Answer

What we think of as the ego is in fact the seat of all our suffering, the seventh consciousness. To "purify the self" would therefore mean "to become kinder" or "less angry". But the aim of Buddhist practice is not to become kind or helpful. It's to replace our little ego, which in reality is nothing but an illusion, with the universal ego of the Buddha, the ego that perceives the true aspect of things through the vision of the threefold truth in its heart.

Nichiren Daishōnin's doctrine is based on that of the Tendai. In the Treatise that Opens the Eyes, he writes:

"So although my knowledge and understanding of the Lotus Sutra is only one ten millionth of that of Tiantai and Dengyō, my ability to persevere despite difficulties and the extent of my compassion should not be underestimated."

The practice of Tendai has two aspects: the doctrinal aspect (in other words, study) and the contemplation of the mind (in other words, practice). These two facets are absolutely inaccessible to the beings of the End of the Dharma, hence the first part of the sentence from the Treatise that opens the eyes, quoted just now.

As for the compassion he speaks of in the second part of the said sentence, it is explained by this sentence from the Treatise on the Honzon for the Contemplation of the Mind:

"For those who do not know the doctrine of Three Thousand worlds in a single thought, the Buddha showed great compassion and wrapped this pearl in these five ideograms which he hung around the necks of the infantile beings of the End of the Dharma".

In the End of the Dharma, the practice of contemplating the Tendai mind is replaced by 'receiving and keeping' the Gohonzon. Nichikan Shōnin commented:

"Observing one's own mind means having faith in the Honzon.

The Gohonzon is the materialization of the true aspect of the dharmas, to which we have access through our faith. 

Quoting the passage "They desire with all their heart to see the Buddha and spare neither their body nor their life for it", taken from the Jiga stanzas of the Lifespan chapter of the Lotus Sutra, Nichiren Daishōnin wrote to the monk Gijō-bō:

"It is with this phrase that Nichiren manifests the world of the Buddha from his own heart.

It is therefore also with this phrase that we must practice before the Gohonzon.