criterion on the CASimIR simi- larity data with anonymised profiles.
larity data from over 256 participants: We divide the com-plete set of similarity ratings R into two age-bounded sub-sets 3.1 Constraints from Relative Similarity Ratings R25 of data provided by participants not older than 25 years and R>25 containing data of older participants.
The boundary of 25 years was chosen as the best approxi- The MagnaTagATune and CASimIR datasets both contain mation to equal sizes of the subsets (data input is only in 5 relative similarity ratings. A participant's rating of Ck as year bands). As shown in Table 1, the number of ratings is higher for the R25 dataset.
Proceedings of the 16th ISMIR Conference, M´ alaga, Spain, October 26-30, 2015 4.1 Mahalanobis Distances We use the inverse of the distance of two feature vectors as the similarity of the two corresponding clips. The mathe-matical form of the Mahalanobis distance is used to spec- Table 1. Number of votes, unique constraints and refer- ify a parametrised distance measure. Given two feature enced clips, after filtering inconsistencies, per dataset.
vectors xi, xj 2 RN, the distance can be expressed as 539 similarity ratings are not associated to a valid age and stored separately in R;. For the two age-bounded datasets,we furthermore define complementary datasets R{(25) and where W 2 RN⇥N is a square matrix parametrising the R{(>25) combining the remaining similarity data, e.g. R{(25) distance function: the Mahalanobis matrix. dW qualifies= R>25 [ R;. These complementary sets will be used for as a metric if W is positive definite and symmetric.
training of template models for transfer learning.
After splitting, the above (sub)sets of ratings are trans- 5. MODEL TRAINING WITH RITML ferred into constraints (see Section 3.1) and separately fil-tered for inconsistencies. We now use the corresponding We now discuss our algorithm which can adapt Mahala- sets of unique constraints Q, Q25, Q>25, Q{(25) and nobis distances in order to fit relative similarity data. It is Q{(>25) for training and testing of models. The number of based on the ITML algorithm as described below, which constraints are also noted in Table 1, together with the total cannot be used directly with relative similarity data. In- number of clips referenced by the constraint sets. Due to stead, ITML requires upper or lower bounds on the sim- multiple ratings referring to the same constraint and filter- ilarity of two clips, e.g. dW (xi, xj) < mi,j for similar ing the constraint count is lower than the number of ratings.
clips. In Section 5.2 we will iteratively derive such con-straints during the RITML optimisation process.
4. SIMILARITY MODELLING 5.1 Information-Theoretic Metric Learning The computational representations of music through fea- Davis et al. [1] describe Information-Theoretic Metric Lear- tures, related to physical, musical, and cultural attributes ning (ITML) for learning a Mahalanobis distance from ab- determine the basis of similarity models. Both the Magna- solute distance constraints (e.g. requiring dW (xi, xj) < TagATune and CASimIR datasets contain pre-computed 0.5). A particularly interesting feature of ITML is that features created by The Echo Nest API. For our exper- a template Mahalanobis matrix W0 2 Rn⇥n can be pro- iments with CASimIR we derive acoustic features from vided for regularisation. This W0 can be from a metric that this data which are aggregated to the clip-level. The 41- is predefined or learnt on a different dataset. If W0 is not dimensional features contain 12 chroma and 12 timbre fea- specified, the identity transform is used. The regularisation tures, both aggregated via averaging, 2 weight vectors and of ITML exploits an interpretation of Mahalanobis matri- further features after [8, 11]: ces as multivariate Gaussian distributions: The distancebetween two Mahalanobis distance functions parametrised by W and W0 is measured by the relative entropy of the corresponding distributions, which in [1] uses the LogDet Dld(W, W0) = tr(W W 1 = 2 ⇤ KL (P (xi; W0) k P (xi; W )) .
KL refers to the Kullback-Leibler divergence. For detailsof the transformation see [1]. Given the constraints in form Table 2. Features used in our experiments.
of similar (Rs) and dissimilar (Rd) clip indices as well as upper and lower bounds uij, lij, the optimisation problem For experiments with the MagnaTagATune dataset we will is then posed as follows: use the similar features provided in [12] which contain pre-processed tag information in addition to the acoustic fea- ITML(W, ⇠, c, Rs, Rd) = tures described above. For the CASimIR dataset, using un- argmin Dld(W, W0) + c · Dld(diag(⇠), diag(⇠0)) processed tags from Last.fm did not increase performance in earlier experiments due to very sparse tag assignments.
s.t. tr(W dLi,j(dLi,j) )  ⇠ij 8(i, j) 2 Rs Therefore, our experiments on CASimIR use acoustic fea- tures only. For a clip Ci, we refer to its feature vector as Proceedings of the 16th ISMIR Conference, M´ alaga, Spain, October 26-30, 2015 Here, ⇠ij are slack variables enabling and controlling the Algorithm 1: Relative Training with RITML violation of individual constraints. The ⇠ij are initialised to Data: Constraints Q given upper bounds t, features xi, template matrix W0, uij, if (i, j) 2 Rs or lower bounds lij, regularisation factor c, shrinkage factor ⌘, margin if (i, j) 2 Rd. During optimisation, they are regularised by ⌧ , number of cycles k comparison to the template slack ⇠0 using triangular matri- (⇠) and diag(⇠0).
while m  k Q⇤ 6= ; do Update training sets Qm, Rm and 5.2 Relative Learning with RITML Update absolute constraints ⇠m ;Calculate parameter change W ;Calculate W m+1 ; In order to allow for training with relative similarity con- straints, we present Relative Information-Theoretic Metric Learning (RITML) based on ITML. Motivated by [14], we return Mahalanobis matrix W k embed ITML into an iterative adaptation of the upper andlower bounds.
We start with a training set of relative constraints (i, j, k) 2 5.3 Transfer Learning with W0-RITML Qt. We require standard ITML parameters such as c, as well as the relative learning parameters including shrink- The property that motivates our usage of RITML is that age factor ⌘, margin ⌧ and number of cycles k at the be- it enables transfer learning: If a specific starting value or ginning. We use the identity matrix for the template W 0 other than the identity matrix is provided, During iteration m, the active training set of violated con- the optimisation tends to produce results close to the pro- straints Qm is calculated as vided W0. In order to sustain this effect for large numbers of iterations we modify Equation (1) such that regularisa- tion is fixed towards W t dW m (xi, xj ) > dW m (xi, xk)} .
0 instead of the Euclidean distance: Qm is then further divided into the sets of similar and dis- W = ITML(W0, ⇠m, Rm similar constraints Rm and This constitutes the W0-RITML algorithm for transfer learn- ing with Mahalanobis matrices.
s = {(i, j) (i, j, k) 2 Qm} d = {(i, k) (i, j, k) 2 Qm}, Afterwards, absolute distance constraints ⇠ For all our experiments we use the 10-fold cross-validation lowing ITML instance are acquired by adding a margin ⌧ with inductive sampling as described in [11]: Instead of di- to the average distance values viding the similarity constraints themselves into test/training µ = dWm (xi,xj)+dWm (xi,xk) of the clip pairs: sets, the data are divided on the basis of connected clustersin the similarity data. This approach prevents the recur- rence of clips from a training-set in the corresponding test set. It also leads to a greater variance in test-set sizes for CASimIR where the clusters of connected similarity dataare larger.
Now, with ⇠m containing the upper and lower bounds, Wcan be calculated using We evaluate the algorithms' performance based on the per-centage of training and test constraints fulfilled by the trained W = ITML(W m, ⇠m, Rm model. Our main focus is on the test-set results as we are interested how well the learnt models generalise to unseen and the final Mahalanobis matrix is accumulated over iter- data. As a baseline we use the Euclidean distance on the ations using the model update function features. We have tested results for statistical significanceusing the Wilcoxon signed rank test on cross-validation folds' results with a threshold of p < 5%.
Both SVM as implemented in svmlight[7] and RITML havehyper-parameters affecting the performance on different In order for the algorithm to converge, the cardinality of the datasets. The results reported here were selected on the active training set Qm needs to decrease. In our experi- basis of best test-set performances after a grid-search over ments, k = 200 training iterations are usually sufficient.
a range of value combinations identified as reasonable in Otherwise an early stopping of the algorithm takes place if preliminary experiments: The regularisation trade-off c is a Qm does not decrease for 50 iterations. In this case the parameter common to SVM, RITML and W0-RITML with W m for the smallest Qm within the last 50 iterations is a similar effective range: we explored a c 2 [0.001, 10] us- returned. RITML does not guarantee dW to be a metric.
ing an approximately logarithmic scale. For RITML and Proceedings of the 16th ISMIR Conference, M´ alaga, Spain, October 26-30, 2015 0-RITML we additionally used ⌘ 2 {0.1, 0.15 . . 0.95}.
6.1 Comparing the Performance of RITML For a comparable evaluation of RITML we chose the Magna- TagATune-based dataset and constraint sampling publishedin [12]. Their evaluation compares various algorithms for Table 4. Comparison of Test / Training set performance learning a Mahalanobis metric using two different sam- on the age-bounded datasets. Training on single datasets plings. The inductive sampling used here corresponds to (top 3 rows) and transfer learning with W0-RITML and the sampling B in their text. Table 3 shows the results on MagnaTagATune and on the complete CASimIR dataset( Figure 1. Flow diagram for transfer learning, exemplified Table 3. Comparison of Test / Training set performance on for the Q>25 dataset.
the MagnaTagATune and CASimIR datasets for baseline,RITML and SVM. Reported are the number of constraintsfulfilled by the learnt distance measures.
Q{(>25) and Q{(25) using cross-validation with trainingand test data from only these sets. Comparing the indi- For MagnaTagATune, RITML achieves similar generalisa- vidual results for validation folds we choose the Maha- tion results as SVM (with parameters SVM: c = 0.7 and lanobis matrices with the greatest test-set performance as RITML: c = 1, ⌘ = 0.85, ⌧ = 0.5), while MLR over- template matrix W0. The template matrix W0 learnt on fits to the training data. For both the MagnaTagATune Q{(25) is then used for transfer learning on Q25, us- and CASimIR datasets all methods perform significantly ing W0-RITML. For comparison of the effectiveness of the better than the baseline. The RITML results are therefore fine-tuning with W0-RITML, we report the performance comparable to the state-of-the-art. The training results on achieved with the unmodified W0 on Q25 as W0-Direct.
MagnaTagATune with SVM and MLR are far better than This process is repeated analogously for Q25 by applying the test results, indicating overfitting, which does not oc- the template matrix W0 from Q{(25) on Q25.
cur for RITML. Interestingly, on the CASimIR dataset, the The highlighted lower columns of Table 4 show the results situation between RITML and SVM is reversed. Results for transfer learning: Row W published by [11] for acoustic-only features on MagnaTag- 0-Direct reports the direct performances of the template Mahalanobis matrices W ATune show a performance of 66% on MagnaTagATune, The results of fine-tuning these models with W but the lower performance on CASimIR can be explained are reported in the last row. We here find that using the ma- by the smaller number of training examples.
trices trained on the larger datasets, and thus transfer learn-ing, generally improves results. Only the results for W0- 6.2 Transfer Learning RITML provide gains > 6.21% that are statistically signif- A core motivation for transfer learning is the training on icant when compared to the baseline. As the average result highly specialised but small datasets. To evaluate the 0-RITML also significantly outperforms the average RITML method for transfer learning, we firstly compared SVM performance, W0-RITML works best for adapting the SVM and RITML algorithms with the baseline on the models to specialised datasets.
age-bounded datasets Q>25 and Q25 in Table 4. The A drawback of RITML is that it is computationally de- rightmost column shows the average performance across manding: For the Q dataset, RITML uses 50 seconds where both age-bounded datasets. Expectedly, on these smaller SVM converges in 5 seconds. On the other hand, SVM datasets generalisation results for RITML as well as the learns a diagonal W which reduces the number of param- reference SVM and MLR are lower than on the whole CA- eters and model flexibility.
SimIR. Only for RITML an increase of 4.37% from thebaseline is notable for the slightly larger Q>25 which im- 6.3 Model Comparison proves the average score for RITML.
In order to identify specificities of the Q>25 dataset in We now apply transfer learning to improve generalisation comparison to the remaining Q{(>25), we now analyse changes results on the age-bounded sets. The overall process is de- made to the template matrix W0 in the fine-tuning pro- picted in Figure 1. First, an similarity modelling experi- cess. Instead of starting from the Euclidean metric, models ment is performed on both of the complementary subsets learnt from the W0-RITML method have a model already Proceedings of the 16th ISMIR Conference, M´ alaga, Spain, October 26-30, 2015 adapted to similarity data as basis.
Figure 2 shows the relative difference ˆ halanobis matrix before (W 0) and after (W ) fine tuning.
As the fine tuning process rescales the similarity measure and thereby W , the matrices have been normalised to the C· · · · · · · · · · · ·T· · · · · · · · · · · ·S·L· · · · ·B· · · · · · C· · · · · · · · · · · ·T· · · · · · · · · · · ·S·L· · · · ·B· · · · · · The axes of the figure correspond to feature types, whichfor better overview have been grouped into chroma, timbre Figure 3. (a) Template matrix W0 before and (b) final ma- and ranges of the features in Table 2. The template matrix W after fine-tuning with W0-RITML on Q>25. The latter shows higher variance in off-diagonal entries for the W0 in Figure 3a has large values only in the diagonal and specialised model. Axis labels represent ranges of fea- homogeneous small values off the diagonal. In comparison ture types: (C)hroma, (T)imbre, as well as (S)egment, to this, Figure 2 shows that specific combinations of tim- (L)oudness and (B)eat+Tempo statistics. Dark red colours bre features (in the bottom centre) with (B)eat and tempo correspond to strong weight increase, light yellow to de- statistics were raised in importance by W0-RITML, result- ing in the final matrix W as shown in Figure 3b. Also,the centre of the matrix shows increased values for combi-nations of different timbre coefficients. The strongest in- 7. CONCLUSION & FUTURE WORK creases (20-24%) in weights are reported for the off-dia-gonal fields of C11C1, T6T5, B4T4 and B4T5, where C, T We presented a method for analysing music similarity data relate to chroma and timbre coefficients and B4 refers to of different user groups via models trained with transfer the tatumConfidence feature. Weights are increased mainly learning. To this end, the new RITML algorithm was de- at the cost of diagonal elements, and suggest at a speciali- veloped extending ITML to relative similarity data. A key sation of the model to the specificities of the Q>25 similar- feature of RITML is that it enables transfer learning with ity subset. For this data collected from users aged over 25, template Mahalanobis matrices via W 0-RITML. Our eval- W0-RITML model with stronger influence of uation of the algorithm was performed on two datasets: the timbre and beat-statistics features performs best in our The evaluation on the commonly used MagnaTagATune dataset showed that RITML performs comparably to state-of-the-art algorithms for metric learning.
For evaluation of transfer learning with W provide the CASimIR similarity dataset, the first open dataset containing user attributes associated to relative similarity data. Tests on the whole CASimIR dataset corroborated our finding that RITML competes with current similarity learning methods. Our analysis of W0-RITML was per- formed on age-bounded subsets of the dataset. Results showed that transfer learning with W0-RITML outperforms the standard SVM algorithm on small datasets.
Our comparison of models allowed us to point out specific features and combinations that determine similarity in user data. For this first evaluation we chose age to group users.
We hope this will motivate further research in comparison of similarity models and adaptation to data with regard to cultural and user context.
C· · · · · · · · · · · ·T· · · · · · · · · · · ·S·L· · · · ·B· · · · · · For future work we are interested in collecting larger sim- Figure 2. Learnt model difference for W0-RITML on ilarity datasets, and applying the methods introduced here Axis labels represent ranges of feature types: for improved validation of results and the analysis of more (C)hroma, (T)imbre, as well as (S)egment, (L)oudness and specific user groups. The set-up used for our experiments (B)eat+Tempo statistics. Dark red / blue colours corre- motivates transfer learning across the MagnaTagATune and spond to strong weight increase / decrease.
CASimIR datasets with W0-RITML for further analysis of the transferability of similarity information via Mahalano- 3 Subtraction and division are applied to W in a point-wise manner.
bis matrices.
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