def generate_item(s, i, d):
    mean = np.zeros(d)
    mean[i] = s
    cov = np.identity(d)
    return np.random.multivariate_normal(mean, cov, 1)[0]

def generate_X(s, n, k=3, d=10):
    labels = np.random.choice(k, n)
    return labels, np.array([generate_item(s, i, d) for i in labels])