# Fast uniform negative sampling for rating matrix

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Sometimes, we want to reduce the training time by using a subset of a very large dataset while the negative samples outnumbers the positive ones, e.g. word embedding. Another situation when we deal with implicit data. In this case, we may need to populate new data for negative values. This post demonstrates how to generate data for training using uniform negative sampling.

## The data

Originally, the rating matrix tells who rated which items. Now we want to get the data that tell who interacted with which items. The interaction does not tell the user like or dislike an item. Doing so means that we transform a rating matrix (explicit data) into an implicit dataset.

If we consider interaction has value 1 and 0 otherwise, then the original rating data will become all 1s. So, you can see that with only 1s in the label, the model cannot distinguish between `interact` and `not interact` as shown in the following tables.

This is the interaction matrix:

## The sampling method

We want to get `n` negative samples per one positive. The naive method can be:

1. Loop through all `user ids`
2. For each `user id`, get a random `item id` and check if the pair `user-item` does not exist in the dataset
3. Add the found `user-item` as a negative sample to the dataset.

If you follow these steps, then you may find the execution times can be really long (~20 mins). To accelerate the result, we utilize some useful libraries as follows:

1. Generate a dense matrix from the dataset using `scipy`,
• rows and cols are users and items
2. For each row, extract `k`random items’ indices of 0 values using `random.samples`
• `k` is the number of non zero values in that row.
3. Append the list of `user-item` from `k` extract index and append to the dataset.

## Python Implementation

``````import random
import time
import scipy
def neg_sampling(ratings_df, n_neg=1, neg_val=0, pos_val=1, percent_print=5):
"""version 1.2: 1 positive 1 neg (2 times bigger than the original dataset by default)
Parameters:
input rating data as pandas dataframe: userId|movieId|rating
n_neg: take n_negative / 1 positive
Returns:
negative sampled set as pandas dataframe
userId|movieId|interact (implicit)
"""
ratings_df.userId = ratings_df.userId.astype('category').cat.codes.values
ratings_df.movieId = ratings_df.movieId.astype('category').cat.codes.values
sparse_mat = scipy.sparse.coo_matrix((ratings_df.rating, (ratings_df.userId, ratings_df.movieId)))
dense_mat = np.asarray(sparse_mat.todense())
print(dense_mat.shape)
nsamples = ratings_df[['userId', 'movieId']]
nsamples['interact'] = nsamples.apply(lambda row: 1, axis=1)
length = dense_mat.shape
printpc = int(length * percent_print/100)
nTempData = []
i = 0
start_time = time.time()
stop_time = time.time()
extra_samples = 0
for row in dense_mat:
if(i%printpc==0):
stop_time = time.time()
print("processed ... {0:0.2f}% ...{1:0.2f}secs".format(float(i)*100 / length, stop_time - start_time))
start_time = stop_time
n_non_0 = len(np.nonzero(row))
zero_indices = np.where(row==0)
if(n_non_0 * n_neg + extra_samples > len(zero_indices)):
print(i, "non 0:", n_non_0,": len ",len(zero_indices))
neg_indices = zero_indices.tolist()
extra_samples = n_non_0 * n_neg + extra_samples - len(zero_indices)
else:
neg_indices = random.sample(zero_indices.tolist(), n_non_0 * n_neg + extra_samples)
extra_samples = 0
nTempData.extend([(uu, ii, rr) for (uu, ii, rr) in zip(np.repeat(i, len(neg_indices))
, neg_indices, np.repeat(neg_val, len(neg_indices)))])
i+=1
nsamples=nsamples.append(pd.DataFrame(nTempData, columns=["userId","movieId", "interact"]),ignore_index=True)
return nsamples``````

## Result

``````(69878, 10677)
processed ... 0.00% ...0.00secs
processed ... 5.00% ...0.07secs
processed ... 10.00% ...0.07secs
processed ... 15.00% ...0.08secs
processed ... 20.00% ...0.08secs
processed ... 25.00% ...0.08secs
processed ... 30.00% ...0.08secs
processed ... 35.00% ...0.08secs
processed ... 40.00% ...0.07secs
processed ... 45.00% ...0.07secs
processed ... 50.00% ...0.08secs
processed ... 55.00% ...0.08secs
processed ... 60.00% ...0.08secs
processed ... 65.00% ...0.08secs
4168 non 0: 2314 : len  1392
processed ... 70.00% ...0.08secs
processed ... 75.00% ...0.09secs
processed ... 80.00% ...0.08secs
processed ... 85.00% ...0.08secs
processed ... 90.00% ...0.07secs
processed ... 95.00% ...0.07secs
done:  (20000108, 3)``````

## Wrapping up

Negative sampling is an efficient method to reduce the training time of imbalanced large dataset. The introduced method, i.e `neg_sampling`(…), can uniformly sample negative values. 2 million rating records can be generated within ~2 seconds (600 times faster than the naive method).

### 1 comment

• […] purposes, we use the dataset generated from negative samples using the technique mentioned in this post. The data contain user_id, item_id, and interaction (0-non-interact, 1 – has interact). The […]

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