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latentartists
====== Differences ====== This shows you the differences between two versions of the page.
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latentartists [2013/06/30 16:36] ben |
latentartists [2013/06/30 17:09] (current) ben |
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| - | Assume a fixed vocabulary $V$, which in our experiments is a company internal list | + | Assume a fixed vocabulary $V$, which in our experiments is a list compiled by the Echonest |
| of music related multiword terms. | of music related multiword terms. | ||
| Line 50: | Line 50: | ||
| Distance between can be computed with KL-divergence, which for Multivariate Gaussian's is given as | Distance between can be computed with KL-divergence, which for Multivariate Gaussian's is given as | ||
| - | $KL(\mathcal{N}_0||\mathcal{N}_1) \propto (\mu_0 - \mu_1)\Sigma^-1(\mu_0 - \mu_1)^T + C | + | $KL(\mathcal{N}_0||\mathcal{N}_1) \propto (\mathbb{E}[z_0] - \mathbb{E}[z_1])\Sigma^{-1}(\mathbb{E}[z_0] - \mathbb{E}[z_1])^T + C$ |
| - | + | ||
| - | if the covariance matrix $\Sigma$ is the same for both Gaussians. | + | |
| + | if the covariance matrix $\Sigma$ is the same for both Gaussians. This shows that if $\Sigma^{-1}$ is a multiple | ||
| + | of the identity matrix, the ranking retrieved will be the same as that of Euclidian distance between posterior means. | ||
| We can calculate the artists that are similar to an arbitrary artist by calculating their distance to all other artists using one of these | We can calculate the artists that are similar to an arbitrary artist by calculating their distance to all other artists using one of these | ||
| Line 65: | Line 65: | ||
| an ROC curve. | an ROC curve. | ||
| - | {{::1000.ps|}} | + | Our results, contained in the ROC plots below, correspond to training on the full dataset and only the top 1000 by hotttness. |
| + | In both experimental setups the same top 300 artists are used for evaluation, the only difference is the amount of information available | ||
| + | during training. | ||
| + | |||
| + | == Hottt 1000 == | ||
| - | {{::full.ps|}} | + | {{::1000.jpg?600|}} |
| + | == Full Dataset == | ||
| + | {{::full.jpg?600|}} | ||
| + | The results do not support our hypothesis that taking uncertainty into account would create a more robust notion of similarity. | ||
| + | While both methods clearly capture the information in the Echonest artist similar lists, the area under the ROC curve is clearly | ||
| + | greater for the simple Euclidean distance based approach. | ||
| + | The reason that the experimental results do not match our intuition is unclear. One possibility is that KL divergence | ||
| + | is not an appropriate metric for similarity. | ||
latentartists.1372624575.txt.gz · Last modified: 2013/06/30 16:36 by ben
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